9"""Z3 is a high performance theorem prover developed at Microsoft Research.
11Z3 is used in many applications such as: software/hardware verification and testing,
12constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13and geometrical problems.
16Please send feedback, comments and/or corrections on the Issue tracker for
17https://github.com/Z3prover/z3.git. Your comments are very valuable.
38... x = BitVec('x', 32)
40... # the expression x + y is type incorrect
42... except Z3Exception as ex:
43... print("failed: %s" % ex)
49from .z3consts
import *
50from .z3printer
import *
51from fractions
import Fraction
56if sys.version_info.major >= 3:
57 from typing
import Iterable, Iterator
59from collections.abc
import Callable
75if sys.version_info.major < 3:
77 return isinstance(v, (int, long))
80 return isinstance(v, int)
92 major = ctypes.c_uint(0)
93 minor = ctypes.c_uint(0)
94 build = ctypes.c_uint(0)
95 rev = ctypes.c_uint(0)
97 return "%s.%s.%s" % (major.value, minor.value, build.value)
101 major = ctypes.c_uint(0)
102 minor = ctypes.c_uint(0)
103 build = ctypes.c_uint(0)
104 rev = ctypes.c_uint(0)
106 return (major.value, minor.value, build.value, rev.value)
115 raise Z3Exception(msg)
119 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
123 """Log interaction to a file. This function must be invoked immediately after init(). """
128 """Append user-defined string to interaction log. """
133 """Convert an integer or string into a Z3 symbol."""
141 """Convert a Z3 symbol back into a Python object. """
154 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
156 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
157 return [arg
for arg
in args[0]]
158 elif len(args) == 1
and isinstance(args[0], Iterator):
170 if isinstance(args, (set, AstVector, tuple)):
171 return [arg
for arg
in args]
179 if isinstance(val, bool):
180 return "true" if val
else "false"
191 """A Context manages all other Z3 objects, global configuration options, etc.
193 Z3Py uses a default global context. For most applications this is sufficient.
194 An application may use multiple Z3 contexts. Objects created in one context
195 cannot be used in another one. However, several objects may be "translated" from
196 one context to another. It is not safe to access Z3 objects from multiple threads.
197 The only exception is the method `interrupt()` that can be used to interrupt() a long
199 The initialization method receives global configuration options for the new context.
204 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
223 if Z3_del_context
is not None and self.
owner:
229 """Return a reference to the actual C pointer to the Z3 context."""
233 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
235 This method can be invoked from a thread different from the one executing the
236 interruptible procedure.
241 """Return the global parameter description set."""
250 """Return a reference to the global Z3 context.
253 >>> x.ctx == main_ctx()
258 >>> x2 = Real('x', c)
265 if _main_ctx
is None:
282 """Set Z3 global (or module) parameters.
284 >>> set_param(precision=10)
287 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
291 if not set_pp_option(k, v):
306 """Reset all global (or module) parameters.
312 """Alias for 'set_param' for backward compatibility.
318 """Return the value of a Z3 global (or module) parameter
320 >>> get_param('nlsat.reorder')
323 ptr = (ctypes.c_char_p * 1)()
325 r = z3core._to_pystr(ptr[0])
327 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
339 """Superclass for all Z3 objects that have support for pretty printing."""
345 in_html = in_html_mode()
348 set_html_mode(in_html)
353 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
361 if self.
ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
369 return obj_to_string(self)
372 return obj_to_string(self)
375 return self.
eq(other)
388 elif is_eq(self)
and self.num_args() == 2:
389 return self.arg(0).
eq(self.arg(1))
391 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
394 """Return a string representing the AST node in s-expression notation.
397 >>> ((x + 1)*x).sexpr()
403 """Return a pointer to the corresponding C Z3_ast object."""
407 """Return unique identifier for object. It can be used for hash-tables and maps."""
411 """Return a reference to the C context where this AST node is stored."""
412 return self.
ctx.ref()
415 """Return `True` if `self` and `other` are structurally identical.
422 >>> n1 = simplify(n1)
423 >>> n2 = simplify(n2)
432 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
438 >>> # Nodes in different contexts can't be mixed.
439 >>> # However, we can translate nodes from one context to another.
440 >>> x.translate(c2) + y
444 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
451 """Return a hashcode for the `self`.
453 >>> n1 = simplify(Int('x') + 1)
454 >>> n2 = simplify(2 + Int('x') - 1)
455 >>> n1.hash() == n2.hash()
461 """Return a Python value that is equivalent to `self`."""
466 """Return `True` if `a` is an AST node.
470 >>> is_ast(IntVal(10))
474 >>> is_ast(BoolSort())
476 >>> is_ast(Function('f', IntSort(), IntSort()))
483 return isinstance(a, AstRef)
486def eq(a : AstRef, b : AstRef) -> bool:
487 """Return `True` if `a` and `b` are structurally identical AST nodes.
497 >>> eq(simplify(x + 1), simplify(1 + x))
531 _args = (FuncDecl * sz)()
533 _args[i] = args[i].as_func_decl()
541 _args[i] = args[i].as_ast()
549 _args[i] = args[i].as_ast()
557 elif k == Z3_FUNC_DECL_AST:
574 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
583 """Return the Z3 internal kind of a sort.
584 This method can be used to test if `self` is one of the Z3 builtin sorts.
587 >>> b.kind() == Z3_BOOL_SORT
589 >>> b.kind() == Z3_INT_SORT
591 >>> A = ArraySort(IntSort(), IntSort())
592 >>> A.kind() == Z3_ARRAY_SORT
594 >>> A.kind() == Z3_INT_SORT
600 """Return `True` if `self` is a subsort of `other`.
602 >>> IntSort().subsort(RealSort())
608 """Try to cast `val` as an element of sort `self`.
610 This method is used in Z3Py to convert Python objects such as integers,
611 floats, longs and strings into Z3 expressions.
614 >>> RealSort().cast(x)
623 """Return the name (string) of sort `self`.
625 >>> BoolSort().name()
627 >>> ArraySort(IntSort(), IntSort()).name()
633 """Return `True` if `self` and `other` are the same Z3 sort.
636 >>> p.sort() == BoolSort()
638 >>> p.sort() == IntSort()
646 """Return `True` if `self` and `other` are not the same Z3 sort.
649 >>> p.sort() != BoolSort()
651 >>> p.sort() != IntSort()
658 return AstRef.__hash__(self)
662 """Return `True` if `s` is a Z3 sort.
664 >>> is_sort(IntSort())
666 >>> is_sort(Int('x'))
668 >>> is_expr(Int('x'))
671 return isinstance(s, SortRef)
676 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
678 if k == Z3_BOOL_SORT:
680 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
682 elif k == Z3_BV_SORT:
684 elif k == Z3_ARRAY_SORT:
686 elif k == Z3_DATATYPE_SORT:
688 elif k == Z3_FINITE_DOMAIN_SORT:
690 elif k == Z3_FLOATING_POINT_SORT:
692 elif k == Z3_ROUNDING_MODE_SORT:
694 elif k == Z3_RE_SORT:
696 elif k == Z3_SEQ_SORT:
698 elif k == Z3_CHAR_SORT:
700 elif k == Z3_TYPE_VAR:
705def _sort(ctx : Context, a : Any) -> SortRef:
710 """Create a new uninterpreted sort named `name`.
712 If `ctx=None`, then the new sort is declared in the global Z3Py context.
714 >>> A = DeclareSort('A')
715 >>> a = Const('a', A)
716 >>> b = Const('b', A)
728 """Type variable reference"""
738 """Create a new type variable named `name`.
740 If `ctx=None`, then the new sort is declared in the global Z3Py context.
755 """Function declaration. Every constant and function have an associated declaration.
757 The declaration assigns a name, a sort (i.e., type), and for function
758 the sort (i.e., type) of each of its arguments. Note that, in Z3,
759 a constant is a function with 0 arguments.
772 """Return the name of the function declaration `self`.
774 >>> f = Function('f', IntSort(), IntSort())
777 >>> isinstance(f.name(), str)
783 """Return the number of arguments of a function declaration.
784 If `self` is a constant, then `self.arity()` is 0.
786 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
793 """Return the sort of the argument `i` of a function declaration.
794 This method assumes that `0 <= i < self.arity()`.
796 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
805 """Return the sort of the range of a function declaration.
806 For constants, this is the sort of the constant.
808 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
815 """Return the internal kind of a function declaration.
816 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
819 >>> d = (x + 1).decl()
820 >>> d.kind() == Z3_OP_ADD
822 >>> d.kind() == Z3_OP_MUL
830 result = [
None for i
in range(n)]
833 if k == Z3_PARAMETER_INT:
835 elif k == Z3_PARAMETER_DOUBLE:
837 elif k == Z3_PARAMETER_RATIONAL:
839 elif k == Z3_PARAMETER_SYMBOL:
841 elif k == Z3_PARAMETER_SORT:
843 elif k == Z3_PARAMETER_AST:
845 elif k == Z3_PARAMETER_FUNC_DECL:
847 elif k == Z3_PARAMETER_INTERNAL:
848 result[i] =
"internal parameter"
849 elif k == Z3_PARAMETER_ZSTRING:
850 result[i] =
"internal string"
856 """Create a Z3 application expression using the function `self`, and the given arguments.
858 The arguments must be Z3 expressions. This method assumes that
859 the sorts of the elements in `args` match the sorts of the
860 domain. Limited coercion is supported. For example, if
861 args[0] is a Python integer, and the function expects a Z3
862 integer, then the argument is automatically converted into a
865 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
875 _args = (Ast * num)()
880 tmp = self.
domain(i).cast(args[i])
882 _args[i] = tmp.as_ast()
887 """Return `True` if `a` is a Z3 function declaration.
889 >>> f = Function('f', IntSort(), IntSort())
896 return isinstance(a, FuncDeclRef)
900 """Create a new Z3 uninterpreted function with the given sorts.
902 >>> f = Function('f', IntSort(), IntSort())
908 _z3_assert(len(sig) > 0,
"At least two arguments expected")
913 dom = (Sort * arity)()
914 for i
in range(arity):
923 """Create a new fresh Z3 uninterpreted function with the given sorts.
927 _z3_assert(len(sig) > 0,
"At least two arguments expected")
932 dom = (z3.Sort * arity)()
933 for i
in range(arity):
946 """Create a new Z3 recursive with the given sorts."""
949 _z3_assert(len(sig) > 0,
"At least two arguments expected")
954 dom = (Sort * arity)()
955 for i
in range(arity):
964 """Set the body of a recursive function.
965 Recursive definitions can be simplified if they are applied to ground
968 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
969 >>> n = Int('n', ctx)
970 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
973 >>> s = Solver(ctx=ctx)
974 >>> s.add(fac(n) < 3)
977 >>> s.model().eval(fac(5))
987 _args[i] = args[i].ast
998 """Constraints, formulas and terms are expressions in Z3.
1000 Expressions are ASTs. Every expression has a sort.
1001 There are three main kinds of expressions:
1002 function applications, quantifiers and bounded variables.
1003 A constant is a function application with 0 arguments.
1004 For quantifier free problems, all expressions are
1005 function applications.
1015 """Return the sort of expression `self`.
1027 """Shorthand for `self.sort().kind()`.
1029 >>> a = Array('a', IntSort(), IntSort())
1030 >>> a.sort_kind() == Z3_ARRAY_SORT
1032 >>> a.sort_kind() == Z3_INT_SORT
1038 """Return a Z3 expression that represents the constraint `self == other`.
1040 If `other` is `None`, then this method simply returns `False`.
1056 return AstRef.__hash__(self)
1059 """Return a Z3 expression that represents the constraint `self != other`.
1061 If `other` is `None`, then this method simply returns `True`.
1080 """Return the Z3 function declaration associated with a Z3 application.
1082 >>> f = Function('f', IntSort(), IntSort())
1095 """Return the Z3 internal kind of a function application."""
1102 """Return the number of arguments of a Z3 application.
1106 >>> (a + b).num_args()
1108 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1118 """Return argument `idx` of the application `self`.
1120 This method assumes that `self` is a function application with at least `idx+1` arguments.
1124 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1139 """Return a list containing the children of the given expression
1143 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1149 return [self.
arg(i)
for i
in range(self.
num_args())]
1163 """inverse function to the serialize method on ExprRef.
1164 It is made available to make it easier for users to serialize expressions back and forth between
1165 strings. Solvers can be serialized using the 'sexpr()' method.
1169 if len(s.assertions()) != 1:
1170 raise Z3Exception(
"single assertion expected")
1171 fml = s.assertions()[0]
1172 if fml.num_args() != 1:
1173 raise Z3Exception(
"dummy function 'F' expected")
1177 if isinstance(a, Pattern):
1181 if k == Z3_QUANTIFIER_AST:
1184 if sk == Z3_BOOL_SORT:
1186 if sk == Z3_INT_SORT:
1187 if k == Z3_NUMERAL_AST:
1190 if sk == Z3_REAL_SORT:
1191 if k == Z3_NUMERAL_AST:
1196 if sk == Z3_BV_SORT:
1197 if k == Z3_NUMERAL_AST:
1201 if sk == Z3_ARRAY_SORT:
1203 if sk == Z3_DATATYPE_SORT:
1205 if sk == Z3_FLOATING_POINT_SORT:
1209 return FPRef(a, ctx)
1210 if sk == Z3_FINITE_DOMAIN_SORT:
1211 if k == Z3_NUMERAL_AST:
1215 if sk == Z3_ROUNDING_MODE_SORT:
1217 if sk == Z3_SEQ_SORT:
1219 if sk == Z3_CHAR_SORT:
1221 if sk == Z3_RE_SORT:
1222 return ReRef(a, ctx)
1239 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1249 if isinstance(a, str)
and isinstance(b, SeqRef):
1251 if isinstance(b, str)
and isinstance(a, SeqRef):
1253 if isinstance(a, float)
and isinstance(b, ArithRef):
1255 if isinstance(b, float)
and isinstance(a, ArithRef):
1268 for element
in sequence:
1269 result = func(result, element)
1280 alist = [
_py2expr(a, ctx)
for a
in alist]
1281 s =
_reduce(_coerce_expr_merge, alist,
None)
1282 return [s.cast(a)
for a
in alist]
1286 """Return `True` if `a` is a Z3 expression.
1293 >>> is_expr(IntSort())
1297 >>> is_expr(IntVal(1))
1300 >>> is_expr(ForAll(x, x >= 0))
1302 >>> is_expr(FPVal(1.0))
1305 return isinstance(a, ExprRef)
1309 """Return `True` if `a` is a Z3 function application.
1311 Note that, constants are function applications with 0 arguments.
1318 >>> is_app(IntSort())
1322 >>> is_app(IntVal(1))
1325 >>> is_app(ForAll(x, x >= 0))
1328 if not isinstance(a, ExprRef):
1331 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1335 """Return `True` if `a` is Z3 constant/variable expression.
1344 >>> is_const(IntVal(1))
1347 >>> is_const(ForAll(x, x >= 0))
1350 return is_app(a)
and a.num_args() == 0
1354 """Return `True` if `a` is variable.
1356 Z3 uses de-Bruijn indices for representing bound variables in
1364 >>> f = Function('f', IntSort(), IntSort())
1365 >>> # Z3 replaces x with bound variables when ForAll is executed.
1366 >>> q = ForAll(x, f(x) == x)
1372 >>> is_var(b.arg(1))
1379 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1387 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1388 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1389 >>> q = ForAll([x, y], f(x, y) == x + y)
1391 f(Var(1), Var(0)) == Var(1) + Var(0)
1395 >>> v1 = b.arg(0).arg(0)
1396 >>> v2 = b.arg(0).arg(1)
1401 >>> get_var_index(v1)
1403 >>> get_var_index(v2)
1412 """Return `True` if `a` is an application of the given kind `k`.
1416 >>> is_app_of(n, Z3_OP_ADD)
1418 >>> is_app_of(n, Z3_OP_MUL)
1421 return is_app(a)
and a.kind() == k
1424def If(a, b, c, ctx=None):
1425 """Create a Z3 if-then-else expression.
1429 >>> max = If(x > y, x, y)
1435 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1436 return Cond(a, b, c, ctx)
1443 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1448 """Create a Z3 distinct expression.
1455 >>> Distinct(x, y, z)
1457 >>> simplify(Distinct(x, y, z))
1459 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1460 And(Not(x == y), Not(x == z), Not(y == z))
1465 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1474 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1475 args[0] = a.as_ast()
1476 args[1] = b.as_ast()
1477 return f(a.ctx.ref(), 2, args)
1481 """Create a constant of the given sort.
1483 >>> Const('x', IntSort())
1487 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1493 """Create several constants of the given sort.
1495 `names` is a string containing the names of all constants to be created.
1496 Blank spaces separate the names of different constants.
1498 >>> x, y, z = Consts('x y z', IntSort())
1502 if isinstance(names, str):
1503 names = names.split(
" ")
1504 return [
Const(name, sort)
for name
in names]
1508 """Create a fresh constant of a specified sort"""
1513def Var(idx : int, s : SortRef) -> ExprRef:
1514 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1515 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1518 >>> Var(0, IntSort())
1520 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1530 Create a real free variable. Free variables are used to create quantified formulas.
1531 They are also used to create polynomials.
1540 Create a list of Real free variables.
1541 The variables have ids: 0, 1, ..., n-1
1543 >>> x0, x1, x2, x3 = RealVarVector(4)
1547 return [
RealVar(i, ctx)
for i
in range(n)]
1560 """Try to cast `val` as a Boolean.
1562 >>> x = BoolSort().cast(True)
1572 if isinstance(val, bool):
1576 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1578 if not self.
eq(val.sort()):
1579 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1583 return isinstance(other, ArithSortRef)
1593 """All Boolean expressions are instances of this class."""
1599 if isinstance(other, BoolRef):
1600 other =
If(other, 1, 0)
1601 return If(self, 1, 0) + other
1610 """Create the Z3 expression `self * other`.
1612 if isinstance(other, int)
and other == 1:
1613 return If(self, 1, 0)
1614 if isinstance(other, int)
and other == 0:
1616 if isinstance(other, BoolRef):
1617 other =
If(other, 1, 0)
1618 return If(self, other, 0)
1621 return And(self, other)
1624 return Or(self, other)
1627 return Xor(self, other)
1643 """Return `True` if `a` is a Z3 Boolean expression.
1649 >>> is_bool(And(p, q))
1657 return isinstance(a, BoolRef)
1661 """Return `True` if `a` is the Z3 true expression.
1666 >>> is_true(simplify(p == p))
1671 >>> # True is a Python Boolean expression
1679 """Return `True` if `a` is the Z3 false expression.
1686 >>> is_false(BoolVal(False))
1693 """Return `True` if `a` is a Z3 and expression.
1695 >>> p, q = Bools('p q')
1696 >>> is_and(And(p, q))
1698 >>> is_and(Or(p, q))
1705 """Return `True` if `a` is a Z3 or expression.
1707 >>> p, q = Bools('p q')
1710 >>> is_or(And(p, q))
1717 """Return `True` if `a` is a Z3 implication expression.
1719 >>> p, q = Bools('p q')
1720 >>> is_implies(Implies(p, q))
1722 >>> is_implies(And(p, q))
1729 """Return `True` if `a` is a Z3 not expression.
1741 """Return `True` if `a` is a Z3 equality expression.
1743 >>> x, y = Ints('x y')
1751 """Return `True` if `a` is a Z3 distinct expression.
1753 >>> x, y, z = Ints('x y z')
1754 >>> is_distinct(x == y)
1756 >>> is_distinct(Distinct(x, y, z))
1763 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1767 >>> p = Const('p', BoolSort())
1770 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1773 >>> is_bool(r(0, 1))
1781 """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
1785 >>> is_true(BoolVal(True))
1789 >>> is_false(BoolVal(False))
1800 """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
1812 """Return a tuple of Boolean constants.
1814 `names` is a single string containing all names separated by blank spaces.
1815 If `ctx=None`, then the global context is used.
1817 >>> p, q, r = Bools('p q r')
1818 >>> And(p, Or(q, r))
1822 if isinstance(names, str):
1823 names = names.split(
" ")
1824 return [
Bool(name, ctx)
for name
in names]
1828 """Return a list of Boolean constants of size `sz`.
1830 The constants are named using the given prefix.
1831 If `ctx=None`, then the global context is used.
1833 >>> P = BoolVector('p', 3)
1837 And(p__0, p__1, p__2)
1839 return [
Bool(
"%s__%s" % (prefix, i))
for i
in range(sz)]
1843 """Return a fresh Boolean constant in the given context using the given prefix.
1845 If `ctx=None`, then the global context is used.
1847 >>> b1 = FreshBool()
1848 >>> b2 = FreshBool()
1857 """Create a Z3 implies expression.
1859 >>> p, q = Bools('p q')
1871 """Create a Z3 Xor expression.
1873 >>> p, q = Bools('p q')
1876 >>> simplify(Xor(p, q))
1887 """Create a Z3 not expression or probe.
1892 >>> simplify(Not(Not(p)))
1913 """Return `True` if one of the elements of the given collection is a Z3 probe."""
1921 """Create a Z3 and-expression or and-probe.
1923 >>> p, q, r = Bools('p q r')
1926 >>> P = BoolVector('p', 5)
1928 And(p__0, p__1, p__2, p__3, p__4)
1932 last_arg = args[len(args) - 1]
1933 if isinstance(last_arg, Context):
1934 ctx = args[len(args) - 1]
1935 args = args[:len(args) - 1]
1936 elif len(args) == 1
and isinstance(args[0], AstVector):
1938 args = [a
for a
in args[0]]
1944 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1954 """Create a Z3 or-expression or or-probe.
1956 >>> p, q, r = Bools('p q r')
1959 >>> P = BoolVector('p', 5)
1961 Or(p__0, p__1, p__2, p__3, p__4)
1965 last_arg = args[len(args) - 1]
1966 if isinstance(last_arg, Context):
1967 ctx = args[len(args) - 1]
1968 args = args[:len(args) - 1]
1969 elif len(args) == 1
and isinstance(args[0], AstVector):
1971 args = [a
for a
in args[0]]
1977 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression or probe")
1993 """Patterns are hints for quantifier instantiation.
2005 """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
2007 >>> f = Function('f', IntSort(), IntSort())
2009 >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
2011 ForAll(x, f(x) == 0)
2012 >>> q.num_patterns()
2014 >>> is_pattern(q.pattern(0))
2019 return isinstance(a, PatternRef)
2023 """Create a Z3 multi-pattern using the given expressions `*args`
2025 >>> f = Function('f', IntSort(), IntSort())
2026 >>> g = Function('g', IntSort(), IntSort())
2028 >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
2030 ForAll(x, f(x) != g(x))
2031 >>> q.num_patterns()
2033 >>> is_pattern(q.pattern(0))
2036 MultiPattern(f(Var(0)), g(Var(0)))
2039 _z3_assert(len(args) > 0,
"At least one argument expected")
2060 """Universally and Existentially quantified formulas."""
2069 """Return the Boolean sort or sort of Lambda."""
2075 """Return `True` if `self` is a universal quantifier.
2077 >>> f = Function('f', IntSort(), IntSort())
2079 >>> q = ForAll(x, f(x) == 0)
2082 >>> q = Exists(x, f(x) != 0)
2089 """Return `True` if `self` is an existential quantifier.
2091 >>> f = Function('f', IntSort(), IntSort())
2093 >>> q = ForAll(x, f(x) == 0)
2096 >>> q = Exists(x, f(x) != 0)
2103 """Return `True` if `self` is a lambda expression.
2105 >>> f = Function('f', IntSort(), IntSort())
2107 >>> q = Lambda(x, f(x))
2110 >>> q = Exists(x, f(x) != 0)
2117 """Return the Z3 expression `self[arg]`.
2124 """Return the weight annotation of `self`.
2126 >>> f = Function('f', IntSort(), IntSort())
2128 >>> q = ForAll(x, f(x) == 0)
2131 >>> q = ForAll(x, f(x) == 0, weight=10)
2138 """Return the skolem id of `self`.
2143 """Return the quantifier id of `self`.
2148 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2150 >>> f = Function('f', IntSort(), IntSort())
2151 >>> g = Function('g', IntSort(), IntSort())
2153 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2154 >>> q.num_patterns()
2160 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2162 >>> f = Function('f', IntSort(), IntSort())
2163 >>> g = Function('g', IntSort(), IntSort())
2165 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2166 >>> q.num_patterns()
2178 """Return the number of no-patterns."""
2182 """Return a no-pattern."""
2188 """Return the expression being quantified.
2190 >>> f = Function('f', IntSort(), IntSort())
2192 >>> q = ForAll(x, f(x) == 0)
2199 """Return the number of variables bounded by this quantifier.
2201 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2204 >>> q = ForAll([x, y], f(x, y) >= x)
2211 """Return a string representing a name used when displaying the quantifier.
2213 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2216 >>> q = ForAll([x, y], f(x, y) >= x)
2227 """Return the sort of a bound variable.
2229 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2232 >>> q = ForAll([x, y], f(x, y) >= x)
2243 """Return a list containing a single element self.body()
2245 >>> f = Function('f', IntSort(), IntSort())
2247 >>> q = ForAll(x, f(x) == 0)
2251 return [self.
body()]
2255 """Return `True` if `a` is a Z3 quantifier.
2257 >>> f = Function('f', IntSort(), IntSort())
2259 >>> q = ForAll(x, f(x) == 0)
2260 >>> is_quantifier(q)
2262 >>> is_quantifier(f(x))
2265 return isinstance(a, QuantifierRef)
2268def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2273 _z3_assert(all([
is_expr(p)
for p
in no_patterns]),
"no patterns are Z3 expressions")
2284 _vs = (Ast * num_vars)()
2285 for i
in range(num_vars):
2287 _vs[i] = vs[i].as_ast()
2289 num_pats = len(patterns)
2290 _pats = (Pattern * num_pats)()
2291 for i
in range(num_pats):
2292 _pats[i] = patterns[i].ast
2299 num_no_pats, _no_pats,
2300 body.as_ast()), ctx)
2303def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2304 """Create a Z3 forall formula.
2306 The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
2308 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2311 >>> ForAll([x, y], f(x, y) >= x)
2312 ForAll([x, y], f(x, y) >= x)
2313 >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2314 ForAll([x, y], f(x, y) >= x)
2315 >>> ForAll([x, y], f(x, y) >= x, weight=10)
2316 ForAll([x, y], f(x, y) >= x)
2318 return _mk_quantifier(
True, vs, body, weight, qid, skid, patterns, no_patterns)
2321def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2322 """Create a Z3 exists formula.
2324 The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
2327 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2330 >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
2332 Exists([x, y], f(x, y) >= x)
2333 >>> is_quantifier(q)
2335 >>> r = Tactic('nnf')(q).as_expr()
2336 >>> is_quantifier(r)
2339 return _mk_quantifier(
False, vs, body, weight, qid, skid, patterns, no_patterns)
2343 """Create a Z3 lambda expression.
2345 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2346 >>> mem0 = Array('mem0', IntSort(), IntSort())
2347 >>> lo, hi, e, i = Ints('lo hi e i')
2348 >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
2350 Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
2356 _vs = (Ast * num_vars)()
2357 for i
in range(num_vars):
2359 _vs[i] = vs[i].as_ast()
2370 """Real and Integer sorts."""
2373 """Return `True` if `self` is of the sort Real.
2378 >>> (x + 1).is_real()
2384 return self.
kind() == Z3_REAL_SORT
2387 """Return `True` if `self` is of the sort Integer.
2392 >>> (x + 1).is_int()
2398 return self.
kind() == Z3_INT_SORT
2404 """Return `True` if `self` is a subsort of `other`."""
2408 """Try to cast `val` as an Integer or Real.
2410 >>> IntSort().cast(10)
2412 >>> is_int(IntSort().cast(10))
2416 >>> RealSort().cast(10)
2418 >>> is_real(RealSort().cast(10))
2427 if val_s.is_int()
and self.
is_real():
2429 if val_s.is_bool()
and self.
is_int():
2430 return If(val, 1, 0)
2431 if val_s.is_bool()
and self.
is_real():
2434 _z3_assert(
False,
"Z3 Integer/Real expression expected")
2441 msg =
"int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2446 """Return `True` if s is an arithmetical sort (type).
2448 >>> is_arith_sort(IntSort())
2450 >>> is_arith_sort(RealSort())
2452 >>> is_arith_sort(BoolSort())
2454 >>> n = Int('x') + 1
2455 >>> is_arith_sort(n.sort())
2458 return isinstance(s, ArithSortRef)
2462 """Integer and Real expressions."""
2465 """Return the sort (type) of the arithmetical expression `self`.
2469 >>> (Real('x') + 1).sort()
2475 """Return `True` if `self` is an integer expression.
2480 >>> (x + 1).is_int()
2483 >>> (x + y).is_int()
2489 """Return `True` if `self` is an real expression.
2494 >>> (x + 1).is_real()
2500 """Create the Z3 expression `self + other`.
2513 """Create the Z3 expression `other + self`.
2523 """Create the Z3 expression `self * other`.
2532 if isinstance(other, BoolRef):
2533 return If(other, self, 0)
2538 """Create the Z3 expression `other * self`.
2548 """Create the Z3 expression `self - other`.
2561 """Create the Z3 expression `other - self`.
2571 """Create the Z3 expression `self**other` (** is the power operator).
2578 >>> simplify(IntVal(2)**8)
2585 """Create the Z3 expression `other**self` (** is the power operator).
2592 >>> simplify(2**IntVal(8))
2599 """Create the Z3 expression `other/self`.
2622 """Create the Z3 expression `other/self`."""
2626 """Create the Z3 expression `other/self`.
2643 """Create the Z3 expression `other/self`."""
2647 """Create the Z3 expression `other%self`.
2653 >>> simplify(IntVal(10) % IntVal(3))
2658 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2662 """Create the Z3 expression `other%self`.
2670 _z3_assert(a.is_int(),
"Z3 integer expression expected")
2674 """Return an expression representing `-self`.
2694 """Create the Z3 expression `other <= self`.
2696 >>> x, y = Ints('x y')
2707 """Create the Z3 expression `other < self`.
2709 >>> x, y = Ints('x y')
2720 """Create the Z3 expression `other > self`.
2722 >>> x, y = Ints('x y')
2733 """Create the Z3 expression `other >= self`.
2735 >>> x, y = Ints('x y')
2747 """Return `True` if `a` is an arithmetical expression.
2756 >>> is_arith(IntVal(1))
2764 return isinstance(a, ArithRef)
2768 """Return `True` if `a` is an integer expression.
2775 >>> is_int(IntVal(1))
2787 """Return `True` if `a` is a real expression.
2799 >>> is_real(RealVal(1))
2814 """Return `True` if `a` is an integer value of sort Int.
2816 >>> is_int_value(IntVal(1))
2820 >>> is_int_value(Int('x'))
2822 >>> n = Int('x') + 1
2827 >>> is_int_value(n.arg(1))
2829 >>> is_int_value(RealVal("1/3"))
2831 >>> is_int_value(RealVal(1))
2838 """Return `True` if `a` is rational value of sort Real.
2840 >>> is_rational_value(RealVal(1))
2842 >>> is_rational_value(RealVal("3/5"))
2844 >>> is_rational_value(IntVal(1))
2846 >>> is_rational_value(1)
2848 >>> n = Real('x') + 1
2851 >>> is_rational_value(n.arg(1))
2853 >>> is_rational_value(Real('x'))
2860 """Return `True` if `a` is an algebraic value of sort Real.
2862 >>> is_algebraic_value(RealVal("3/5"))
2864 >>> n = simplify(Sqrt(2))
2867 >>> is_algebraic_value(n)
2874 """Return `True` if `a` is an expression of the form b + c.
2876 >>> x, y = Ints('x y')
2886 """Return `True` if `a` is an expression of the form b * c.
2888 >>> x, y = Ints('x y')
2898 """Return `True` if `a` is an expression of the form b - c.
2900 >>> x, y = Ints('x y')
2910 """Return `True` if `a` is an expression of the form b / c.
2912 >>> x, y = Reals('x y')
2917 >>> x, y = Ints('x y')
2927 """Return `True` if `a` is an expression of the form b div c.
2929 >>> x, y = Ints('x y')
2939 """Return `True` if `a` is an expression of the form b % c.
2941 >>> x, y = Ints('x y')
2951 """Return `True` if `a` is an expression of the form b <= c.
2953 >>> x, y = Ints('x y')
2963 """Return `True` if `a` is an expression of the form b < c.
2965 >>> x, y = Ints('x y')
2975 """Return `True` if `a` is an expression of the form b >= c.
2977 >>> x, y = Ints('x y')
2987 """Return `True` if `a` is an expression of the form b > c.
2989 >>> x, y = Ints('x y')
2999 """Return `True` if `a` is an expression of the form IsInt(b).
3002 >>> is_is_int(IsInt(x))
3011 """Return `True` if `a` is an expression of the form ToReal(b).
3026 """Return `True` if `a` is an expression of the form ToInt(b).
3041 """Integer values."""
3044 """Return a Z3 integer numeral as a Python long (bignum) numeral.
3057 """Return a Z3 integer numeral as a Python string.
3065 """Return a Z3 integer numeral as a Python binary string.
3067 >>> v.as_binary_string()
3077 """Rational values."""
3080 """ Return the numerator of a Z3 rational numeral.
3082 >>> is_rational_value(RealVal("3/5"))
3084 >>> n = RealVal("3/5")
3087 >>> is_rational_value(Q(3,5))
3089 >>> Q(3,5).numerator()
3095 """ Return the denominator of a Z3 rational numeral.
3097 >>> is_rational_value(Q(3,5))
3106 """ Return the numerator as a Python long.
3108 >>> v = RealVal(10000000000)
3113 >>> v.numerator_as_long() + 1 == 10000000001
3119 """ Return the denominator as a Python long.
3121 >>> v = RealVal("1/3")
3124 >>> v.denominator_as_long()
3143 """ Return a Z3 rational value as a string in decimal notation using at most `prec` decimal places.
3145 >>> v = RealVal("1/5")
3148 >>> v = RealVal("1/3")
3155 """Return a Z3 rational numeral as a Python string.
3164 """Return a Z3 rational as a Python Fraction object.
3166 >>> v = RealVal("1/5")
3177 """Algebraic irrational values."""
3180 """Return a Z3 rational number that approximates the algebraic number `self`.
3181 The result `r` is such that |r - self| <= 1/10^precision
3183 >>> x = simplify(Sqrt(2))
3185 6838717160008073720548335/4835703278458516698824704
3192 """Return a string representation of the algebraic number `self` in decimal notation
3193 using `prec` decimal places.
3195 >>> x = simplify(Sqrt(2))
3196 >>> x.as_decimal(10)
3198 >>> x.as_decimal(20)
3199 '1.41421356237309504880?'
3211 if isinstance(a, bool):
3215 if isinstance(a, float):
3217 if isinstance(a, str):
3222 _z3_assert(
False,
"Python bool, int, long or float expected")
3226 """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
3230 >>> x = Const('x', IntSort())
3233 >>> x.sort() == IntSort()
3235 >>> x.sort() == BoolSort()
3243 """Return the real sort in the given context. If `ctx=None`, then the global context is used.
3247 >>> x = Const('x', RealSort())
3252 >>> x.sort() == RealSort()
3260 if isinstance(val, float):
3261 return str(int(val))
3262 elif isinstance(val, bool):
3272 """Return a Z3 integer value. If `ctx=None`, then the global context is used.
3284 """Return a Z3 real value.
3286 `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
3287 If `ctx=None`, then the global context is used.
3291 >>> RealVal(1).sort()
3303 """Return a Z3 rational a/b.
3305 If `ctx=None`, then the global context is used.
3309 >>> RatVal(3,5).sort()
3313 _z3_assert(
_is_int(a)
or isinstance(a, str),
"First argument cannot be converted into an integer")
3314 _z3_assert(
_is_int(b)
or isinstance(b, str),
"Second argument cannot be converted into an integer")
3318def Q(a, b, ctx=None):
3319 """Return a Z3 rational a/b.
3321 If `ctx=None`, then the global context is used.
3332 """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
3345 """Return a tuple of Integer constants.
3347 >>> x, y, z = Ints('x y z')
3352 if isinstance(names, str):
3353 names = names.split(
" ")
3354 return [
Int(name, ctx)
for name
in names]
3358 """Return a list of integer constants of size `sz`.
3360 >>> X = IntVector('x', 3)
3367 return [
Int(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3371 """Return a fresh integer constant in the given context using the given prefix.
3385 """Return a real constant named `name`. If `ctx=None`, then the global context is used.
3398 """Return a tuple of real constants.
3400 >>> x, y, z = Reals('x y z')
3403 >>> Sum(x, y, z).sort()
3407 if isinstance(names, str):
3408 names = names.split(
" ")
3409 return [
Real(name, ctx)
for name
in names]
3413 """Return a list of real constants of size `sz`.
3415 >>> X = RealVector('x', 3)
3424 return [
Real(
"%s__%s" % (prefix, i), ctx)
for i
in range(sz)]
3428 """Return a fresh real constant in the given context using the given prefix.
3442 """ Return the Z3 expression ToReal(a).
3454 if isinstance(a, BoolRef):
3457 _z3_assert(a.is_int(),
"Z3 integer expression expected.")
3462 """ Return the Z3 expression ToInt(a).
3474 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3480 """ Return the Z3 predicate IsInt(a).
3483 >>> IsInt(x + "1/2")
3485 >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
3487 >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
3491 _z3_assert(a.is_real(),
"Z3 real expression expected.")
3497 """ Return a Z3 expression which represents the square root of a.
3510 """ Return a Z3 expression which represents the cubic root of a.
3529 """Bit-vector sort."""
3532 """Return the size (number of bits) of the bit-vector sort `self`.
3534 >>> b = BitVecSort(32)
3544 """Try to cast `val` as a Bit-Vector.
3546 >>> b = BitVecSort(32)
3549 >>> b.cast(10).sexpr()
3562 """Return True if `s` is a Z3 bit-vector sort.
3564 >>> is_bv_sort(BitVecSort(32))
3566 >>> is_bv_sort(IntSort())
3569 return isinstance(s, BitVecSortRef)
3573 """Bit-vector expressions."""
3576 """Return the sort of the bit-vector expression `self`.
3578 >>> x = BitVec('x', 32)
3581 >>> x.sort() == BitVecSort(32)
3587 """Return the number of bits of the bit-vector expression `self`.
3589 >>> x = BitVec('x', 32)
3592 >>> Concat(x, x).size()
3598 """Create the Z3 expression `self + other`.
3600 >>> x = BitVec('x', 32)
3601 >>> y = BitVec('y', 32)
3611 """Create the Z3 expression `other + self`.
3613 >>> x = BitVec('x', 32)
3621 """Create the Z3 expression `self * other`.
3623 >>> x = BitVec('x', 32)
3624 >>> y = BitVec('y', 32)
3634 """Create the Z3 expression `other * self`.
3636 >>> x = BitVec('x', 32)
3644 """Create the Z3 expression `self - other`.
3646 >>> x = BitVec('x', 32)
3647 >>> y = BitVec('y', 32)
3657 """Create the Z3 expression `other - self`.
3659 >>> x = BitVec('x', 32)
3667 """Create the Z3 expression bitwise-or `self | other`.
3669 >>> x = BitVec('x', 32)
3670 >>> y = BitVec('y', 32)
3680 """Create the Z3 expression bitwise-or `other | self`.
3682 >>> x = BitVec('x', 32)
3690 """Create the Z3 expression bitwise-and `self & other`.
3692 >>> x = BitVec('x', 32)
3693 >>> y = BitVec('y', 32)
3703 """Create the Z3 expression bitwise-or `other & self`.
3705 >>> x = BitVec('x', 32)
3713 """Create the Z3 expression bitwise-xor `self ^ other`.
3715 >>> x = BitVec('x', 32)
3716 >>> y = BitVec('y', 32)
3726 """Create the Z3 expression bitwise-xor `other ^ self`.
3728 >>> x = BitVec('x', 32)
3738 >>> x = BitVec('x', 32)
3745 """Return an expression representing `-self`.
3747 >>> x = BitVec('x', 32)
3756 """Create the Z3 expression bitwise-not `~self`.
3758 >>> x = BitVec('x', 32)
3767 """Create the Z3 expression (signed) division `self / other`.
3769 Use the function UDiv() for unsigned division.
3771 >>> x = BitVec('x', 32)
3772 >>> y = BitVec('y', 32)
3779 >>> UDiv(x, y).sexpr()
3786 """Create the Z3 expression (signed) division `self / other`."""
3790 """Create the Z3 expression (signed) division `other / self`.
3792 Use the function UDiv() for unsigned division.
3794 >>> x = BitVec('x', 32)
3797 >>> (10 / x).sexpr()
3798 '(bvsdiv #x0000000a x)'
3799 >>> UDiv(10, x).sexpr()
3800 '(bvudiv #x0000000a x)'
3806 """Create the Z3 expression (signed) division `other / self`."""
3810 """Create the Z3 expression (signed) mod `self % other`.
3812 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3814 >>> x = BitVec('x', 32)
3815 >>> y = BitVec('y', 32)
3822 >>> URem(x, y).sexpr()
3824 >>> SRem(x, y).sexpr()
3831 """Create the Z3 expression (signed) mod `other % self`.
3833 Use the function URem() for unsigned remainder, and SRem() for signed remainder.
3835 >>> x = BitVec('x', 32)
3838 >>> (10 % x).sexpr()
3839 '(bvsmod #x0000000a x)'
3840 >>> URem(10, x).sexpr()
3841 '(bvurem #x0000000a x)'
3842 >>> SRem(10, x).sexpr()
3843 '(bvsrem #x0000000a x)'
3849 """Create the Z3 expression (signed) `other <= self`.
3851 Use the function ULE() for unsigned less than or equal to.
3853 >>> x, y = BitVecs('x y', 32)
3856 >>> (x <= y).sexpr()
3858 >>> ULE(x, y).sexpr()
3865 """Create the Z3 expression (signed) `other < self`.
3867 Use the function ULT() for unsigned less than.
3869 >>> x, y = BitVecs('x y', 32)
3874 >>> ULT(x, y).sexpr()
3881 """Create the Z3 expression (signed) `other > self`.
3883 Use the function UGT() for unsigned greater than.
3885 >>> x, y = BitVecs('x y', 32)
3890 >>> UGT(x, y).sexpr()
3897 """Create the Z3 expression (signed) `other >= self`.
3899 Use the function UGE() for unsigned greater than or equal to.
3901 >>> x, y = BitVecs('x y', 32)
3904 >>> (x >= y).sexpr()
3906 >>> UGE(x, y).sexpr()
3913 """Create the Z3 expression (arithmetical) right shift `self >> other`
3915 Use the function LShR() for the right logical shift
3917 >>> x, y = BitVecs('x y', 32)
3920 >>> (x >> y).sexpr()
3922 >>> LShR(x, y).sexpr()
3926 >>> BitVecVal(4, 3).as_signed_long()
3928 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
3930 >>> simplify(BitVecVal(4, 3) >> 1)
3932 >>> simplify(LShR(BitVecVal(4, 3), 1))
3934 >>> simplify(BitVecVal(2, 3) >> 1)
3936 >>> simplify(LShR(BitVecVal(2, 3), 1))
3943 """Create the Z3 expression left shift `self << other`
3945 >>> x, y = BitVecs('x y', 32)
3948 >>> (x << y).sexpr()
3950 >>> simplify(BitVecVal(2, 3) << 1)
3957 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3959 Use the function LShR() for the right logical shift
3961 >>> x = BitVec('x', 32)
3964 >>> (10 >> x).sexpr()
3965 '(bvashr #x0000000a x)'
3971 """Create the Z3 expression left shift `other << self`.
3973 Use the function LShR() for the right logical shift
3975 >>> x = BitVec('x', 32)
3978 >>> (10 << x).sexpr()
3979 '(bvshl #x0000000a x)'
3986 """Bit-vector values."""
3989 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
3991 >>> v = BitVecVal(0xbadc0de, 32)
3994 >>> print("0x%.8x" % v.as_long())
4000 """Return a Z3 bit-vector numeral as a Python long (bignum) numeral.
4001 The most significant bit is assumed to be the sign.
4003 >>> BitVecVal(4, 3).as_signed_long()
4005 >>> BitVecVal(7, 3).as_signed_long()
4007 >>> BitVecVal(3, 3).as_signed_long()
4009 >>> BitVecVal(2**32 - 1, 32).as_signed_long()
4011 >>> BitVecVal(2**64 - 1, 64).as_signed_long()
4016 if val >= 2**(sz - 1):
4018 if val < -2**(sz - 1):
4029 """Return the Python value of a Z3 bit-vector numeral."""
4035 """Return `True` if `a` is a Z3 bit-vector expression.
4037 >>> b = BitVec('b', 32)
4045 return isinstance(a, BitVecRef)
4049 """Return `True` if `a` is a Z3 bit-vector numeral value.
4051 >>> b = BitVec('b', 32)
4054 >>> b = BitVecVal(10, 32)
4064 """Return the Z3 expression BV2Int(a).
4066 >>> b = BitVec('b', 3)
4067 >>> BV2Int(b).sort()
4072 >>> x > BV2Int(b, is_signed=False)
4074 >>> x > BV2Int(b, is_signed=True)
4075 x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
4076 >>> solve(x > BV2Int(b), b == 1, x < 3)
4080 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4087 """Return the z3 expression Int2BV(a, num_bits).
4088 It is a bit-vector of width num_bits and represents the
4089 modulo of a by 2^num_bits
4096 """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
4098 >>> Byte = BitVecSort(8)
4099 >>> Word = BitVecSort(16)
4102 >>> x = Const('x', Byte)
4103 >>> eq(x, BitVec('x', 8))
4111 """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
4113 >>> v = BitVecVal(10, 32)
4116 >>> print("0x%.8x" % v.as_long())
4128 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4129 If `ctx=None`, then the global context is used.
4131 >>> x = BitVec('x', 16)
4138 >>> word = BitVecSort(16)
4139 >>> x2 = BitVec('x', word)
4143 if isinstance(bv, BitVecSortRef):
4152 """Return a tuple of bit-vector constants of size bv.
4154 >>> x, y, z = BitVecs('x y z', 16)
4161 >>> Product(x, y, z)
4163 >>> simplify(Product(x, y, z))
4167 if isinstance(names, str):
4168 names = names.split(
" ")
4169 return [
BitVec(name, bv, ctx)
for name
in names]
4173 """Create a Z3 bit-vector concatenation expression.
4175 >>> v = BitVecVal(1, 4)
4176 >>> Concat(v, v+1, v)
4177 Concat(Concat(1, 1 + 1), 1)
4178 >>> simplify(Concat(v, v+1, v))
4180 >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
4186 _z3_assert(sz >= 2,
"At least two arguments expected.")
4193 if is_seq(args[0])
or isinstance(args[0], str):
4196 _z3_assert(all([
is_seq(a)
for a
in args]),
"All arguments must be sequence expressions.")
4199 v[i] = args[i].as_ast()
4204 _z3_assert(all([
is_re(a)
for a
in args]),
"All arguments must be regular expressions.")
4207 v[i] = args[i].as_ast()
4211 _z3_assert(all([
is_bv(a)
for a
in args]),
"All arguments must be Z3 bit-vector expressions.")
4213 for i
in range(sz - 1):
4219 """Create a Z3 bit-vector extraction expression.
4220 Extract is overloaded to also work on sequence extraction.
4221 The functions SubString and SubSeq are redirected to Extract.
4222 For this case, the arguments are reinterpreted as:
4223 high - is a sequence (string)
4225 a - is the length to be extracted
4227 >>> x = BitVec('x', 8)
4228 >>> Extract(6, 2, x)
4230 >>> Extract(6, 2, x).sort()
4232 >>> simplify(Extract(StringVal("abcd"),2,1))
4235 if isinstance(high, str):
4242 _z3_assert(low <= high,
"First argument must be greater than or equal to second argument")
4244 "First and second arguments must be non negative integers")
4245 _z3_assert(
is_bv(a),
"Third argument must be a Z3 bit-vector expression")
4251 _z3_assert(
is_bv(a)
or is_bv(b),
"First or second argument must be a Z3 bit-vector expression")
4255 """Create the Z3 expression (unsigned) `other <= self`.
4257 Use the operator <= for signed less than or equal to.
4259 >>> x, y = BitVecs('x y', 32)
4262 >>> (x <= y).sexpr()
4264 >>> ULE(x, y).sexpr()
4273 """Create the Z3 expression (unsigned) `other < self`.
4275 Use the operator < for signed less than.
4277 >>> x, y = BitVecs('x y', 32)
4282 >>> ULT(x, y).sexpr()
4291 """Create the Z3 expression (unsigned) `other >= self`.
4293 Use the operator >= for signed greater than or equal to.
4295 >>> x, y = BitVecs('x y', 32)
4298 >>> (x >= y).sexpr()
4300 >>> UGE(x, y).sexpr()
4309 """Create the Z3 expression (unsigned) `other > self`.
4311 Use the operator > for signed greater than.
4313 >>> x, y = BitVecs('x y', 32)
4318 >>> UGT(x, y).sexpr()
4327 """Create the Z3 expression (unsigned) division `self / other`.
4329 Use the operator / for signed division.
4331 >>> x = BitVec('x', 32)
4332 >>> y = BitVec('y', 32)
4335 >>> UDiv(x, y).sort()
4339 >>> UDiv(x, y).sexpr()
4348 """Create the Z3 expression (unsigned) remainder `self % other`.
4350 Use the operator % for signed modulus, and SRem() for signed remainder.
4352 >>> x = BitVec('x', 32)
4353 >>> y = BitVec('y', 32)
4356 >>> URem(x, y).sort()
4360 >>> URem(x, y).sexpr()
4369 """Create the Z3 expression signed remainder.
4371 Use the operator % for signed modulus, and URem() for unsigned remainder.
4373 >>> x = BitVec('x', 32)
4374 >>> y = BitVec('y', 32)
4377 >>> SRem(x, y).sort()
4381 >>> SRem(x, y).sexpr()
4390 """Create the Z3 expression logical right shift.
4392 Use the operator >> for the arithmetical right shift.
4394 >>> x, y = BitVecs('x y', 32)
4397 >>> (x >> y).sexpr()
4399 >>> LShR(x, y).sexpr()
4403 >>> BitVecVal(4, 3).as_signed_long()
4405 >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
4407 >>> simplify(BitVecVal(4, 3) >> 1)
4409 >>> simplify(LShR(BitVecVal(4, 3), 1))
4411 >>> simplify(BitVecVal(2, 3) >> 1)
4413 >>> simplify(LShR(BitVecVal(2, 3), 1))
4422 """Return an expression representing `a` rotated to the left `b` times.
4424 >>> a, b = BitVecs('a b', 16)
4425 >>> RotateLeft(a, b)
4427 >>> simplify(RotateLeft(a, 0))
4429 >>> simplify(RotateLeft(a, 16))
4438 """Return an expression representing `a` rotated to the right `b` times.
4440 >>> a, b = BitVecs('a b', 16)
4441 >>> RotateRight(a, b)
4443 >>> simplify(RotateRight(a, 0))
4445 >>> simplify(RotateRight(a, 16))
4454 """Return a bit-vector expression with `n` extra sign-bits.
4456 >>> x = BitVec('x', 16)
4457 >>> n = SignExt(8, x)
4464 >>> v0 = BitVecVal(2, 2)
4469 >>> v = simplify(SignExt(6, v0))
4474 >>> print("%.x" % v.as_long())
4479 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4484 """Return a bit-vector expression with `n` extra zero-bits.
4486 >>> x = BitVec('x', 16)
4487 >>> n = ZeroExt(8, x)
4494 >>> v0 = BitVecVal(2, 2)
4499 >>> v = simplify(ZeroExt(6, v0))
4507 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4512 """Return an expression representing `n` copies of `a`.
4514 >>> x = BitVec('x', 8)
4515 >>> n = RepeatBitVec(4, x)
4520 >>> v0 = BitVecVal(10, 4)
4521 >>> print("%.x" % v0.as_long())
4523 >>> v = simplify(RepeatBitVec(4, v0))
4526 >>> print("%.x" % v.as_long())
4531 _z3_assert(
is_bv(a),
"Second argument must be a Z3 bit-vector expression")
4536 """Return the reduction-and expression of `a`."""
4538 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4543 """Return the reduction-or expression of `a`."""
4545 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4550 """A predicate the determines that bit-vector addition does not overflow"""
4557 """A predicate the determines that signed bit-vector addition does not underflow"""
4564 """A predicate the determines that bit-vector subtraction does not overflow"""
4571 """A predicate the determines that bit-vector subtraction does not underflow"""
4578 """A predicate the determines that bit-vector signed division does not overflow"""
4585 """A predicate the determines that bit-vector unary negation does not overflow"""
4587 _z3_assert(
is_bv(a),
"First argument must be a Z3 bit-vector expression")
4592 """A predicate the determines that bit-vector multiplication does not overflow"""
4599 """A predicate the determines that bit-vector signed multiplication does not underflow"""
4615 """Return the domain of the array sort `self`.
4617 >>> A = ArraySort(IntSort(), BoolSort())
4624 """Return the domain of the array sort `self`.
4629 """Return the range of the array sort `self`.
4631 >>> A = ArraySort(IntSort(), BoolSort())
4639 """Array expressions. """
4642 """Return the array sort of the array expression `self`.
4644 >>> a = Array('a', IntSort(), BoolSort())
4651 """Shorthand for `self.sort().domain()`.
4653 >>> a = Array('a', IntSort(), BoolSort())
4660 """Shorthand for self.sort().domain_n(i)`."""
4664 """Shorthand for `self.sort().range()`.
4666 >>> a = Array('a', IntSort(), BoolSort())
4673 """Return the Z3 expression `self[arg]`.
4675 >>> a = Array('a', IntSort(), BoolSort())
4689 if isinstance(arg, tuple):
4690 args = [ar.sort().domain_n(i).cast(arg[i])
for i
in range(len(arg))]
4693 arg = ar.sort().domain().cast(arg)
4702 """Return `True` if `a` is a Z3 array expression.
4704 >>> a = Array('a', IntSort(), IntSort())
4707 >>> is_array(Store(a, 0, 1))
4712 return isinstance(a, ArrayRef)
4716 """Return `True` if `a` is a Z3 constant array.
4718 >>> a = K(IntSort(), 10)
4719 >>> is_const_array(a)
4721 >>> a = Array('a', IntSort(), IntSort())
4722 >>> is_const_array(a)
4729 """Return `True` if `a` is a Z3 constant array.
4731 >>> a = K(IntSort(), 10)
4734 >>> a = Array('a', IntSort(), IntSort())
4742 """Return `True` if `a` is a Z3 map array expression.
4744 >>> f = Function('f', IntSort(), IntSort())
4745 >>> b = Array('b', IntSort(), IntSort())
4758 """Return `True` if `a` is a Z3 default array expression.
4759 >>> d = Default(K(IntSort(), 10))
4763 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4767 """Return the function declaration associated with a Z3 map array expression.
4769 >>> f = Function('f', IntSort(), IntSort())
4770 >>> b = Array('b', IntSort(), IntSort())
4772 >>> eq(f, get_map_func(a))
4776 >>> get_map_func(a)(0)
4791 """Return the Z3 array sort with the given domain and range sorts.
4793 >>> A = ArraySort(IntSort(), BoolSort())
4800 >>> AA = ArraySort(IntSort(), A)
4802 Array(Int, Array(Int, Bool))
4806 _z3_assert(len(sig) > 1,
"At least two arguments expected")
4807 arity = len(sig) - 1
4813 _z3_assert(s.ctx == r.ctx,
"Context mismatch")
4817 dom = (Sort * arity)()
4818 for i
in range(arity):
4824 """Return an array constant named `name` with the given domain and range sorts.
4826 >>> a = Array('a', IntSort(), IntSort())
4838 """Return a Z3 store array expression.
4840 >>> a = Array('a', IntSort(), IntSort())
4841 >>> i, v = Ints('i v')
4842 >>> s = Update(a, i, v)
4845 >>> prove(s[i] == v)
4848 >>> prove(Implies(i != j, s[j] == a[j]))
4856 raise Z3Exception(
"array update requires index and value arguments")
4860 i = a.sort().domain().cast(i)
4861 v = a.sort().range().cast(v)
4863 v = a.sort().range().cast(args[-1])
4864 idxs = [a.sort().domain_n(i).cast(args[i])
for i
in range(len(args)-1)]
4870 """ Return a default value for array expression.
4871 >>> b = K(IntSort(), 1)
4872 >>> prove(Default(b) == 1)
4881 """Return a Z3 store array expression.
4883 >>> a = Array('a', IntSort(), IntSort())
4884 >>> i, v = Ints('i v')
4885 >>> s = Store(a, i, v)
4888 >>> prove(s[i] == v)
4891 >>> prove(Implies(i != j, s[j] == a[j]))
4898 """Return a Z3 select array expression.
4900 >>> a = Array('a', IntSort(), IntSort())
4904 >>> eq(Select(a, i), a[i])
4914 """Return a Z3 map array expression.
4916 >>> f = Function('f', IntSort(), IntSort(), IntSort())
4917 >>> a1 = Array('a1', IntSort(), IntSort())
4918 >>> a2 = Array('a2', IntSort(), IntSort())
4919 >>> b = Map(f, a1, a2)
4922 >>> prove(b[0] == f(a1[0], a2[0]))
4927 _z3_assert(len(args) > 0,
"At least one Z3 array expression expected")
4930 _z3_assert(len(args) == f.arity(),
"Number of arguments mismatch")
4937 """Return a Z3 constant array expression.
4939 >>> a = K(IntSort(), 10)
4959 """Return extensionality index for one-dimensional arrays.
4960 >> a, b = Consts('a b', SetSort(IntSort()))
4977 """Return `True` if `a` is a Z3 array select application.
4979 >>> a = Array('a', IntSort(), IntSort())
4990 """Return `True` if `a` is a Z3 array store application.
4992 >>> a = Array('a', IntSort(), IntSort())
4995 >>> is_store(Store(a, 0, 1))
5008 """ Create a set sort over element sort s"""
5013 """Create the empty set
5014 >>> EmptySet(IntSort())
5022 """Create the full set
5023 >>> FullSet(IntSort())
5031 """ Take the union of sets
5032 >>> a = Const('a', SetSort(IntSort()))
5033 >>> b = Const('b', SetSort(IntSort()))
5044 """ Take the union of sets
5045 >>> a = Const('a', SetSort(IntSort()))
5046 >>> b = Const('b', SetSort(IntSort()))
5047 >>> SetIntersect(a, b)
5057 """ Add element e to set s
5058 >>> a = Const('a', SetSort(IntSort()))
5068 """ Remove element e to set s
5069 >>> a = Const('a', SetSort(IntSort()))
5079 """ The complement of set s
5080 >>> a = Const('a', SetSort(IntSort()))
5081 >>> SetComplement(a)
5089 """ The set difference of a and b
5090 >>> a = Const('a', SetSort(IntSort()))
5091 >>> b = Const('b', SetSort(IntSort()))
5092 >>> SetDifference(a, b)
5100 """ Check if e is a member of set s
5101 >>> a = Const('a', SetSort(IntSort()))
5111 """ Check if a is a subset of b
5112 >>> a = Const('a', SetSort(IntSort()))
5113 >>> b = Const('b', SetSort(IntSort()))
5128 """Return `True` if acc is pair of the form (String, Datatype or Sort). """
5129 if not isinstance(acc, tuple):
5133 return isinstance(acc[0], str)
and (isinstance(acc[1], Datatype)
or is_sort(acc[1]))
5137 """Helper class for declaring Z3 datatypes.
5139 >>> List = Datatype('List')
5140 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5141 >>> List.declare('nil')
5142 >>> List = List.create()
5143 >>> # List is now a Z3 declaration
5146 >>> List.cons(10, List.nil)
5148 >>> List.cons(10, List.nil).sort()
5150 >>> cons = List.cons
5154 >>> n = cons(1, cons(0, nil))
5156 cons(1, cons(0, nil))
5157 >>> simplify(cdr(n))
5159 >>> simplify(car(n))
5175 _z3_assert(isinstance(name, str),
"String expected")
5176 _z3_assert(isinstance(rec_name, str),
"String expected")
5179 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5184 """Declare constructor named `name` with the given accessors `args`.
5185 Each accessor is a pair `(name, sort)`, where `name` is a string and `sort` a Z3 sort
5186 or a reference to the datatypes being declared.
5188 In the following example `List.declare('cons', ('car', IntSort()), ('cdr', List))`
5189 declares the constructor named `cons` that builds a new List using an integer and a List.
5190 It also declares the accessors `car` and `cdr`. The accessor `car` extracts the integer
5191 of a `cons` cell, and `cdr` the list of a `cons` cell. After all constructors were declared,
5192 we use the method create() to create the actual datatype in Z3.
5194 >>> List = Datatype('List')
5195 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5196 >>> List.declare('nil')
5197 >>> List = List.create()
5200 _z3_assert(isinstance(name, str),
"String expected")
5201 _z3_assert(name !=
"",
"Constructor name cannot be empty")
5208 """Create a Z3 datatype based on the constructors declared using the method `declare()`.
5210 The function `CreateDatatypes()` must be used to define mutually recursive datatypes.
5212 >>> List = Datatype('List')
5213 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5214 >>> List.declare('nil')
5215 >>> List = List.create()
5218 >>> List.cons(10, List.nil)
5225 """Auxiliary object used to create Z3 datatypes."""
5232 if self.
ctx.ref()
is not None and Z3_del_constructor
is not None:
5237 """Auxiliary object used to create Z3 datatypes."""
5244 if self.
ctx.ref()
is not None and Z3_del_constructor_list
is not None:
5249 """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
5251 In the following example we define a Tree-List using two mutually recursive datatypes.
5253 >>> TreeList = Datatype('TreeList')
5254 >>> Tree = Datatype('Tree')
5255 >>> # Tree has two constructors: leaf and node
5256 >>> Tree.declare('leaf', ('val', IntSort()))
5257 >>> # a node contains a list of trees
5258 >>> Tree.declare('node', ('children', TreeList))
5259 >>> TreeList.declare('nil')
5260 >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
5261 >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
5262 >>> Tree.val(Tree.leaf(10))
5264 >>> simplify(Tree.val(Tree.leaf(10)))
5266 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5268 node(cons(leaf(10), cons(leaf(20), nil)))
5269 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5270 >>> simplify(n2 == n1)
5272 >>> simplify(TreeList.car(Tree.children(n2)) == n1)
5277 _z3_assert(len(ds) > 0,
"At least one Datatype must be specified")
5278 _z3_assert(all([isinstance(d, Datatype)
for d
in ds]),
"Arguments must be Datatypes")
5279 _z3_assert(all([d.ctx == ds[0].ctx
for d
in ds]),
"Context mismatch")
5280 _z3_assert(all([d.constructors != []
for d
in ds]),
"Non-empty Datatypes expected")
5283 names = (Symbol * num)()
5284 out = (Sort * num)()
5285 clists = (ConstructorList * num)()
5287 for i
in range(num):
5290 num_cs = len(d.constructors)
5291 cs = (Constructor * num_cs)()
5292 for j
in range(num_cs):
5293 c = d.constructors[j]
5298 fnames = (Symbol * num_fs)()
5299 sorts = (Sort * num_fs)()
5300 refs = (ctypes.c_uint * num_fs)()
5301 for k
in range(num_fs):
5305 if isinstance(ftype, Datatype):
5308 ds.count(ftype) == 1,
5309 "One and only one occurrence of each datatype is expected",
5312 refs[k] = ds.index(ftype)
5316 sorts[k] = ftype.ast
5325 for i
in range(num):
5327 num_cs = dref.num_constructors()
5328 for j
in range(num_cs):
5329 cref = dref.constructor(j)
5330 cref_name = cref.name()
5331 cref_arity = cref.arity()
5332 if cref.arity() == 0:
5334 setattr(dref, cref_name, cref)
5335 rref = dref.recognizer(j)
5336 setattr(dref,
"is_" + cref_name, rref)
5337 for k
in range(cref_arity):
5338 aref = dref.accessor(j, k)
5339 setattr(dref, aref.name(), aref)
5341 return tuple(result)
5345 """Datatype sorts."""
5348 """Return the number of constructors in the given Z3 datatype.
5350 >>> List = Datatype('List')
5351 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5352 >>> List.declare('nil')
5353 >>> List = List.create()
5354 >>> # List is now a Z3 declaration
5355 >>> List.num_constructors()
5361 """Return a constructor of the datatype `self`.
5363 >>> List = Datatype('List')
5364 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5365 >>> List.declare('nil')
5366 >>> List = List.create()
5367 >>> # List is now a Z3 declaration
5368 >>> List.num_constructors()
5370 >>> List.constructor(0)
5372 >>> List.constructor(1)
5380 """In Z3, each constructor has an associated recognizer predicate.
5382 If the constructor is named `name`, then the recognizer `is_name`.
5384 >>> List = Datatype('List')
5385 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5386 >>> List.declare('nil')
5387 >>> List = List.create()
5388 >>> # List is now a Z3 declaration
5389 >>> List.num_constructors()
5391 >>> List.recognizer(0)
5393 >>> List.recognizer(1)
5395 >>> simplify(List.is_nil(List.cons(10, List.nil)))
5397 >>> simplify(List.is_cons(List.cons(10, List.nil)))
5399 >>> l = Const('l', List)
5400 >>> simplify(List.is_cons(l))
5408 """In Z3, each constructor has 0 or more accessor.
5409 The number of accessors is equal to the arity of the constructor.
5411 >>> List = Datatype('List')
5412 >>> List.declare('cons', ('car', IntSort()), ('cdr', List))
5413 >>> List.declare('nil')
5414 >>> List = List.create()
5415 >>> List.num_constructors()
5417 >>> List.constructor(0)
5419 >>> num_accs = List.constructor(0).arity()
5422 >>> List.accessor(0, 0)
5424 >>> List.accessor(0, 1)
5426 >>> List.constructor(1)
5428 >>> num_accs = List.constructor(1).arity()
5442 """Datatype expressions."""
5445 """Return the datatype sort of the datatype expression `self`."""
5449 """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
5454 """Create a named tuple sort base on a set of underlying sorts
5456 >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
5459 projects = [(
"project%d" % i, sorts[i])
for i
in range(len(sorts))]
5460 tuple.declare(name, *projects)
5461 tuple = tuple.create()
5462 return tuple, tuple.constructor(0), [tuple.accessor(0, i)
for i
in range(len(sorts))]
5466 """Create a named tagged union sort base on a set of underlying sorts
5468 >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
5471 for i
in range(len(sorts)):
5472 sum.declare(
"inject%d" % i, (
"project%d" % i, sorts[i]))
5474 return sum, [(sum.constructor(i), sum.accessor(i, 0))
for i
in range(len(sorts))]
5478 """Return a new enumeration sort named `name` containing the given values.
5480 The result is a pair (sort, list of constants).
5482 >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
5485 _z3_assert(isinstance(name, str),
"Name must be a string")
5486 _z3_assert(all([isinstance(v, str)
for v
in values]),
"Enumeration sort values must be strings")
5487 _z3_assert(len(values) > 0,
"At least one value expected")
5490 _val_names = (Symbol * num)()
5491 for i
in range(num):
5492 _val_names[i] =
to_symbol(values[i], ctx)
5493 _values = (FuncDecl * num)()
5494 _testers = (FuncDecl * num)()
5498 for i
in range(num):
5500 V = [a()
for a
in V]
5511 """Set of parameters used to configure Solvers, Tactics and Simplifiers in Z3.
5513 Consider using the function `args2params` to create instances of this object.
5528 if self.
ctx.ref()
is not None and Z3_params_dec_ref
is not None:
5532 """Set parameter name with value val."""
5534 _z3_assert(isinstance(name, str),
"parameter name must be a string")
5536 if isinstance(val, bool):
5540 elif isinstance(val, float):
5542 elif isinstance(val, str):
5552 _z3_assert(isinstance(ds, ParamDescrsRef),
"parameter description set expected")
5557 """Convert python arguments into a Z3_params object.
5558 A ':' is added to the keywords, and '_' is replaced with '-'
5560 >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
5561 (params model true relevancy 2 elim_and true)
5564 _z3_assert(len(arguments) % 2 == 0,
"Argument list must have an even number of elements.")
5580 """Set of parameter descriptions for Solvers, Tactics and Simplifiers in Z3.
5584 _z3_assert(isinstance(descr, ParamDescrs),
"parameter description object expected")
5590 return ParamsDescrsRef(self.
descr, self.
ctx)
5593 if self.
ctx.ref()
is not None and Z3_param_descrs_dec_ref
is not None:
5597 """Return the size of in the parameter description `self`.
5602 """Return the size of in the parameter description `self`.
5607 """Return the i-th parameter name in the parameter description `self`.
5612 """Return the kind of the parameter named `n`.
5617 """Return the documentation string of the parameter named `n`.
5638 """Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).
5640 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5641 A goal has a solution if one of its subgoals has a solution.
5642 A goal is unsatisfiable if all subgoals are unsatisfiable.
5645 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5648 "If goal is different from None, then ctx must be also different from None")
5651 if self.
goal is None:
5656 if self.
goal is not None and self.
ctx.ref()
is not None and Z3_goal_dec_ref
is not None:
5660 """Return the depth of the goal `self`.
5661 The depth corresponds to the number of tactics applied to `self`.
5663 >>> x, y = Ints('x y')
5665 >>> g.add(x == 0, y >= x + 1)
5668 >>> r = Then('simplify', 'solve-eqs')(g)
5669 >>> # r has 1 subgoal
5678 """Return `True` if `self` contains the `False` constraints.
5680 >>> x, y = Ints('x y')
5682 >>> g.inconsistent()
5684 >>> g.add(x == 0, x == 1)
5687 >>> g.inconsistent()
5689 >>> g2 = Tactic('propagate-values')(g)[0]
5690 >>> g2.inconsistent()
5696 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5699 >>> g.prec() == Z3_GOAL_PRECISE
5701 >>> x, y = Ints('x y')
5702 >>> g.add(x == y + 1)
5703 >>> g.prec() == Z3_GOAL_PRECISE
5705 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5708 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5709 >>> g2.prec() == Z3_GOAL_PRECISE
5711 >>> g2.prec() == Z3_GOAL_UNDER
5717 """Alias for `prec()`.
5720 >>> g.precision() == Z3_GOAL_PRECISE
5726 """Return the number of constraints in the goal `self`.
5731 >>> x, y = Ints('x y')
5732 >>> g.add(x == 0, y > x)
5739 """Return the number of constraints in the goal `self`.
5744 >>> x, y = Ints('x y')
5745 >>> g.add(x == 0, y > x)
5752 """Return a constraint in the goal `self`.
5755 >>> x, y = Ints('x y')
5756 >>> g.add(x == 0, y > x)
5765 """Return a constraint in the goal `self`.
5768 >>> x, y = Ints('x y')
5769 >>> g.add(x == 0, y > x)
5775 if arg >= len(self):
5777 return self.
get(arg)
5780 """Assert constraints into the goal.
5784 >>> g.assert_exprs(x > 0, x < 2)
5799 >>> g.append(x > 0, x < 2)
5810 >>> g.insert(x > 0, x < 2)
5821 >>> g.add(x > 0, x < 2)
5828 """Retrieve model from a satisfiable goal
5829 >>> a, b = Ints('a b')
5831 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5832 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5835 [Or(b == 0, b == 1), Not(0 <= b)]
5837 [Or(b == 0, b == 1), Not(1 <= b)]
5838 >>> # Remark: the subgoal r[0] is unsatisfiable
5839 >>> # Creating a solver for solving the second subgoal
5846 >>> # Model s.model() does not assign a value to `a`
5847 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5848 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5849 >>> r[1].convert_model(s.model())
5853 _z3_assert(isinstance(model, ModelRef),
"Z3 Model expected")
5857 return obj_to_string(self)
5860 """Return a textual representation of the s-expression representing the goal."""
5864 """Return a textual representation of the goal in DIMACS format."""
5868 """Copy goal `self` to context `target`.
5876 >>> g2 = g.translate(c2)
5879 >>> g.ctx == main_ctx()
5883 >>> g2.ctx == main_ctx()
5887 _z3_assert(isinstance(target, Context),
"target must be a context")
5897 """Return a new simplified goal.
5899 This method is essentially invoking the simplify tactic.
5903 >>> g.add(x + 1 >= 2)
5906 >>> g2 = g.simplify()
5909 >>> # g was not modified
5914 return t.apply(self, *arguments, **keywords)[0]
5917 """Return goal `self` as a single Z3 expression.
5936 return And([self.
get(i)
for i
in range(len(self))], self.
ctx)
5946 """A collection (vector) of ASTs."""
5955 assert ctx
is not None
5960 if self.
vector is not None and self.
ctx.ref()
is not None and Z3_ast_vector_dec_ref
is not None:
5964 """Return the size of the vector `self`.
5969 >>> A.push(Int('x'))
5970 >>> A.push(Int('x'))
5977 """Return the AST at position `i`.
5980 >>> A.push(Int('x') + 1)
5981 >>> A.push(Int('y'))
5988 if isinstance(i, int):
5996 elif isinstance(i, slice):
5998 for ii
in range(*i.indices(self.
__len__())):
6006 """Update AST at position `i`.
6009 >>> A.push(Int('x') + 1)
6010 >>> A.push(Int('y'))
6022 """Add `v` in the end of the vector.
6027 >>> A.push(Int('x'))
6034 """Resize the vector to `sz` elements.
6040 >>> for i in range(10): A[i] = Int('x')
6047 """Return `True` if the vector contains `item`.
6070 """Copy vector `self` to context `other_ctx`.
6076 >>> B = A.translate(c2)
6092 return obj_to_string(self)
6095 """Return a textual representation of the s-expression representing the vector."""
6106 """A mapping from ASTs to ASTs."""
6115 assert ctx
is not None
6123 if self.
map is not None and self.
ctx.ref()
is not None and Z3_ast_map_dec_ref
is not None:
6127 """Return the size of the map.
6133 >>> M[x] = IntVal(1)
6140 """Return `True` if the map contains key `key`.
6153 """Retrieve the value associated with key `key`.
6164 """Add/Update key `k` with value `v`.
6173 >>> M[x] = IntVal(1)
6183 """Remove the entry associated with key `k`.
6197 """Remove all entries from the map.
6202 >>> M[x+x] = IntVal(1)
6212 """Return an AstVector containing all keys in the map.
6217 >>> M[x+x] = IntVal(1)
6231 """Store the value of the interpretation of a function in a particular point."""
6242 if self.
ctx.ref()
is not None and Z3_func_entry_dec_ref
is not None:
6246 """Return the number of arguments in the given entry.
6248 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6250 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6255 >>> f_i.num_entries()
6257 >>> e = f_i.entry(0)
6264 """Return the value of argument `idx`.
6266 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6268 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6273 >>> f_i.num_entries()
6275 >>> e = f_i.entry(0)
6286 ... except IndexError:
6287 ... print("index error")
6295 """Return the value of the function at point `self`.
6297 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6299 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6304 >>> f_i.num_entries()
6306 >>> e = f_i.entry(0)
6317 """Return entry `self` as a Python list.
6318 >>> f = Function('f', IntSort(), IntSort(), IntSort())
6320 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6325 >>> f_i.num_entries()
6327 >>> e = f_i.entry(0)
6332 args.append(self.
value())
6340 """Stores the interpretation of a function in a Z3 model."""
6345 if self.
f is not None:
6349 if self.
f is not None and self.
ctx.ref()
is not None and Z3_func_interp_dec_ref
is not None:
6354 Return the `else` value for a function interpretation.
6355 Return None if Z3 did not specify the `else` value for
6358 >>> f = Function('f', IntSort(), IntSort())
6360 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6366 >>> m[f].else_value()
6376 """Return the number of entries/points in the function interpretation `self`.
6378 >>> f = Function('f', IntSort(), IntSort())
6380 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6386 >>> m[f].num_entries()
6392 """Return the number of arguments for each entry in the function interpretation `self`.
6394 >>> f = Function('f', IntSort(), IntSort())
6396 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6406 """Return an entry at position `idx < self.num_entries()` in the function interpretation `self`.
6408 >>> f = Function('f', IntSort(), IntSort())
6410 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6416 >>> m[f].num_entries()
6426 """Copy model 'self' to context 'other_ctx'.
6437 """Return the function interpretation as a Python list.
6438 >>> f = Function('f', IntSort(), IntSort())
6440 >>> s.add(f(0) == 1, f(1) == 1, f(2) == 0)
6454 return obj_to_string(self)
6458 """Model/Solution of a satisfiability problem (aka system of constraints)."""
6461 assert ctx
is not None
6467 if self.
ctx.ref()
is not None and Z3_model_dec_ref
is not None:
6471 return obj_to_string(self)
6474 """Return a textual representation of the s-expression representing the model."""
6477 def eval(self, t, model_completion=False):
6478 """Evaluate the expression `t` in the model `self`.
6479 If `model_completion` is enabled, then a default interpretation is automatically added
6480 for symbols that do not have an interpretation in the model `self`.
6484 >>> s.add(x > 0, x < 2)
6497 >>> m.eval(y, model_completion=True)
6499 >>> # Now, m contains an interpretation for y
6506 raise Z3Exception(
"failed to evaluate expression in the model")
6509 """Alias for `eval`.
6513 >>> s.add(x > 0, x < 2)
6517 >>> m.evaluate(x + 1)
6519 >>> m.evaluate(x == 1)
6522 >>> m.evaluate(y + x)
6526 >>> m.evaluate(y, model_completion=True)
6528 >>> # Now, m contains an interpretation for y
6529 >>> m.evaluate(y + x)
6532 return self.
eval(t, model_completion)
6535 """Return the number of constant and function declarations in the model `self`.
6537 >>> f = Function('f', IntSort(), IntSort())
6540 >>> s.add(x > 0, f(x) != x)
6549 return num_consts + num_funcs
6552 """Return the interpretation for a given declaration or constant.
6554 >>> f = Function('f', IntSort(), IntSort())
6557 >>> s.add(x > 0, x < 2, f(x) == 0)
6567 _z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6571 if decl.arity() == 0:
6573 if _r.value
is None:
6589 sz = fi.num_entries()
6593 e =
Store(e, fe.arg_value(0), fe.value())
6604 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6606 >>> A = DeclareSort('A')
6607 >>> a, b = Consts('a b', A)
6619 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6621 >>> A = DeclareSort('A')
6622 >>> B = DeclareSort('B')
6623 >>> a1, a2 = Consts('a1 a2', A)
6624 >>> b1, b2 = Consts('b1 b2', B)
6626 >>> s.add(a1 != a2, b1 != b2)
6642 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6644 >>> A = DeclareSort('A')
6645 >>> B = DeclareSort('B')
6646 >>> a1, a2 = Consts('a1 a2', A)
6647 >>> b1, b2 = Consts('b1 b2', B)
6649 >>> s.add(a1 != a2, b1 != b2)
6659 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6661 >>> A = DeclareSort('A')
6662 >>> a, b = Consts('a b', A)
6668 >>> m.get_universe(A)
6672 _z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
6679 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6680 If `idx` is a declaration, then the actual interpretation is returned.
6682 The elements can be retrieved using position or the actual declaration.
6684 >>> f = Function('f', IntSort(), IntSort())
6687 >>> s.add(x > 0, x < 2, f(x) == 0)
6701 >>> for d in m: print("%s -> %s" % (d, m[d]))
6706 if idx >= len(self):
6709 if (idx < num_consts):
6713 if isinstance(idx, FuncDeclRef):
6717 if isinstance(idx, SortRef):
6720 _z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
6724 """Return a list with all symbols that have an interpretation in the model `self`.
6725 >>> f = Function('f', IntSort(), IntSort())
6728 >>> s.add(x > 0, x < 2, f(x) == 0)
6743 """Update the interpretation of a constant"""
6746 if is_func_decl(x)
and x.arity() != 0
and isinstance(value, FuncInterp):
6750 for i
in range(value.num_entries()):
6755 v.push(e.arg_value(j))
6760 raise Z3Exception(
"Expecting 0-ary function or constant expression")
6765 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6768 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6773 """Perform model-based projection on fml with respect to vars.
6774 Assume that the model satisfies fml. Then compute a projection fml_p, such
6775 that vars do not occur free in fml_p, fml_p is true in the model and
6776 fml_p => exists vars . fml
6778 ctx = self.
ctx.ref()
6779 _vars = (Ast * len(vars))()
6780 for i
in range(len(vars)):
6781 _vars[i] = vars[i].as_ast()
6785 """Perform model-based projection, but also include realizer terms for the projected variables"""
6786 ctx = self.
ctx.ref()
6787 _vars = (Ast * len(vars))()
6788 for i
in range(len(vars)):
6789 _vars[i] = vars[i].as_ast()
6791 result = Z3_qe_model_project_with_witness(ctx, self.
model, len(vars), _vars, fml.ast, defs.map)
6806 for k, v
in eval.items():
6807 mdl.update_value(k, v)
6812 """Return true if n is a Z3 expression of the form (_ as-array f)."""
6813 return isinstance(n, ExprRef)
and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6817 """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
6830 """Statistics for `Solver.check()`."""
6841 if self.
ctx.ref()
is not None and Z3_stats_dec_ref
is not None:
6848 out.write(u(
'<table border="1" cellpadding="2" cellspacing="0">'))
6851 out.write(u(
'<tr style="background-color:#CFCFCF">'))
6854 out.write(u(
"<tr>"))
6856 out.write(u(
"<td>%s</td><td>%s</td></tr>" % (k, v)))
6857 out.write(u(
"</table>"))
6858 return out.getvalue()
6863 """Return the number of statistical counters.
6866 >>> s = Then('simplify', 'nlsat').solver()
6870 >>> st = s.statistics()
6877 """Return the value of statistical counter at position `idx`. The result is a pair (key, value).
6880 >>> s = Then('simplify', 'nlsat').solver()
6884 >>> st = s.statistics()
6888 ('nlsat propagations', 2)
6890 ('nlsat restarts', 1)
6892 if idx >= len(self):
6901 """Return the list of statistical counters.
6904 >>> s = Then('simplify', 'nlsat').solver()
6908 >>> st = s.statistics()
6913 """Return the value of a particular statistical counter.
6916 >>> s = Then('simplify', 'nlsat').solver()
6920 >>> st = s.statistics()
6921 >>> st.get_key_value('nlsat propagations')
6924 for idx
in range(len(self)):
6930 raise Z3Exception(
"unknown key")
6933 """Access the value of statistical using attributes.
6935 Remark: to access a counter containing blank spaces (e.g., 'nlsat propagations'),
6936 we should use '_' (e.g., 'nlsat_propagations').
6939 >>> s = Then('simplify', 'nlsat').solver()
6943 >>> st = s.statistics()
6944 >>> st.nlsat_propagations
6949 key = name.replace(
"_",
" ")
6953 raise AttributeError
6963 """Represents the result of a satisfiability check: sat, unsat, unknown.
6969 >>> isinstance(r, CheckSatResult)
6980 return isinstance(other, CheckSatResult)
and self.
r == other.r
6983 return not self.
__eq__(other)
6987 if self.
r == Z3_L_TRUE:
6989 elif self.
r == Z3_L_FALSE:
6990 return "<b>unsat</b>"
6992 return "<b>unknown</b>"
6994 if self.
r == Z3_L_TRUE:
6996 elif self.
r == Z3_L_FALSE:
7002 in_html = in_html_mode()
7005 set_html_mode(in_html)
7016 Solver API provides methods for implementing the main SMT 2.0 commands:
7017 push, pop, check, get-model, etc.
7020 def __init__(self, solver=None, ctx=None, logFile=None):
7021 assert solver
is None or ctx
is not None
7030 if logFile
is not None:
7031 self.
set(
"smtlib2_log", logFile)
7034 if self.
solver is not None and self.
ctx.ref()
is not None and Z3_solver_dec_ref
is not None:
7045 """Set a configuration option.
7046 The method `help()` return a string containing all available options.
7049 >>> # The option MBQI can be set using three different approaches.
7050 >>> s.set(mbqi=True)
7051 >>> s.set('MBQI', True)
7052 >>> s.set(':mbqi', True)
7058 """Create a backtracking point.
7080 """Backtrack \\c num backtracking points.
7102 """Return the current number of backtracking points.
7120 """Remove all asserted constraints and backtracking points created using `push()`.
7134 """Assert constraints into the solver.
7138 >>> s.assert_exprs(x > 0, x < 2)
7145 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7153 """Assert constraints into the solver.
7157 >>> s.add(x > 0, x < 2)
7168 """Assert constraints into the solver.
7172 >>> s.append(x > 0, x < 2)
7179 """Assert constraints into the solver.
7183 >>> s.insert(x > 0, x < 2)
7190 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7192 If `p` is a string, it will be automatically converted into a Boolean constant.
7197 >>> s.set(unsat_core=True)
7198 >>> s.assert_and_track(x > 0, 'p1')
7199 >>> s.assert_and_track(x != 1, 'p2')
7200 >>> s.assert_and_track(x < 0, p3)
7201 >>> print(s.check())
7203 >>> c = s.unsat_core()
7213 if isinstance(p, str):
7215 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7220 """Check whether the assertions in the given solver plus the optional assumptions are consistent or not.
7226 >>> s.add(x > 0, x < 2)
7229 >>> s.model().eval(x)
7235 >>> s.add(2**x == 4)
7241 num = len(assumptions)
7242 _assumptions = (Ast * num)()
7243 for i
in range(num):
7244 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7249 """Return a model for the last `check()`.
7251 This function raises an exception if
7252 a model is not available (e.g., last `check()` returned unsat).
7256 >>> s.add(a + 2 == 0)
7265 raise Z3Exception(
"model is not available")
7268 """Import model converter from other into the current solver"""
7269 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7271 def interrupt(self):
7272 """Interrupt the execution of the solver object.
7273 Remarks: This ensures that the interrupt applies only
7274 to the given solver object and it applies only if it is running.
7276 Z3_solver_interrupt(self.ctx.ref(), self.solver)
7278 def unsat_core(self):
7279 """Return a subset (as an AST vector) of the assumptions provided to the last check().
7281 These are the assumptions Z3 used in the unsatisfiability proof.
7282 Assumptions are available in Z3. They are used to extract unsatisfiable cores.
7283 They may be also used to "retract" assumptions. Note that, assumptions are not really
7284 "soft constraints", but they can be used to implement them.
7286 >>> p1, p2, p3 = Bools('p1 p2 p3')
7287 >>> x, y = Ints('x y')
7289 >>> s.add(Implies(p1, x > 0))
7290 >>> s.add(Implies(p2, y > x))
7291 >>> s.add(Implies(p2, y < 1))
7292 >>> s.add(Implies(p3, y > -3))
7293 >>> s.check(p1, p2, p3)
7295 >>> core = s.unsat_core()
7304 >>> # "Retracting" p2
7308 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7310 def consequences(self, assumptions, variables):
7311 """Determine fixed values for the variables based on the solver state and assumptions.
7313 >>> a, b, c, d = Bools('a b c d')
7314 >>> s.add(Implies(a,b), Implies(b, c))
7315 >>> s.consequences([a],[b,c,d])
7316 (sat, [Implies(a, b), Implies(a, c)])
7317 >>> s.consequences([Not(c),d],[a,b,c,d])
7318 (sat, [Implies(d, d), Implies(Not(c), Not(c)), Implies(Not(c), Not(b)), Implies(Not(c), Not(a))])
7320 if isinstance(assumptions, list):
7321 _asms = AstVector(None, self.ctx)
7322 for a in assumptions:
7325 if isinstance(variables, list):
7326 _vars = AstVector(None, self.ctx)
7330 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7331 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7332 consequences = AstVector(None, self.ctx)
7333 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7334 variables.vector, consequences.vector)
7335 sz = len(consequences)
7336 consequences = [consequences[i] for i in range(sz)]
7337 return CheckSatResult(r), consequences
7339 def from_file(self, filename):
7340 """Parse assertions from a file"""
7341 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7343 def from_string(self, s):
7344 """Parse assertions from a string"""
7345 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7347 def cube(self, vars=None):
7349 The method takes an optional set of variables that restrict which
7350 variables may be used as a starting point for cubing.
7351 If vars is not None, then the first case split is based on a variable in
7354 self.cube_vs = AstVector(None, self.ctx)
7355 if vars is not None:
7357 self.cube_vs.push(v)
7359 lvl = self.backtrack_level
7360 self.backtrack_level = 4000000000
7361 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7362 if (len(r) == 1 and is_false(r[0])):
7368 def cube_vars(self):
7369 """Access the set of variables that were touched by the most recently generated cube.
7370 This set of variables can be used as a starting point for additional cubes.
7371 The idea is that variables that appear in clauses that are reduced by the most recent
7372 cube are likely more useful to cube on."""
7376 """Retrieve congruence closure root of the term t relative to the current search state
7377 The function primarily works for SimpleSolver. Terms and variables that are
7378 eliminated during pre-processing are not visible to the congruence closure.
7380 t = _py2expr(t, self.ctx)
7381 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7384 """Retrieve congruence closure sibling of the term t relative to the current search state
7385 The function primarily works for SimpleSolver. Terms and variables that are
7386 eliminated during pre-processing are not visible to the congruence closure.
7388 t = _py2expr(t, self.ctx)
7389 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7391 def explain_congruent(self, a, b):
7392 """Explain congruence of a and b relative to the current search state"""
7393 a = _py2expr(a, self.ctx)
7394 b = _py2expr(b, self.ctx)
7395 return _to_expr_ref(Z3_solver_congruence_explain(self.ctx.ref(), self.solver, a.ast, b.ast), self.ctx)
7397 def solve_for1(self, t):
7398 """Retrieve a solution for t relative to linear equations maintained in the current state.
7399 The function primarily works for SimpleSolver and when there is a solution using linear arithmetic."""
7400 t = _py2expr(t, self.ctx)
7401 return _to_expr_ref(Z3_solver_solve_for1(self.ctx.ref(), self.solver, t.ast), self.ctx)
7403 def solve_for(self, ts):
7404 """Retrieve a solution for t relative to linear equations maintained in the current state."""
7405 vars = AstVector(ctx=self.ctx);
7406 terms = AstVector(ctx=self.ctx);
7407 guards = AstVector(ctx=self.ctx);
7409 t = _py2expr(t, self.ctx)
7411 Z3_solver_solve_for(self.ctx.ref(), self.solver, vars.vector, terms.vector, guards.vector)
7412 return [(vars[i], terms[i], guards[i]) for i in range(len(vars))]
7416 """Return a proof for the last `check()`. Proof construction must be enabled."""
7417 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7419 def assertions(self):
7420 """Return an AST vector containing all added constraints.
7431 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7434 """Return an AST vector containing all currently inferred units.
7436 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7438 def non_units(self):
7439 """Return an AST vector containing all atomic formulas in solver state that are not units.
7441 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7443 def trail_levels(self):
7444 """Return trail and decision levels of the solver state after a check() call.
7446 trail = self.trail()
7447 levels = (ctypes.c_uint * len(trail))()
7448 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7449 return trail, levels
7451 def set_initial_value(self, var, value):
7452 """initialize the solver's state by setting the initial value of var to value
7455 value = s.cast(value)
7456 Z3_solver_set_initial_value(self.ctx.ref(), self.solver, var.ast, value.ast)
7459 """Return trail of the solver state after a check() call.
7461 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7463 def statistics(self):
7464 """Return statistics for the last `check()`.
7466 >>> s = SimpleSolver()
7471 >>> st = s.statistics()
7472 >>> st.get_key_value('final checks')
7479 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7481 def reason_unknown(self):
7482 """Return a string describing why the last `check()` returned `unknown`.
7485 >>> s = SimpleSolver()
7486 >>> s.add(2**x == 4)
7489 >>> s.reason_unknown()
7490 '(incomplete (theory arithmetic))'
7492 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7495 """Display a string describing all available options."""
7496 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7498 def param_descrs(self):
7499 """Return the parameter description set."""
7500 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7503 """Return a formatted string with all added constraints."""
7504 return obj_to_string(self)
7506 def translate(self, target):
7507 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
7511 >>> s1 = Solver(ctx=c1)
7512 >>> s2 = s1.translate(c2)
7515 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7516 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7517 return Solver(solver, target)
7520 return self.translate(self.ctx)
7522 def __deepcopy__(self, memo={}):
7523 return self.translate(self.ctx)
7526 """Return a formatted string (in Lisp-like format) with all added constraints.
7527 We say the string is in s-expression format.
7535 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7537 def dimacs(self, include_names=True):
7538 """Return a textual representation of the solver in DIMACS format."""
7539 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7542 """return SMTLIB2 formatted benchmark for solver's assertions"""
7543 es = self.assertions()
7549 for i in range(sz1):
7550 v[i] = es[i].as_ast()
7552 e = es[sz1].as_ast()
7554 e = BoolVal(True, self.ctx).as_ast()
7555 return Z3_benchmark_to_smtlib_string(
7556 self.ctx.ref(), "benchmark generated from python API", "", "unknown", "", sz1, v, e,
7560def SolverFor(logic, ctx=None, logFile=None):
7561 """Create a solver customized for the given logic.
7563 The parameter `logic` is a string. It should be contains
7564 the name of a SMT-LIB logic.
7565 See http://www.smtlib.org/ for the name of all available logics.
7567 >>> s = SolverFor("QF_LIA")
7577 logic = to_symbol(logic)
7578 return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
7581def SimpleSolver(ctx=None, logFile=None):
7582 """Return a simple general purpose solver with limited amount of preprocessing.
7584 >>> s = SimpleSolver()
7591 return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
7593#########################################
7597#########################################
7600class Fixedpoint(Z3PPObject):
7601 """Fixedpoint API provides methods for solving with recursive predicates"""
7603 def __init__(self, fixedpoint=None, ctx=None):
7604 assert fixedpoint is None or ctx is not None
7605 self.ctx = _get_ctx(ctx)
7606 self.fixedpoint = None
7607 if fixedpoint is None:
7608 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7610 self.fixedpoint = fixedpoint
7611 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7614 def __deepcopy__(self, memo={}):
7615 return FixedPoint(self.fixedpoint, self.ctx)
7618 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7619 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7621 def set(self, *args, **keys):
7622 """Set a configuration option. The method `help()` return a string containing all available options.
7624 p = args2params(args, keys, self.ctx)
7625 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7628 """Display a string describing all available options."""
7629 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7631 def param_descrs(self):
7632 """Return the parameter description set."""
7633 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7635 def assert_exprs(self, *args):
7636 """Assert constraints as background axioms for the fixedpoint solver."""
7637 args = _get_args(args)
7638 s = BoolSort(self.ctx)
7640 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7642 f = self.abstract(f)
7643 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7646 arg = self.abstract(arg)
7647 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7649 def add(self, *args):
7650 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7651 self.assert_exprs(*args)
7653 def __iadd__(self, fml):
7657 def append(self, *args):
7658 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7659 self.assert_exprs(*args)
7661 def insert(self, *args):
7662 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7663 self.assert_exprs(*args)
7665 def add_rule(self, head, body=None, name=None):
7666 """Assert rules defining recursive predicates to the fixedpoint solver.
7669 >>> s = Fixedpoint()
7670 >>> s.register_relation(a.decl())
7671 >>> s.register_relation(b.decl())
7679 name = to_symbol(name, self.ctx)
7681 head = self.abstract(head)
7682 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7684 body = _get_args(body)
7685 f = self.abstract(Implies(And(body, self.ctx), head))
7686 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7688 def rule(self, head, body=None, name=None):
7689 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7690 self.add_rule(head, body, name)
7692 def fact(self, head, name=None):
7693 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7694 self.add_rule(head, None, name)
7696 def query(self, *query):
7697 """Query the fixedpoint engine whether formula is derivable.
7698 You can also pass an tuple or list of recursive predicates.
7700 query = _get_args(query)
7702 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7703 _decls = (FuncDecl * sz)()
7708 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7713 query = And(query, self.ctx)
7714 query = self.abstract(query, False)
7715 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7716 return CheckSatResult(r)
7718 def query_from_lvl(self, lvl, *query):
7719 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7721 query = _get_args(query)
7723 if sz >= 1 and isinstance(query[0], FuncDecl):
7724 _z3_assert(False, "unsupported")
7730 query = self.abstract(query, False)
7731 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7732 return CheckSatResult(r)
7734 def update_rule(self, head, body, name):
7738 name = to_symbol(name, self.ctx)
7739 body = _get_args(body)
7740 f = self.abstract(Implies(And(body, self.ctx), head))
7741 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7743 def get_answer(self):
7744 """Retrieve answer from last query call."""
7745 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7746 return _to_expr_ref(r, self.ctx)
7748 def get_ground_sat_answer(self):
7749 """Retrieve a ground cex from last query call."""
7750 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7751 return _to_expr_ref(r, self.ctx)
7753 def get_rules_along_trace(self):
7754 """retrieve rules along the counterexample trace"""
7755 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7757 def get_rule_names_along_trace(self):
7758 """retrieve rule names along the counterexample trace"""
7759 # this is a hack as I don't know how to return a list of symbols from C++;
7760 # obtain names as a single string separated by semicolons
7761 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7762 # split into individual names
7763 return names.split(";")
7765 def get_num_levels(self, predicate):
7766 """Retrieve number of levels used for predicate in PDR engine"""
7767 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7769 def get_cover_delta(self, level, predicate):
7770 """Retrieve properties known about predicate for the level'th unfolding.
7771 -1 is treated as the limit (infinity)
7773 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7774 return _to_expr_ref(r, self.ctx)
7776 def add_cover(self, level, predicate, property):
7777 """Add property to predicate for the level'th unfolding.
7778 -1 is treated as infinity (infinity)
7780 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7782 def register_relation(self, *relations):
7783 """Register relation as recursive"""
7784 relations = _get_args(relations)
7786 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7788 def set_predicate_representation(self, f, *representations):
7789 """Control how relation is represented"""
7790 representations = _get_args(representations)
7791 representations = [to_symbol(s) for s in representations]
7792 sz = len(representations)
7793 args = (Symbol * sz)()
7795 args[i] = representations[i]
7796 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7798 def parse_string(self, s):
7799 """Parse rules and queries from a string"""
7800 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7802 def parse_file(self, f):
7803 """Parse rules and queries from a file"""
7804 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7806 def get_rules(self):
7807 """retrieve rules that have been added to fixedpoint context"""
7808 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7810 def get_assertions(self):
7811 """retrieve assertions that have been added to fixedpoint context"""
7812 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7815 """Return a formatted string with all added rules and constraints."""
7819 """Return a formatted string (in Lisp-like format) with all added constraints.
7820 We say the string is in s-expression format.
7822 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7824 def to_string(self, queries):
7825 """Return a formatted string (in Lisp-like format) with all added constraints.
7826 We say the string is in s-expression format.
7827 Include also queries.
7829 args, len = _to_ast_array(queries)
7830 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7832 def statistics(self):
7833 """Return statistics for the last `query()`.
7835 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7837 def reason_unknown(self):
7838 """Return a string describing why the last `query()` returned `unknown`.
7840 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7842 def declare_var(self, *vars):
7843 """Add variable or several variables.
7844 The added variable or variables will be bound in the rules
7847 vars = _get_args(vars)
7851 def abstract(self, fml, is_forall=True):
7855 return ForAll(self.vars, fml)
7857 return Exists(self.vars, fml)
7860#########################################
7864#########################################
7866class FiniteDomainSortRef(SortRef):
7867 """Finite domain sort."""
7870 """Return the size of the finite domain sort"""
7871 r = (ctypes.c_ulonglong * 1)()
7872 if Z3_get_finite_domain_sort_size(self.ctx_ref(), self.ast, r):
7875 raise Z3Exception("Failed to retrieve finite domain sort size")
7878def FiniteDomainSort(name, sz, ctx=None):
7879 """Create a named finite domain sort of a given size sz"""
7880 if not isinstance(name, Symbol):
7881 name = to_symbol(name)
7883 return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
7886def is_finite_domain_sort(s):
7887 """Return True if `s` is a Z3 finite-domain sort.
7889 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7891 >>> is_finite_domain_sort(IntSort())
7894 return isinstance(s, FiniteDomainSortRef)
7897class FiniteDomainRef(ExprRef):
7898 """Finite-domain expressions."""
7901 """Return the sort of the finite-domain expression `self`."""
7902 return FiniteDomainSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
7904 def as_string(self):
7905 """Return a Z3 floating point expression as a Python string."""
7906 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
7909def is_finite_domain(a):
7910 """Return `True` if `a` is a Z3 finite-domain expression.
7912 >>> s = FiniteDomainSort('S', 100)
7913 >>> b = Const('b', s)
7914 >>> is_finite_domain(b)
7916 >>> is_finite_domain(Int('x'))
7919 return isinstance(a, FiniteDomainRef)
7922class FiniteDomainNumRef(FiniteDomainRef):
7923 """Integer values."""
7926 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7928 >>> s = FiniteDomainSort('S', 100)
7929 >>> v = FiniteDomainVal(3, s)
7935 return int(self.as_string())
7937 def as_string(self):
7938 """Return a Z3 finite-domain numeral as a Python string.
7940 >>> s = FiniteDomainSort('S', 100)
7941 >>> v = FiniteDomainVal(42, s)
7945 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
7948def FiniteDomainVal(val, sort, ctx=None):
7949 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7951 >>> s = FiniteDomainSort('S', 256)
7952 >>> FiniteDomainVal(255, s)
7954 >>> FiniteDomainVal('100', s)
7958 _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
7960 return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
7963def is_finite_domain_value(a):
7964 """Return `True` if `a` is a Z3 finite-domain value.
7966 >>> s = FiniteDomainSort('S', 100)
7967 >>> b = Const('b', s)
7968 >>> is_finite_domain_value(b)
7970 >>> b = FiniteDomainVal(10, s)
7973 >>> is_finite_domain_value(b)
7976 return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
7979#########################################
7983#########################################
7985class OptimizeObjective:
7986 def __init__(self, opt, value, is_max):
7989 self._is_max = is_max
7993 return _to_expr_ref(Z3_optimize_get_lower(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7997 return _to_expr_ref(Z3_optimize_get_upper(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
7999 def lower_values(self):
8001 return AstVector(Z3_optimize_get_lower_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
8003 def upper_values(self):
8005 return AstVector(Z3_optimize_get_upper_as_vector(opt.ctx.ref(), opt.optimize, self._value), opt.ctx)
8014 return "%s:%s" % (self._value, self._is_max)
8020def _global_on_model(ctx):
8021 (fn, mdl) = _on_models[ctx]
8025_on_model_eh = on_model_eh_type(_global_on_model)
8028class Optimize(Z3PPObject):
8029 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
8031 def __init__(self, optimize=None, ctx=None):
8032 self.ctx = _get_ctx(ctx)
8033 if optimize is None:
8034 self.optimize = Z3_mk_optimize(self.ctx.ref())
8036 self.optimize = optimize
8037 self._on_models_id = None
8038 Z3_optimize_inc_ref(self.ctx.ref(), self.optimize)
8040 def __deepcopy__(self, memo={}):
8041 return Optimize(self.optimize, self.ctx)
8044 if self.optimize is not None and self.ctx.ref() is not None and Z3_optimize_dec_ref is not None:
8045 Z3_optimize_dec_ref(self.ctx.ref(), self.optimize)
8046 if self._on_models_id is not None:
8047 del _on_models[self._on_models_id]
8049 def __enter__(self):
8053 def __exit__(self, *exc_info):
8056 def set(self, *args, **keys):
8057 """Set a configuration option.
8058 The method `help()` return a string containing all available options.
8060 p = args2params(args, keys, self.ctx)
8061 Z3_optimize_set_params(self.ctx.ref(), self.optimize, p.params)
8064 """Display a string describing all available options."""
8065 print(Z3_optimize_get_help(self.ctx.ref(), self.optimize))
8067 def param_descrs(self):
8068 """Return the parameter description set."""
8069 return ParamDescrsRef(Z3_optimize_get_param_descrs(self.ctx.ref(), self.optimize), self.ctx)
8071 def assert_exprs(self, *args):
8072 """Assert constraints as background axioms for the optimize solver."""
8073 args = _get_args(args)
8074 s = BoolSort(self.ctx)
8076 if isinstance(arg, Goal) or isinstance(arg, AstVector):
8078 Z3_optimize_assert(self.ctx.ref(), self.optimize, f.as_ast())
8081 Z3_optimize_assert(self.ctx.ref(), self.optimize, arg.as_ast())
8083 def add(self, *args):
8084 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
8085 self.assert_exprs(*args)
8087 def __iadd__(self, fml):
8091 def assert_and_track(self, a, p):
8092 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
8094 If `p` is a string, it will be automatically converted into a Boolean constant.
8099 >>> s.assert_and_track(x > 0, 'p1')
8100 >>> s.assert_and_track(x != 1, 'p2')
8101 >>> s.assert_and_track(x < 0, p3)
8102 >>> print(s.check())
8104 >>> c = s.unsat_core()
8114 if isinstance(p, str):
8115 p = Bool(p, self.ctx)
8116 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
8117 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
8118 Z3_optimize_assert_and_track(self.ctx.ref(), self.optimize, a.as_ast(), p.as_ast())
8120 def add_soft(self, arg, weight="1", id=None):
8121 """Add soft constraint with optional weight and optional identifier.
8122 If no weight is supplied, then the penalty for violating the soft constraint
8124 Soft constraints are grouped by identifiers. Soft constraints that are
8125 added without identifiers are grouped by default.
8128 weight = "%d" % weight
8129 elif isinstance(weight, float):
8130 weight = "%f" % weight
8131 if not isinstance(weight, str):
8132 raise Z3Exception("weight should be a string or an integer")
8135 id = to_symbol(id, self.ctx)
8138 v = Z3_optimize_assert_soft(self.ctx.ref(), self.optimize, a.as_ast(), weight, id)
8139 return OptimizeObjective(self, v, False)
8140 if sys.version_info.major >= 3 and isinstance(arg, Iterable):
8141 return [asoft(a) for a in arg]
8144 def set_initial_value(self, var, value):
8145 """initialize the solver's state by setting the initial value of var to value
8148 value = s.cast(value)
8149 Z3_optimize_set_initial_value(self.ctx.ref(), self.optimize, var.ast, value.ast)
8151 def maximize(self, arg):
8152 """Add objective function to maximize."""
8153 return OptimizeObjective(
8155 Z3_optimize_maximize(self.ctx.ref(), self.optimize, arg.as_ast()),
8159 def minimize(self, arg):
8160 """Add objective function to minimize."""
8161 return OptimizeObjective(
8163 Z3_optimize_minimize(self.ctx.ref(), self.optimize, arg.as_ast()),
8168 """create a backtracking point for added rules, facts and assertions"""
8169 Z3_optimize_push(self.ctx.ref(), self.optimize)
8172 """restore to previously created backtracking point"""
8173 Z3_optimize_pop(self.ctx.ref(), self.optimize)
8175 def check(self, *assumptions):
8176 """Check consistency and produce optimal values."""
8177 assumptions = _get_args(assumptions)
8178 num = len(assumptions)
8179 _assumptions = (Ast * num)()
8180 for i in range(num):
8181 _assumptions[i] = assumptions[i].as_ast()
8182 return CheckSatResult(Z3_optimize_check(self.ctx.ref(), self.optimize, num, _assumptions))
8184 def reason_unknown(self):
8185 """Return a string that describes why the last `check()` returned `unknown`."""
8186 return Z3_optimize_get_reason_unknown(self.ctx.ref(), self.optimize)
8189 """Return a model for the last check()."""
8191 return ModelRef(Z3_optimize_get_model(self.ctx.ref(), self.optimize), self.ctx)
8193 raise Z3Exception("model is not available")
8195 def unsat_core(self):
8196 return AstVector(Z3_optimize_get_unsat_core(self.ctx.ref(), self.optimize), self.ctx)
8198 def lower(self, obj):
8199 if not isinstance(obj, OptimizeObjective):
8200 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8203 def upper(self, obj):
8204 if not isinstance(obj, OptimizeObjective):
8205 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8208 def lower_values(self, obj):
8209 if not isinstance(obj, OptimizeObjective):
8210 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8211 return obj.lower_values()
8213 def upper_values(self, obj):
8214 if not isinstance(obj, OptimizeObjective):
8215 raise Z3Exception("Expecting objective handle returned by maximize/minimize")
8216 return obj.upper_values()
8218 def from_file(self, filename):
8219 """Parse assertions and objectives from a file"""
8220 Z3_optimize_from_file(self.ctx.ref(), self.optimize, filename)
8222 def from_string(self, s):
8223 """Parse assertions and objectives from a string"""
8224 Z3_optimize_from_string(self.ctx.ref(), self.optimize, s)
8226 def assertions(self):
8227 """Return an AST vector containing all added constraints."""
8228 return AstVector(Z3_optimize_get_assertions(self.ctx.ref(), self.optimize), self.ctx)
8230 def objectives(self):
8231 """returns set of objective functions"""
8232 return AstVector(Z3_optimize_get_objectives(self.ctx.ref(), self.optimize), self.ctx)
8235 """Return a formatted string with all added rules and constraints."""
8239 """Return a formatted string (in Lisp-like format) with all added constraints.
8240 We say the string is in s-expression format.
8242 return Z3_optimize_to_string(self.ctx.ref(), self.optimize)
8244 def statistics(self):
8245 """Return statistics for the last check`.
8247 return Statistics(Z3_optimize_get_statistics(self.ctx.ref(), self.optimize), self.ctx)
8249 def set_on_model(self, on_model):
8250 """Register a callback that is invoked with every incremental improvement to
8251 objective values. The callback takes a model as argument.
8252 The life-time of the model is limited to the callback so the
8253 model has to be (deep) copied if it is to be used after the callback
8255 id = len(_on_models) + 41
8256 mdl = Model(self.ctx)
8257 _on_models[id] = (on_model, mdl)
8258 self._on_models_id = id
8259 Z3_optimize_register_model_eh(
8260 self.ctx.ref(), self.optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8264#########################################
8268#########################################
8269class ApplyResult(Z3PPObject):
8270 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8271 It also contains model and proof converters.
8274 def __init__(self, result, ctx):
8275 self.result = result
8277 Z3_apply_result_inc_ref(self.ctx.ref(), self.result)
8279 def __deepcopy__(self, memo={}):
8280 return ApplyResult(self.result, self.ctx)
8283 if self.ctx.ref() is not None and Z3_apply_result_dec_ref is not None:
8284 Z3_apply_result_dec_ref(self.ctx.ref(), self.result)
8287 """Return the number of subgoals in `self`.
8289 >>> a, b = Ints('a b')
8291 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8292 >>> t = Tactic('split-clause')
8296 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8299 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8303 return int(Z3_apply_result_get_num_subgoals(self.ctx.ref(), self.result))
8305 def __getitem__(self, idx):
8306 """Return one of the subgoals stored in ApplyResult object `self`.
8308 >>> a, b = Ints('a b')
8310 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8311 >>> t = Tactic('split-clause')
8314 [a == 0, Or(b == 0, b == 1), a > b]
8316 [a == 1, Or(b == 0, b == 1), a > b]
8318 if idx >= len(self):
8320 return Goal(goal=Z3_apply_result_get_subgoal(self.ctx.ref(), self.result, idx), ctx=self.ctx)
8323 return obj_to_string(self)
8326 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8327 return Z3_apply_result_to_string(self.ctx.ref(), self.result)
8330 """Return a Z3 expression consisting of all subgoals.
8335 >>> g.add(Or(x == 2, x == 3))
8336 >>> r = Tactic('simplify')(g)
8338 [[Not(x <= 1), Or(x == 2, x == 3)]]
8340 And(Not(x <= 1), Or(x == 2, x == 3))
8341 >>> r = Tactic('split-clause')(g)
8343 [[x > 1, x == 2], [x > 1, x == 3]]
8345 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8349 return BoolVal(False, self.ctx)
8351 return self[0].as_expr()
8353 return Or([self[i].as_expr() for i in range(len(self))])
8355#########################################
8359#########################################
8362 """Simplifiers act as pre-processing utilities for solvers.
8363 Build a custom simplifier and add it to a solve
r"""
8365 def __init__(self, simplifier, ctx=None):
8366 self.ctx = _get_ctx(ctx)
8367 self.simplifier = None
8368 if isinstance(simplifier, SimplifierObj):
8369 self.simplifier = simplifier
8370 elif isinstance(simplifier, list):
8371 simps = [Simplifier(s, ctx) for s in simplifier]
8372 self.simplifier = simps[0].simplifier
8373 for i in range(1, len(simps)):
8374 self.simplifier = Z3_simplifier_and_then(self.ctx.ref(), self.simplifier, simps[i].simplifier)
8375 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8379 _z3_assert(isinstance(simplifier, str), "simplifier name expected")
8381 self.simplifier = Z3_mk_simplifier(self.ctx.ref(), str(simplifier))
8383 raise Z3Exception("unknown simplifier '%s'" % simplifier)
8384 Z3_simplifier_inc_ref(self.ctx.ref(), self.simplifier)
8386 def __deepcopy__(self, memo={}):
8387 return Simplifier(self.simplifier, self.ctx)
8390 if self.simplifier is not None and self.ctx.ref() is not None and Z3_simplifier_dec_ref is not None:
8391 Z3_simplifier_dec_ref(self.ctx.ref(), self.simplifier)
8393 def using_params(self, *args, **keys):
8394 """Return a simplifier that uses the given configuration options"""
8395 p = args2params(args, keys, self.ctx)
8396 return Simplifier(Z3_simplifier_using_params(self.ctx.ref(), self.simplifier, p.params), self.ctx)
8398 def add(self, solver):
8399 """Return a solver that applies the simplification pre-processing specified by the simplifie
r"""
8400 return Solver(Z3_solver_add_simplifier(self.ctx.ref(), solver.solver, self.simplifier), self.ctx)
8403 """Display a string containing a description of the available options for the `self` simplifier."""
8404 print(Z3_simplifier_get_help(self.ctx.ref(), self.simplifier))
8406 def param_descrs(self):
8407 """Return the parameter description set."""
8408 return ParamDescrsRef(Z3_simplifier_get_param_descrs(self.ctx.ref(), self.simplifier), self.ctx)
8411#########################################
8415#########################################
8419 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8420 A Tactic can be converted into a Solver using the method solver().
8422 Several combinators are available for creating new tactics using the built-in ones:
8423 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8426 def __init__(self, tactic, ctx=None):
8427 self.ctx = _get_ctx(ctx)
8429 if isinstance(tactic, TacticObj):
8430 self.tactic = tactic
8433 _z3_assert(isinstance(tactic, str), "tactic name expected")
8435 self.tactic = Z3_mk_tactic(self.ctx.ref(), str(tactic))
8437 raise Z3Exception("unknown tactic '%s'" % tactic)
8438 Z3_tactic_inc_ref(self.ctx.ref(), self.tactic)
8440 def __deepcopy__(self, memo={}):
8441 return Tactic(self.tactic, self.ctx)
8444 if self.tactic is not None and self.ctx.ref() is not None and Z3_tactic_dec_ref is not None:
8445 Z3_tactic_dec_ref(self.ctx.ref(), self.tactic)
8447 def solver(self, logFile=None):
8448 """Create a solver using the tactic `self`.
8450 The solver supports the methods `push()` and `pop()`, but it
8451 will always solve each `check()` from scratch.
8453 >>> t = Then('simplify', 'nlsat')
8456 >>> s.add(x**2 == 2, x > 0)
8462 return Solver(Z3_mk_solver_from_tactic(self.ctx.ref(), self.tactic), self.ctx, logFile)
8464 def apply(self, goal, *arguments, **keywords):
8465 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8467 >>> x, y = Ints('x y')
8468 >>> t = Tactic('solve-eqs')
8469 >>> t.apply(And(x == 0, y >= x + 1))
8473 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expressions expected")
8474 goal = _to_goal(goal)
8475 if len(arguments) > 0 or len(keywords) > 0:
8476 p = args2params(arguments, keywords, self.ctx)
8477 return ApplyResult(Z3_tactic_apply_ex(self.ctx.ref(), self.tactic, goal.goal, p.params), self.ctx)
8479 return ApplyResult(Z3_tactic_apply(self.ctx.ref(), self.tactic, goal.goal), self.ctx)
8481 def __call__(self, goal, *arguments, **keywords):
8482 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8484 >>> x, y = Ints('x y')
8485 >>> t = Tactic('solve-eqs')
8486 >>> t(And(x == 0, y >= x + 1))
8489 return self.apply(goal, *arguments, **keywords)
8492 """Display a string containing a description of the available options for the `self` tactic."""
8493 print(Z3_tactic_get_help(self.ctx.ref(), self.tactic))
8495 def param_descrs(self):
8496 """Return the parameter description set."""
8497 return ParamDescrsRef(Z3_tactic_get_param_descrs(self.ctx.ref(), self.tactic), self.ctx)
8501 if isinstance(a, BoolRef):
8502 goal = Goal(ctx=a.ctx)
8509def _to_tactic(t, ctx=None):
8510 if isinstance(t, Tactic):
8513 return Tactic(t, ctx)
8516def _and_then(t1, t2, ctx=None):
8517 t1 = _to_tactic(t1, ctx)
8518 t2 = _to_tactic(t2, ctx)
8520 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8521 return Tactic(Z3_tactic_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8524def _or_else(t1, t2, ctx=None):
8525 t1 = _to_tactic(t1, ctx)
8526 t2 = _to_tactic(t2, ctx)
8528 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8529 return Tactic(Z3_tactic_or_else(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8532def AndThen(*ts, **ks):
8533 """Return a tactic that applies the tactics in `*ts` in sequence.
8535 >>> x, y = Ints('x y')
8536 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8537 >>> t(And(x == 0, y > x + 1))
8539 >>> t(And(x == 0, y > x + 1)).as_expr()
8543 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8544 ctx = ks.get("ctx", None)
8547 for i in range(num - 1):
8548 r = _and_then(r, ts[i + 1], ctx)
8553 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8555 >>> x, y = Ints('x y')
8556 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8557 >>> t(And(x == 0, y > x + 1))
8559 >>> t(And(x == 0, y > x + 1)).as_expr()
8562 return AndThen(*ts, **ks)
8565def OrElse(*ts, **ks):
8566 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8569 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8570 >>> # Tactic split-clause fails if there is no clause in the given goal.
8573 >>> t(Or(x == 0, x == 1))
8574 [[x == 0], [x == 1]]
8577 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8578 ctx = ks.get("ctx", None)
8581 for i in range(num - 1):
8582 r = _or_else(r, ts[i + 1], ctx)
8586def ParOr(*ts, **ks):
8587 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8590 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8595 _z3_assert(len(ts) >= 2, "At least two arguments expected")
8596 ctx = _get_ctx(ks.get("ctx", None))
8597 ts = [_to_tactic(t, ctx) for t in ts]
8599 _args = (TacticObj * sz)()
8601 _args[i] = ts[i].tactic
8602 return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
8605def ParThen(t1, t2, ctx=None):
8606 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8607 The subgoals are processed in parallel.
8609 >>> x, y = Ints('x y')
8610 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8611 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8612 [[x == 1, y == 2], [x == 2, y == 3]]
8614 t1 = _to_tactic(t1, ctx)
8615 t2 = _to_tactic(t2, ctx)
8617 _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
8618 return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
8621def ParAndThen(t1, t2, ctx=None):
8622 """Alias for ParThen(t1, t2, ctx)."""
8623 return ParThen(t1, t2, ctx)
8626def With(t, *args, **keys):
8627 """Return a tactic that applies tactic `t` using the given configuration options.
8629 >>> x, y = Ints('x y')
8630 >>> t = With(Tactic('simplify'), som=True)
8631 >>> t((x + 1)*(y + 2) == 0)
8632 [[2*x + y + x*y == -2]]
8634 ctx = keys.pop("ctx", None)
8635 t = _to_tactic(t, ctx)
8636 p = args2params(args, keys, t.ctx)
8637 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8640def WithParams(t, p):
8641 """Return a tactic that applies tactic `t` using the given configuration options.
8643 >>> x, y = Ints('x y')
8645 >>> p.set("som", True)
8646 >>> t = WithParams(Tactic('simplify'), p)
8647 >>> t((x + 1)*(y + 2) == 0)
8648 [[2*x + y + x*y == -2]]
8650 t = _to_tactic(t, None)
8651 return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
8654def Repeat(t, max=4294967295, ctx=None):
8655 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8656 or the maximum number of iterations `max` is reached.
8658 >>> x, y = Ints('x y')
8659 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8660 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8662 >>> for subgoal in r: print(subgoal)
8663 [x == 0, y == 0, x > y]
8664 [x == 0, y == 1, x > y]
8665 [x == 1, y == 0, x > y]
8666 [x == 1, y == 1, x > y]
8667 >>> t = Then(t, Tactic('propagate-values'))
8671 t = _to_tactic(t, ctx)
8672 return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
8675def TryFor(t, ms, ctx=None):
8676 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8678 If `t` does not terminate in `ms` milliseconds, then it fails.
8680 t = _to_tactic(t, ctx)
8681 return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
8684def tactics(ctx=None):
8685 """Return a list of all available tactics in Z3.
8688 >>> l.count('simplify') == 1
8692 return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
8695def tactic_description(name, ctx=None):
8696 """Return a short description for the tactic named `name`.
8698 >>> d = tactic_description('simplify')
8701 return Z3_tactic_get_descr(ctx.ref(), name)
8704def describe_tactics():
8705 """Display a (tabular) description of all available tactics in Z3."""
8708 print('<table border="1" cellpadding="2" cellspacing="0">')
8711 print('<tr style="background-color:#CFCFCF">')
8716 print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
8720 print("%s : %s" % (t, tactic_description(t)))
8724 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8725 to decide which solver and/or preprocessing step will be used.
8728 def __init__(self, probe, ctx=None):
8729 self.ctx = _get_ctx(ctx)
8731 if isinstance(probe, ProbeObj):
8733 elif isinstance(probe, float):
8734 self.probe = Z3_probe_const(self.ctx.ref(), probe)
8735 elif _is_int(probe):
8736 self.probe = Z3_probe_const(self.ctx.ref(), float(probe))
8737 elif isinstance(probe, bool):
8739 self.probe = Z3_probe_const(self.ctx.ref(), 1.0)
8741 self.probe = Z3_probe_const(self.ctx.ref(), 0.0)
8744 _z3_assert(isinstance(probe, str), "probe name expected")
8746 self.probe = Z3_mk_probe(self.ctx.ref(), probe)
8748 raise Z3Exception("unknown probe '%s'" % probe)
8749 Z3_probe_inc_ref(self.ctx.ref(), self.probe)
8751 def __deepcopy__(self, memo={}):
8752 return Probe(self.probe, self.ctx)
8755 if self.probe is not None and self.ctx.ref() is not None and Z3_probe_dec_ref is not None:
8756 Z3_probe_dec_ref(self.ctx.ref(), self.probe)
8758 def __lt__(self, other):
8759 """Return a probe that evaluates to "true" when the value returned by `self`
8760 is less than the value returned by `other`.
8762 >>> p = Probe('size') < 10
8770 return Probe(Z3_probe_lt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8772 def __gt__(self, other):
8773 """Return a probe that evaluates to "true" when the value returned by `self`
8774 is greater than the value returned by `other`.
8776 >>> p = Probe('size') > 10
8784 return Probe(Z3_probe_gt(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8786 def __le__(self, other):
8787 """Return a probe that evaluates to "true" when the value returned by `self`
8788 is less than or equal to the value returned by `other`.
8790 >>> p = Probe('size') <= 2
8798 return Probe(Z3_probe_le(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8800 def __ge__(self, other):
8801 """Return a probe that evaluates to "true" when the value returned by `self`
8802 is greater than or equal to the value returned by `other`.
8804 >>> p = Probe('size') >= 2
8812 return Probe(Z3_probe_ge(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8814 def __eq__(self, other):
8815 """Return a probe that evaluates to "true" when the value returned by `self`
8816 is equal to the value returned by `other`.
8818 >>> p = Probe('size') == 2
8826 return Probe(Z3_probe_eq(self.ctx.ref(), self.probe, _to_probe(other, self.ctx).probe), self.ctx)
8828 def __ne__(self, other):
8829 """Return a probe that evaluates to "true" when the value returned by `self`
8830 is not equal to the value returned by `other`.
8832 >>> p = Probe('size') != 2
8840 p = self.__eq__(other)
8841 return Probe(Z3_probe_not(self.ctx.ref(), p.probe), self.ctx)
8843 def __call__(self, goal):
8844 """Evaluate the probe `self` in the given goal.
8846 >>> p = Probe('size')
8856 >>> p = Probe('num-consts')
8859 >>> p = Probe('is-propositional')
8862 >>> p = Probe('is-qflia')
8867 _z3_assert(isinstance(goal, (Goal, BoolRef)), "Z3 Goal or Boolean expression expected")
8868 goal = _to_goal(goal)
8869 return Z3_probe_apply(self.ctx.ref(), self.probe, goal.goal)
8873 """Return `True` if `p` is a Z3 probe.
8875 >>> is_probe(Int('x'))
8877 >>> is_probe(Probe('memory'))
8880 return isinstance(p, Probe)
8883def _to_probe(p, ctx=None):
8887 return Probe(p, ctx)
8890def probes(ctx=None):
8891 """Return a list of all available probes in Z3.
8894 >>> l.count('memory') == 1
8898 return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
8901def probe_description(name, ctx=None):
8902 """Return a short description for the probe named `name`.
8904 >>> d = probe_description('memory')
8907 return Z3_probe_get_descr(ctx.ref(), name)
8910def describe_probes():
8911 """Display a (tabular) description of all available probes in Z3."""
8914 print('<table border="1" cellpadding="2" cellspacing="0">')
8917 print('<tr style="background-color:#CFCFCF">')
8922 print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
8926 print("%s : %s" % (p, probe_description(p)))
8929def _probe_nary(f, args, ctx):
8931 _z3_assert(len(args) > 0, "At least one argument expected")
8933 r = _to_probe(args[0], ctx)
8934 for i in range(num - 1):
8935 r = Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8939def _probe_and(args, ctx):
8940 return _probe_nary(Z3_probe_and, args, ctx)
8943def _probe_or(args, ctx):
8944 return _probe_nary(Z3_probe_or, args, ctx)
8947def FailIf(p, ctx=None):
8948 """Return a tactic that fails if the probe `p` evaluates to true.
8949 Otherwise, it returns the input goal unmodified.
8951 In the following example, the tactic applies 'simplify' if and only if there are
8952 more than 2 constraints in the goal.
8954 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8955 >>> x, y = Ints('x y')
8961 >>> g.add(x == y + 1)
8963 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8965 p = _to_probe(p, ctx)
8966 return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
8969def When(p, t, ctx=None):
8970 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8971 Otherwise, it returns the input goal unmodified.
8973 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8974 >>> x, y = Ints('x y')
8980 >>> g.add(x == y + 1)
8982 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8984 p = _to_probe(p, ctx)
8985 t = _to_tactic(t, ctx)
8986 return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
8989def Cond(p, t1, t2, ctx=None):
8990 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8992 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8994 p = _to_probe(p, ctx)
8995 t1 = _to_tactic(t1, ctx)
8996 t2 = _to_tactic(t2, ctx)
8997 return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
8999#########################################
9003#########################################
9006def simplify(a, *arguments, **keywords):
9007 """Simplify the expression `a` using the given options.
9009 This function has many options. Use `help_simplify` to obtain the complete list.
9013 >>> simplify(x + 1 + y + x + 1)
9015 >>> simplify((x + 1)*(y + 1), som=True)
9017 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
9018 And(Not(x == y), Not(x == 1), Not(y == 1))
9019 >>> simplify(And(x == 0, y == 1), elim_and=True)
9020 Not(Or(Not(x == 0), Not(y == 1)))
9023 _z3_assert(is_expr(a), "Z3 expression expected")
9024 if len(arguments) > 0 or len(keywords) > 0:
9025 p = args2params(arguments, keywords, a.ctx)
9026 return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
9028 return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
9032 """Return a string describing all options available for Z3 `simplify` procedure."""
9033 print(Z3_simplify_get_help(main_ctx().ref()))
9036def simplify_param_descrs():
9037 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
9038 return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
9041def substitute(t, *m):
9042 """Apply substitution m on t, m is a list of pairs of the form (from, to).
9043 Every occurrence in t of from is replaced with to.
9047 >>> substitute(x + 1, (x, y + 1))
9049 >>> f = Function('f', IntSort(), IntSort())
9050 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
9053 if isinstance(m, tuple):
9055 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9058 _z3_assert(is_expr(t), "Z3 expression expected")
9060 all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
9061 "Z3 invalid substitution, expression pairs expected.")
9063 all([p[0].sort().eq(p[1].sort()) for p in m]),
9064 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
9066 _from = (Ast * num)()
9068 for i in range(num):
9069 _from[i] = m[i][0].as_ast()
9070 _to[i] = m[i][1].as_ast()
9071 return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9074def substitute_vars(t, *m):
9075 """Substitute the free variables in t with the expression in m.
9077 >>> v0 = Var(0, IntSort())
9078 >>> v1 = Var(1, IntSort())
9080 >>> f = Function('f', IntSort(), IntSort(), IntSort())
9081 >>> # replace v0 with x+1 and v1 with x
9082 >>> substitute_vars(f(v0, v1), x + 1, x)
9086 _z3_assert(is_expr(t), "Z3 expression expected")
9087 _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
9090 for i in range(num):
9091 _to[i] = m[i].as_ast()
9092 return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
9094def substitute_funs(t, *m):
9095 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
9096 Every occurrence in to of the function from is replaced with the expression to.
9097 The expression to can have free variables, that refer to the arguments of from.
9100 if isinstance(m, tuple):
9102 if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
9105 _z3_assert(is_expr(t), "Z3 expression expected")
9106 _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, function pairs expected.")
9108 _from = (FuncDecl * num)()
9110 for i in range(num):
9111 _from[i] = m[i][0].as_func_decl()
9112 _to[i] = m[i][1].as_ast()
9113 return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
9117 """Create the sum of the Z3 expressions.
9119 >>> a, b, c = Ints('a b c')
9124 >>> A = IntVector('a', 5)
9126 a__0 + a__1 + a__2 + a__3 + a__4
9128 args = _get_args(args)
9131 ctx = _ctx_from_ast_arg_list(args)
9133 return _reduce(lambda a, b: a + b, args, 0)
9134 args = _coerce_expr_list(args, ctx)
9136 return _reduce(lambda a, b: a + b, args, 0)
9138 _args, sz = _to_ast_array(args)
9139 return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
9143 """Create the product of the Z3 expressions.
9145 >>> a, b, c = Ints('a b c')
9146 >>> Product(a, b, c)
9148 >>> Product([a, b, c])
9150 >>> A = IntVector('a', 5)
9152 a__0*a__1*a__2*a__3*a__4
9154 args = _get_args(args)
9157 ctx = _ctx_from_ast_arg_list(args)
9159 return _reduce(lambda a, b: a * b, args, 1)
9160 args = _coerce_expr_list(args, ctx)
9162 return _reduce(lambda a, b: a * b, args, 1)
9164 _args, sz = _to_ast_array(args)
9165 return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
9168 """Create the absolute value of an arithmetic expression"""
9169 return If(arg > 0, arg, -arg)
9173 """Create an at-most Pseudo-Boolean k constraint.
9175 >>> a, b, c = Bools('a b c')
9176 >>> f = AtMost(a, b, c, 2)
9178 args = _get_args(args)
9180 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9181 ctx = _ctx_from_ast_arg_list(args)
9183 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9184 args1 = _coerce_expr_list(args[:-1], ctx)
9186 _args, sz = _to_ast_array(args1)
9187 return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
9191 """Create an at-least Pseudo-Boolean k constraint.
9193 >>> a, b, c = Bools('a b c')
9194 >>> f = AtLeast(a, b, c, 2)
9196 args = _get_args(args)
9198 _z3_assert(len(args) > 1, "Non empty list of arguments expected")
9199 ctx = _ctx_from_ast_arg_list(args)
9201 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9202 args1 = _coerce_expr_list(args[:-1], ctx)
9204 _args, sz = _to_ast_array(args1)
9205 return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
9208def _reorder_pb_arg(arg):
9210 if not _is_int(b) and _is_int(a):
9215def _pb_args_coeffs(args, default_ctx=None):
9216 args = _get_args_ast_list(args)
9218 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9219 args = [_reorder_pb_arg(arg) for arg in args]
9220 args, coeffs = zip(*args)
9222 _z3_assert(len(args) > 0, "Non empty list of arguments expected")
9223 ctx = _ctx_from_ast_arg_list(args)
9225 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
9226 args = _coerce_expr_list(args, ctx)
9227 _args, sz = _to_ast_array(args)
9228 _coeffs = (ctypes.c_int * len(coeffs))()
9229 for i in range(len(coeffs)):
9230 _z3_check_cint_overflow(coeffs[i], "coefficient")
9231 _coeffs[i] = coeffs[i]
9232 return ctx, sz, _args, _coeffs, args
9236 """Create a Pseudo-Boolean inequality k constraint.
9238 >>> a, b, c = Bools('a b c')
9239 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9241 _z3_check_cint_overflow(k, "k")
9242 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9243 return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
9247 """Create a Pseudo-Boolean inequality k constraint.
9249 >>> a, b, c = Bools('a b c')
9250 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9252 _z3_check_cint_overflow(k, "k")
9253 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9254 return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
9257def PbEq(args, k, ctx=None):
9258 """Create a Pseudo-Boolean equality k constraint.
9260 >>> a, b, c = Bools('a b c')
9261 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9263 _z3_check_cint_overflow(k, "k")
9264 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9265 return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
9268def solve(*args, **keywords):
9269 """Solve the constraints `*args`.
9271 This is a simple function for creating demonstrations. It creates a solver,
9272 configure it using the options in `keywords`, adds the constraints
9273 in `args`, and invokes check.
9276 >>> solve(a > 0, a < 2)
9279 show = keywords.pop("show", False)
9287 print("no solution")
9289 print("failed to solve")
9298def solve_using(s, *args, **keywords):
9299 """Solve the constraints `*args` using solver `s`.
9301 This is a simple function for creating demonstrations. It is similar to `solve`,
9302 but it uses the given solver `s`.
9303 It configures solver `s` using the options in `keywords`, adds the constraints
9304 in `args`, and invokes check.
9306 show = keywords.pop("show", False)
9308 _z3_assert(isinstance(s, Solver), "Solver object expected")
9316 print("no solution")
9318 print("failed to solve")
9329def prove(claim, show=False, **keywords):
9330 """Try to prove the given claim.
9332 This is a simple function for creating demonstrations. It tries to prove
9333 `claim` by showing the negation is unsatisfiable.
9335 >>> p, q = Bools('p q')
9336 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9340 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9350 print("failed to prove")
9353 print("counterexample")
9357def _solve_html(*args, **keywords):
9358 """Version of function `solve` that renders HTML output."""
9359 show = keywords.pop("show", False)
9364 print("<b>Problem:</b>")
9368 print("<b>no solution</b>")
9370 print("<b>failed to solve</b>")
9377 print("<b>Solution:</b>")
9381def _solve_using_html(s, *args, **keywords):
9382 """Version of function `solve_using` that renders HTML."""
9383 show = keywords.pop("show", False)
9385 _z3_assert(isinstance(s, Solver), "Solver object expected")
9389 print("<b>Problem:</b>")
9393 print("<b>no solution</b>")
9395 print("<b>failed to solve</b>")
9402 print("<b>Solution:</b>")
9406def _prove_html(claim, show=False, **keywords):
9407 """Version of function `prove` that renders HTML."""
9409 _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
9417 print("<b>proved</b>")
9419 print("<b>failed to prove</b>")
9422 print("<b>counterexample</b>")
9426def _dict2sarray(sorts, ctx):
9428 _names = (Symbol * sz)()
9429 _sorts = (Sort * sz)()
9434 _z3_assert(isinstance(k, str), "String expected")
9435 _z3_assert(is_sort(v), "Z3 sort expected")
9436 _names[i] = to_symbol(k, ctx)
9439 return sz, _names, _sorts
9442def _dict2darray(decls, ctx):
9444 _names = (Symbol * sz)()
9445 _decls = (FuncDecl * sz)()
9450 _z3_assert(isinstance(k, str), "String expected")
9451 _z3_assert(is_func_decl(v) or is_const(v), "Z3 declaration or constant expected")
9452 _names[i] = to_symbol(k, ctx)
9454 _decls[i] = v.decl().ast
9458 return sz, _names, _decls
9461 def __init__(self, ctx= None):
9462 self.ctx = _get_ctx(ctx)
9463 self.pctx = Z3_mk_parser_context(self.ctx.ref())
9464 Z3_parser_context_inc_ref(self.ctx.ref(), self.pctx)
9467 if self.ctx.ref() is not None and self.pctx is not None and Z3_parser_context_dec_ref is not None:
9468 Z3_parser_context_dec_ref(self.ctx.ref(), self.pctx)
9471 def add_sort(self, sort):
9472 Z3_parser_context_add_sort(self.ctx.ref(), self.pctx, sort.as_ast())
9474 def add_decl(self, decl):
9475 Z3_parser_context_add_decl(self.ctx.ref(), self.pctx, decl.as_ast())
9477 def from_string(self, s):
9478 return AstVector(Z3_parser_context_from_string(self.ctx.ref(), self.pctx, s), self.ctx)
9480def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
9481 """Parse a string in SMT 2.0 format using the given sorts and decls.
9483 The arguments sorts and decls are Python dictionaries used to initialize
9484 the symbol table used for the SMT 2.0 parser.
9486 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9488 >>> x, y = Ints('x y')
9489 >>> f = Function('f', IntSort(), IntSort())
9490 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9492 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9496 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9497 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9498 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9501def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9502 """Parse a file in SMT 2.0 format using the given sorts and decls.
9504 This function is similar to parse_smt2_string().
9507 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9508 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9509 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9512#########################################
9514# Floating-Point Arithmetic
9516#########################################
9519# Global default rounding mode
9520_dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9521_dflt_fpsort_ebits = 11
9522_dflt_fpsort_sbits = 53
9525def get_default_rounding_mode(ctx=None):
9526 """Retrieves the global default rounding mode."""
9527 global _dflt_rounding_mode
9528 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9530 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9532 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9534 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9536 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9540_ROUNDING_MODES = frozenset({
9541 Z3_OP_FPA_RM_TOWARD_ZERO,
9542 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9543 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9544 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9545 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9549def set_default_rounding_mode(rm, ctx=None):
9550 global _dflt_rounding_mode
9551 if is_fprm_value(rm):
9552 _dflt_rounding_mode = rm.kind()
9554 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9555 _dflt_rounding_mode = rm
9558def get_default_fp_sort(ctx=None):
9559 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9562def set_default_fp_sort(ebits, sbits, ctx=None):
9563 global _dflt_fpsort_ebits
9564 global _dflt_fpsort_sbits
9565 _dflt_fpsort_ebits = ebits
9566 _dflt_fpsort_sbits = sbits
9569def _dflt_rm(ctx=None):
9570 return get_default_rounding_mode(ctx)
9573def _dflt_fps(ctx=None):
9574 return get_default_fp_sort(ctx)
9577def _coerce_fp_expr_list(alist, ctx):
9578 first_fp_sort = None
9581 if first_fp_sort is None:
9582 first_fp_sort = a.sort()
9583 elif first_fp_sort == a.sort():
9584 pass # OK, same as before
9586 # we saw at least 2 different float sorts; something will
9587 # throw a sort mismatch later, for now assume None.
9588 first_fp_sort = None
9592 for i in range(len(alist)):
9594 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9595 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9596 r.append(FPVal(a, None, first_fp_sort, ctx))
9599 return _coerce_expr_list(r, ctx)
9604class FPSortRef(SortRef):
9605 """Floating-point sort."""
9608 """Retrieves the number of bits reserved for the exponent in the FloatingPoint sort `self`.
9609 >>> b = FPSort(8, 24)
9613 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9616 """Retrieves the number of bits reserved for the significand in the FloatingPoint sort `self`.
9617 >>> b = FPSort(8, 24)
9621 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9623 def cast(self, val):
9624 """Try to cast `val` as a floating-point expression.
9625 >>> b = FPSort(8, 24)
9628 >>> b.cast(1.0).sexpr()
9629 '(fp #b0 #x7f #b00000000000000000000000)'
9633 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9636 return FPVal(val, None, self, self.ctx)
9639def Float16(ctx=None):
9640 """Floating-point 16-bit (half) sort."""
9642 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9645def FloatHalf(ctx=None):
9646 """Floating-point 16-bit (half) sort."""
9648 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9651def Float32(ctx=None):
9652 """Floating-point 32-bit (single) sort."""
9654 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9657def FloatSingle(ctx=None):
9658 """Floating-point 32-bit (single) sort."""
9660 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9663def Float64(ctx=None):
9664 """Floating-point 64-bit (double) sort."""
9666 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9669def FloatDouble(ctx=None):
9670 """Floating-point 64-bit (double) sort."""
9672 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9675def Float128(ctx=None):
9676 """Floating-point 128-bit (quadruple) sort."""
9678 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9681def FloatQuadruple(ctx=None):
9682 """Floating-point 128-bit (quadruple) sort."""
9684 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9687class FPRMSortRef(SortRef):
9688 """"Floating-point rounding mode sort."""
9692 """Return True if `s` is a Z3 floating-point sort.
9694 >>> is_fp_sort(FPSort(8, 24))
9696 >>> is_fp_sort(IntSort())
9699 return isinstance(s, FPSortRef)
9703 """Return True if `s` is a Z3 floating-point rounding mode sort.
9705 >>> is_fprm_sort(FPSort(8, 24))
9707 >>> is_fprm_sort(RNE().sort())
9710 return isinstance(s, FPRMSortRef)
9715class FPRef(ExprRef):
9716 """Floating-point expressions."""
9719 """Return the sort of the floating-point expression `self`.
9721 >>> x = FP('1.0', FPSort(8, 24))
9724 >>> x.sort() == FPSort(8, 24)
9727 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9730 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9731 >>> b = FPSort(8, 24)
9735 return self.sort().ebits()
9738 """Retrieves the number of bits reserved for the exponent in the FloatingPoint expression `self`.
9739 >>> b = FPSort(8, 24)
9743 return self.sort().sbits()
9745 def as_string(self):
9746 """Return a Z3 floating point expression as a Python string."""
9747 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9749 def __le__(self, other):
9750 return fpLEQ(self, other, self.ctx)
9752 def __lt__(self, other):
9753 return fpLT(self, other, self.ctx)
9755 def __ge__(self, other):
9756 return fpGEQ(self, other, self.ctx)
9758 def __gt__(self, other):
9759 return fpGT(self, other, self.ctx)
9761 def __add__(self, other):
9762 """Create the Z3 expression `self + other`.
9764 >>> x = FP('x', FPSort(8, 24))
9765 >>> y = FP('y', FPSort(8, 24))
9771 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9772 return fpAdd(_dflt_rm(), a, b, self.ctx)
9774 def __radd__(self, other):
9775 """Create the Z3 expression `other + self`.
9777 >>> x = FP('x', FPSort(8, 24))
9781 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9782 return fpAdd(_dflt_rm(), a, b, self.ctx)
9784 def __sub__(self, other):
9785 """Create the Z3 expression `self - other`.
9787 >>> x = FP('x', FPSort(8, 24))
9788 >>> y = FP('y', FPSort(8, 24))
9794 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9795 return fpSub(_dflt_rm(), a, b, self.ctx)
9797 def __rsub__(self, other):
9798 """Create the Z3 expression `other - self`.
9800 >>> x = FP('x', FPSort(8, 24))
9804 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9805 return fpSub(_dflt_rm(), a, b, self.ctx)
9807 def __mul__(self, other):
9808 """Create the Z3 expression `self * other`.
9810 >>> x = FP('x', FPSort(8, 24))
9811 >>> y = FP('y', FPSort(8, 24))
9819 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9820 return fpMul(_dflt_rm(), a, b, self.ctx)
9822 def __rmul__(self, other):
9823 """Create the Z3 expression `other * self`.
9825 >>> x = FP('x', FPSort(8, 24))
9826 >>> y = FP('y', FPSort(8, 24))
9832 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9833 return fpMul(_dflt_rm(), a, b, self.ctx)
9836 """Create the Z3 expression `+self`."""
9840 """Create the Z3 expression `-self`.
9842 >>> x = FP('x', Float32())
9848 def __div__(self, other):
9849 """Create the Z3 expression `self / other`.
9851 >>> x = FP('x', FPSort(8, 24))
9852 >>> y = FP('y', FPSort(8, 24))
9860 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9861 return fpDiv(_dflt_rm(), a, b, self.ctx)
9863 def __rdiv__(self, other):
9864 """Create the Z3 expression `other / self`.
9866 >>> x = FP('x', FPSort(8, 24))
9867 >>> y = FP('y', FPSort(8, 24))
9873 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9874 return fpDiv(_dflt_rm(), a, b, self.ctx)
9876 def __truediv__(self, other):
9877 """Create the Z3 expression division `self / other`."""
9878 return self.__div__(other)
9880 def __rtruediv__(self, other):
9881 """Create the Z3 expression division `other / self`."""
9882 return self.__rdiv__(other)
9884 def __mod__(self, other):
9885 """Create the Z3 expression mod `self % other`."""
9886 return fpRem(self, other)
9888 def __rmod__(self, other):
9889 """Create the Z3 expression mod `other % self`."""
9890 return fpRem(other, self)
9893class FPRMRef(ExprRef):
9894 """Floating-point rounding mode expressions"""
9896 def as_string(self):
9897 """Return a Z3 floating point expression as a Python string."""
9898 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9901def RoundNearestTiesToEven(ctx=None):
9903 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9908 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9911def RoundNearestTiesToAway(ctx=None):
9913 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9918 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9921def RoundTowardPositive(ctx=None):
9923 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9928 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9931def RoundTowardNegative(ctx=None):
9933 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9938 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9941def RoundTowardZero(ctx=None):
9943 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9948 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9952 """Return `True` if `a` is a Z3 floating-point rounding mode expression.
9961 return isinstance(a, FPRMRef)
9964def is_fprm_value(a):
9965 """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
9966 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9971class FPNumRef(FPRef):
9972 """The sign of the numeral.
9974 >>> x = FPVal(+1.0, FPSort(8, 24))
9977 >>> x = FPVal(-1.0, FPSort(8, 24))
9983 num = (ctypes.c_int)()
9984 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9986 raise Z3Exception("error retrieving the sign of a numeral.")
9987 return num.value != 0
9989 """The sign of a floating-point numeral as a bit-vector expression.
9991 Remark: NaN's are invalid arguments.
9994 def sign_as_bv(self):
9995 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9997 """The significand of the numeral.
9999 >>> x = FPVal(2.5, FPSort(8, 24))
10000 >>> x.significand()
10004 def significand(self):
10005 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
10007 """The significand of the numeral as a long.
10009 >>> x = FPVal(2.5, FPSort(8, 24))
10010 >>> x.significand_as_long()
10014 def significand_as_long(self):
10015 ptr = (ctypes.c_ulonglong * 1)()
10016 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
10017 raise Z3Exception("error retrieving the significand of a numeral.")
10020 """The significand of the numeral as a bit-vector expression.
10022 Remark: NaN are invalid arguments.
10025 def significand_as_bv(self):
10026 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
10028 """The exponent of the numeral.
10030 >>> x = FPVal(2.5, FPSort(8, 24))
10035 def exponent(self, biased=True):
10036 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
10038 """The exponent of the numeral as a long.
10040 >>> x = FPVal(2.5, FPSort(8, 24))
10041 >>> x.exponent_as_long()
10045 def exponent_as_long(self, biased=True):
10046 ptr = (ctypes.c_longlong * 1)()
10047 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
10048 raise Z3Exception("error retrieving the exponent of a numeral.")
10051 """The exponent of the numeral as a bit-vector expression.
10053 Remark: NaNs are invalid arguments.
10056 def exponent_as_bv(self, biased=True):
10057 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
10059 """Indicates whether the numeral is a NaN."""
10062 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
10064 """Indicates whether the numeral is +oo or -oo."""
10067 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
10069 """Indicates whether the numeral is +zero or -zero."""
10072 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
10074 """Indicates whether the numeral is normal."""
10076 def isNormal(self):
10077 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
10079 """Indicates whether the numeral is subnormal."""
10081 def isSubnormal(self):
10082 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
10084 """Indicates whether the numeral is positive."""
10086 def isPositive(self):
10087 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
10089 """Indicates whether the numeral is negative."""
10091 def isNegative(self):
10092 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
10095 The string representation of the numeral.
10097 >>> x = FPVal(20, FPSort(8, 24))
10102 def as_string(self):
10103 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
10104 return ("FPVal(%s, %s)" % (s, self.sort()))
10106 def py_value(self):
10107 bv = simplify(fpToIEEEBV(self))
10108 binary = bv.py_value()
10109 if not isinstance(binary, int):
10111 # Decode the IEEE 754 binary representation
10113 bytes_rep = binary.to_bytes(8, byteorder='big')
10114 return struct.unpack('>d', bytes_rep)[0]
10118 """Return `True` if `a` is a Z3 floating-point expression.
10120 >>> b = FP('b', FPSort(8, 24))
10125 >>> is_fp(Int('x'))
10128 return isinstance(a, FPRef)
10132 """Return `True` if `a` is a Z3 floating-point numeral value.
10134 >>> b = FP('b', FPSort(8, 24))
10137 >>> b = FPVal(1.0, FPSort(8, 24))
10143 return is_fp(a) and _is_numeral(a.ctx, a.ast)
10146def FPSort(ebits, sbits, ctx=None):
10147 """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
10149 >>> Single = FPSort(8, 24)
10150 >>> Double = FPSort(11, 53)
10153 >>> x = Const('x', Single)
10154 >>> eq(x, FP('x', FPSort(8, 24)))
10157 ctx = _get_ctx(ctx)
10158 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
10161def _to_float_str(val, exp=0):
10162 if isinstance(val, float):
10163 if math.isnan(val):
10166 sone = math.copysign(1.0, val)
10171 elif val == float("+inf"):
10173 elif val == float("-inf"):
10176 v = val.as_integer_ratio()
10179 rvs = str(num) + "/" + str(den)
10180 res = rvs + "p" + _to_int_str(exp)
10181 elif isinstance(val, bool):
10188 elif isinstance(val, str):
10189 inx = val.find("*(2**")
10192 elif val[-1] == ")":
10194 exp = str(int(val[inx + 5:-1]) + int(exp))
10196 _z3_assert(False, "String does not have floating-point numeral form.")
10198 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10202 return res + "p" + exp
10206 """Create a Z3 floating-point NaN term.
10208 >>> s = FPSort(8, 24)
10209 >>> set_fpa_pretty(True)
10212 >>> pb = get_fpa_pretty()
10213 >>> set_fpa_pretty(False)
10215 fpNaN(FPSort(8, 24))
10216 >>> set_fpa_pretty(pb)
10218 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10219 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10222def fpPlusInfinity(s):
10223 """Create a Z3 floating-point +oo term.
10225 >>> s = FPSort(8, 24)
10226 >>> pb = get_fpa_pretty()
10227 >>> set_fpa_pretty(True)
10228 >>> fpPlusInfinity(s)
10230 >>> set_fpa_pretty(False)
10231 >>> fpPlusInfinity(s)
10232 fpPlusInfinity(FPSort(8, 24))
10233 >>> set_fpa_pretty(pb)
10235 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10236 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10239def fpMinusInfinity(s):
10240 """Create a Z3 floating-point -oo term."""
10241 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10242 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10245def fpInfinity(s, negative):
10246 """Create a Z3 floating-point +oo or -oo term."""
10247 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10248 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10249 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10253 """Create a Z3 floating-point +0.0 term."""
10254 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10255 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10259 """Create a Z3 floating-point -0.0 term."""
10260 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10261 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10264def fpZero(s, negative):
10265 """Create a Z3 floating-point +0.0 or -0.0 term."""
10266 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10267 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10268 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10271def FPVal(sig, exp=None, fps=None, ctx=None):
10272 """Return a floating-point value of value `val` and sort `fps`.
10273 If `ctx=None`, then the global context is used.
10275 >>> v = FPVal(20.0, FPSort(8, 24))
10278 >>> print("0x%.8x" % v.exponent_as_long(False))
10280 >>> v = FPVal(2.25, FPSort(8, 24))
10283 >>> v = FPVal(-2.25, FPSort(8, 24))
10286 >>> FPVal(-0.0, FPSort(8, 24))
10288 >>> FPVal(0.0, FPSort(8, 24))
10290 >>> FPVal(+0.0, FPSort(8, 24))
10293 ctx = _get_ctx(ctx)
10294 if is_fp_sort(exp):
10298 fps = _dflt_fps(ctx)
10299 _z3_assert(is_fp_sort(fps), "sort mismatch")
10302 val = _to_float_str(sig)
10303 if val == "NaN" or val == "nan":
10305 elif val == "-0.0":
10306 return fpMinusZero(fps)
10307 elif val == "0.0" or val == "+0.0":
10308 return fpPlusZero(fps)
10309 elif val == "+oo" or val == "+inf" or val == "+Inf":
10310 return fpPlusInfinity(fps)
10311 elif val == "-oo" or val == "-inf" or val == "-Inf":
10312 return fpMinusInfinity(fps)
10314 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10317def FP(name, fpsort, ctx=None):
10318 """Return a floating-point constant named `name`.
10319 `fpsort` is the floating-point sort.
10320 If `ctx=None`, then the global context is used.
10322 >>> x = FP('x', FPSort(8, 24))
10329 >>> word = FPSort(8, 24)
10330 >>> x2 = FP('x', word)
10334 if isinstance(fpsort, FPSortRef) and ctx is None:
10337 ctx = _get_ctx(ctx)
10338 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10341def FPs(names, fpsort, ctx=None):
10342 """Return an array of floating-point constants.
10344 >>> x, y, z = FPs('x y z', FPSort(8, 24))
10351 >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
10354 ctx = _get_ctx(ctx)
10355 if isinstance(names, str):
10356 names = names.split(" ")
10357 return [FP(name, fpsort, ctx) for name in names]
10360def fpAbs(a, ctx=None):
10361 """Create a Z3 floating-point absolute value expression.
10363 >>> s = FPSort(8, 24)
10365 >>> x = FPVal(1.0, s)
10368 >>> y = FPVal(-20.0, s)
10372 fpAbs(-1.25*(2**4))
10373 >>> fpAbs(-1.25*(2**4))
10374 fpAbs(-1.25*(2**4))
10375 >>> fpAbs(x).sort()
10378 ctx = _get_ctx(ctx)
10379 [a] = _coerce_fp_expr_list([a], ctx)
10380 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10383def fpNeg(a, ctx=None):
10384 """Create a Z3 floating-point addition expression.
10386 >>> s = FPSort(8, 24)
10391 >>> fpNeg(x).sort()
10394 ctx = _get_ctx(ctx)
10395 [a] = _coerce_fp_expr_list([a], ctx)
10396 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10399def _mk_fp_unary(f, rm, a, ctx):
10400 ctx = _get_ctx(ctx)
10401 [a] = _coerce_fp_expr_list([a], ctx)
10403 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10404 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10405 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10408def _mk_fp_unary_pred(f, a, ctx):
10409 ctx = _get_ctx(ctx)
10410 [a] = _coerce_fp_expr_list([a], ctx)
10412 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10413 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10416def _mk_fp_bin(f, rm, a, b, ctx):
10417 ctx = _get_ctx(ctx)
10418 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10420 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10421 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10422 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10425def _mk_fp_bin_norm(f, a, b, ctx):
10426 ctx = _get_ctx(ctx)
10427 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10429 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10430 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10433def _mk_fp_bin_pred(f, a, b, ctx):
10434 ctx = _get_ctx(ctx)
10435 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10437 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10438 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10441def _mk_fp_tern(f, rm, a, b, c, ctx):
10442 ctx = _get_ctx(ctx)
10443 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10445 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10446 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10447 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10448 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10451def fpAdd(rm, a, b, ctx=None):
10452 """Create a Z3 floating-point addition expression.
10454 >>> s = FPSort(8, 24)
10458 >>> fpAdd(rm, x, y)
10460 >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
10462 >>> fpAdd(rm, x, y).sort()
10465 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10468def fpSub(rm, a, b, ctx=None):
10469 """Create a Z3 floating-point subtraction expression.
10471 >>> s = FPSort(8, 24)
10475 >>> fpSub(rm, x, y)
10477 >>> fpSub(rm, x, y).sort()
10480 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10483def fpMul(rm, a, b, ctx=None):
10484 """Create a Z3 floating-point multiplication expression.
10486 >>> s = FPSort(8, 24)
10490 >>> fpMul(rm, x, y)
10492 >>> fpMul(rm, x, y).sort()
10495 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10498def fpDiv(rm, a, b, ctx=None):
10499 """Create a Z3 floating-point division expression.
10501 >>> s = FPSort(8, 24)
10505 >>> fpDiv(rm, x, y)
10507 >>> fpDiv(rm, x, y).sort()
10510 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10513def fpRem(a, b, ctx=None):
10514 """Create a Z3 floating-point remainder expression.
10516 >>> s = FPSort(8, 24)
10521 >>> fpRem(x, y).sort()
10524 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10527def fpMin(a, b, ctx=None):
10528 """Create a Z3 floating-point minimum expression.
10530 >>> s = FPSort(8, 24)
10536 >>> fpMin(x, y).sort()
10539 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10542def fpMax(a, b, ctx=None):
10543 """Create a Z3 floating-point maximum expression.
10545 >>> s = FPSort(8, 24)
10551 >>> fpMax(x, y).sort()
10554 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10557def fpFMA(rm, a, b, c, ctx=None):
10558 """Create a Z3 floating-point fused multiply-add expression.
10560 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10563def fpSqrt(rm, a, ctx=None):
10564 """Create a Z3 floating-point square root expression.
10566 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10569def fpRoundToIntegral(rm, a, ctx=None):
10570 """Create a Z3 floating-point roundToIntegral expression.
10572 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10575def fpIsNaN(a, ctx=None):
10576 """Create a Z3 floating-point isNaN expression.
10578 >>> s = FPSort(8, 24)
10584 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10587def fpIsInf(a, ctx=None):
10588 """Create a Z3 floating-point isInfinite expression.
10590 >>> s = FPSort(8, 24)
10595 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10598def fpIsZero(a, ctx=None):
10599 """Create a Z3 floating-point isZero expression.
10601 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10604def fpIsNormal(a, ctx=None):
10605 """Create a Z3 floating-point isNormal expression.
10607 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10610def fpIsSubnormal(a, ctx=None):
10611 """Create a Z3 floating-point isSubnormal expression.
10613 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10616def fpIsNegative(a, ctx=None):
10617 """Create a Z3 floating-point isNegative expression.
10619 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10622def fpIsPositive(a, ctx=None):
10623 """Create a Z3 floating-point isPositive expression.
10625 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10628def _check_fp_args(a, b):
10630 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10633def fpLT(a, b, ctx=None):
10634 """Create the Z3 floating-point expression `other < self`.
10636 >>> x, y = FPs('x y', FPSort(8, 24))
10639 >>> (x < y).sexpr()
10642 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10645def fpLEQ(a, b, ctx=None):
10646 """Create the Z3 floating-point expression `other <= self`.
10648 >>> x, y = FPs('x y', FPSort(8, 24))
10651 >>> (x <= y).sexpr()
10654 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10657def fpGT(a, b, ctx=None):
10658 """Create the Z3 floating-point expression `other > self`.
10660 >>> x, y = FPs('x y', FPSort(8, 24))
10663 >>> (x > y).sexpr()
10666 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10669def fpGEQ(a, b, ctx=None):
10670 """Create the Z3 floating-point expression `other >= self`.
10672 >>> x, y = FPs('x y', FPSort(8, 24))
10675 >>> (x >= y).sexpr()
10678 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10681def fpEQ(a, b, ctx=None):
10682 """Create the Z3 floating-point expression `fpEQ(other, self)`.
10684 >>> x, y = FPs('x y', FPSort(8, 24))
10687 >>> fpEQ(x, y).sexpr()
10690 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10693def fpNEQ(a, b, ctx=None):
10694 """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
10696 >>> x, y = FPs('x y', FPSort(8, 24))
10699 >>> (x != y).sexpr()
10702 return Not(fpEQ(a, b, ctx))
10705def fpFP(sgn, exp, sig, ctx=None):
10706 """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
10708 >>> s = FPSort(8, 24)
10709 >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
10711 fpFP(1, 127, 4194304)
10712 >>> xv = FPVal(-1.5, s)
10715 >>> slvr = Solver()
10716 >>> slvr.add(fpEQ(x, xv))
10719 >>> xv = FPVal(+1.5, s)
10722 >>> slvr = Solver()
10723 >>> slvr.add(fpEQ(x, xv))
10727 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10728 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10729 ctx = _get_ctx(ctx)
10730 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10731 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10734def fpToFP(a1, a2=None, a3=None, ctx=None):
10735 """Create a Z3 floating-point conversion expression from other term sorts
10738 From a bit-vector term in IEEE 754-2008 format:
10739 >>> x = FPVal(1.0, Float32())
10740 >>> x_bv = fpToIEEEBV(x)
10741 >>> simplify(fpToFP(x_bv, Float32()))
10744 From a floating-point term with different precision:
10745 >>> x = FPVal(1.0, Float32())
10746 >>> x_db = fpToFP(RNE(), x, Float64())
10751 >>> x_r = RealVal(1.5)
10752 >>> simplify(fpToFP(RNE(), x_r, Float32()))
10755 From a signed bit-vector term:
10756 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10757 >>> simplify(fpToFP(RNE(), x_signed, Float32()))
10760 ctx = _get_ctx(ctx)
10761 if is_bv(a1) and is_fp_sort(a2):
10762 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10763 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10764 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10765 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10766 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10767 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10768 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10770 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10773def fpBVToFP(v, sort, ctx=None):
10774 """Create a Z3 floating-point conversion expression that represents the
10775 conversion from a bit-vector term to a floating-point term.
10777 >>> x_bv = BitVecVal(0x3F800000, 32)
10778 >>> x_fp = fpBVToFP(x_bv, Float32())
10784 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10785 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10786 ctx = _get_ctx(ctx)
10787 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10790def fpFPToFP(rm, v, sort, ctx=None):
10791 """Create a Z3 floating-point conversion expression that represents the
10792 conversion from a floating-point term to a floating-point term of different precision.
10794 >>> x_sgl = FPVal(1.0, Float32())
10795 >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
10798 >>> simplify(x_dbl)
10803 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10804 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10805 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10806 ctx = _get_ctx(ctx)
10807 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10810def fpRealToFP(rm, v, sort, ctx=None):
10811 """Create a Z3 floating-point conversion expression that represents the
10812 conversion from a real term to a floating-point term.
10814 >>> x_r = RealVal(1.5)
10815 >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
10821 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10822 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10823 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10824 ctx = _get_ctx(ctx)
10825 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10828def fpSignedToFP(rm, v, sort, ctx=None):
10829 """Create a Z3 floating-point conversion expression that represents the
10830 conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
10832 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10833 >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
10835 fpToFP(RNE(), 4294967291)
10839 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10840 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10841 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10842 ctx = _get_ctx(ctx)
10843 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10846def fpUnsignedToFP(rm, v, sort, ctx=None):
10847 """Create a Z3 floating-point conversion expression that represents the
10848 conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10850 >>> x_signed = BitVecVal(-5, BitVecSort(32))
10851 >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
10853 fpToFPUnsigned(RNE(), 4294967291)
10857 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10858 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10859 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10860 ctx = _get_ctx(ctx)
10861 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10864def fpToFPUnsigned(rm, x, s, ctx=None):
10865 """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
10867 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10868 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10869 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10870 ctx = _get_ctx(ctx)
10871 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10874def fpToSBV(rm, x, s, ctx=None):
10875 """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
10877 >>> x = FP('x', FPSort(8, 24))
10878 >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
10879 >>> print(is_fp(x))
10881 >>> print(is_bv(y))
10883 >>> print(is_fp(y))
10885 >>> print(is_bv(x))
10889 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10890 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10891 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10892 ctx = _get_ctx(ctx)
10893 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10896def fpToUBV(rm, x, s, ctx=None):
10897 """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
10899 >>> x = FP('x', FPSort(8, 24))
10900 >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
10901 >>> print(is_fp(x))
10903 >>> print(is_bv(y))
10905 >>> print(is_fp(y))
10907 >>> print(is_bv(x))
10911 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10912 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10913 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10914 ctx = _get_ctx(ctx)
10915 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10918def fpToReal(x, ctx=None):
10919 """Create a Z3 floating-point conversion expression, from floating-point expression to real.
10921 >>> x = FP('x', FPSort(8, 24))
10922 >>> y = fpToReal(x)
10923 >>> print(is_fp(x))
10925 >>> print(is_real(y))
10927 >>> print(is_fp(y))
10929 >>> print(is_real(x))
10933 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10934 ctx = _get_ctx(ctx)
10935 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10938def fpToIEEEBV(x, ctx=None):
10939 """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
10941 The size of the resulting bit-vector is automatically determined.
10943 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10944 knows only one NaN and it will always produce the same bit-vector representation of
10947 >>> x = FP('x', FPSort(8, 24))
10948 >>> y = fpToIEEEBV(x)
10949 >>> print(is_fp(x))
10951 >>> print(is_bv(y))
10953 >>> print(is_fp(y))
10955 >>> print(is_bv(x))
10959 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10960 ctx = _get_ctx(ctx)
10961 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10964#########################################
10966# Strings, Sequences and Regular expressions
10968#########################################
10970class SeqSortRef(SortRef):
10971 """Sequence sort."""
10973 def is_string(self):
10974 """Determine if sort is a string
10975 >>> s = StringSort()
10978 >>> s = SeqSort(IntSort())
10982 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10985 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10987class CharSortRef(SortRef):
10988 """Character sort."""
10991def StringSort(ctx=None):
10992 """Create a string sort
10993 >>> s = StringSort()
10997 ctx = _get_ctx(ctx)
10998 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
11000def CharSort(ctx=None):
11001 """Create a character sort
11002 >>> ch = CharSort()
11006 ctx = _get_ctx(ctx)
11007 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
11011 """Create a sequence sort over elements provided in the argument
11012 >>> s = SeqSort(IntSort())
11013 >>> s == Unit(IntVal(1)).sort()
11016 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
11019class SeqRef(ExprRef):
11020 """Sequence expression."""
11023 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
11025 def __add__(self, other):
11026 return Concat(self, other)
11028 def __radd__(self, other):
11029 return Concat(other, self)
11031 def __getitem__(self, i):
11033 i = IntVal(i, self.ctx)
11034 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11038 i = IntVal(i, self.ctx)
11039 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
11041 def is_string(self):
11042 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
11044 def is_string_value(self):
11045 return Z3_is_string(self.ctx_ref(), self.as_ast())
11047 def as_string(self):
11048 """Return a string representation of sequence expression."""
11049 if self.is_string_value():
11050 string_length = ctypes.c_uint()
11051 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
11052 return string_at(chars, size=string_length.value).decode("latin-1")
11053 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
11055 def py_value(self):
11056 return self.as_string()
11058 def __le__(self, other):
11059 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11061 def __lt__(self, other):
11062 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11064 def __ge__(self, other):
11065 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11067 def __gt__(self, other):
11068 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
11071def _coerce_char(ch, ctx=None):
11072 if isinstance(ch, str):
11073 ctx = _get_ctx(ctx)
11074 ch = CharVal(ch, ctx)
11075 if not is_expr(ch):
11076 raise Z3Exception("Character expression expected")
11079class CharRef(ExprRef):
11080 """Character expression."""
11082 def __le__(self, other):
11083 other = _coerce_char(other, self.ctx)
11084 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
11087 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
11090 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
11092 def is_digit(self):
11093 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
11096def CharVal(ch, ctx=None):
11097 ctx = _get_ctx(ctx)
11098 if isinstance(ch, str):
11100 if not isinstance(ch, int):
11101 raise Z3Exception("character value should be an ordinal")
11102 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
11105 if not is_expr(bv):
11106 raise Z3Exception("Bit-vector expression needed")
11107 return _to_expr_ref(Z3_mk_char_from_bv(bv.ctx_ref(), bv.as_ast()), bv.ctx)
11109def CharToBv(ch, ctx=None):
11110 ch = _coerce_char(ch, ctx)
11113def CharToInt(ch, ctx=None):
11114 ch = _coerce_char(ch, ctx)
11117def CharIsDigit(ch, ctx=None):
11118 ch = _coerce_char(ch, ctx)
11119 return ch.is_digit()
11121def _coerce_seq(s, ctx=None):
11122 if isinstance(s, str):
11123 ctx = _get_ctx(ctx)
11124 s = StringVal(s, ctx)
11126 raise Z3Exception("Non-expression passed as a sequence")
11128 raise Z3Exception("Non-sequence passed as a sequence")
11132def _get_ctx2(a, b, ctx=None):
11143 """Return `True` if `a` is a Z3 sequence expression.
11144 >>> print (is_seq(Unit(IntVal(0))))
11146 >>> print (is_seq(StringVal("abc")))
11149 return isinstance(a, SeqRef)
11152def is_string(a: Any) -> bool:
11153 """Return `True` if `a` is a Z3 string expression.
11154 >>> print (is_string(StringVal("ab")))
11157 return isinstance(a, SeqRef) and a.is_string()
11160def is_string_value(a: Any) -> bool:
11161 """return 'True' if 'a' is a Z3 string constant expression.
11162 >>> print (is_string_value(StringVal("a")))
11164 >>> print (is_string_value(StringVal("a") + StringVal("b")))
11167 return isinstance(a, SeqRef) and a.is_string_value()
11169def StringVal(s, ctx=None):
11170 """create a string expression"""
11171 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
11172 ctx = _get_ctx(ctx)
11173 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
11176def String(name, ctx=None):
11177 """Return a string constant named `name`. If `ctx=None`, then the global context is used.
11179 >>> x = String('x')
11181 ctx = _get_ctx(ctx)
11182 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
11185def Strings(names, ctx=None):
11186 """Return a tuple of String constants. """
11187 ctx = _get_ctx(ctx)
11188 if isinstance(names, str):
11189 names = names.split(" ")
11190 return [String(name, ctx) for name in names]
11193def SubString(s, offset, length):
11194 """Extract substring or subsequence starting at offset"""
11195 return Extract(s, offset, length)
11198def SubSeq(s, offset, length):
11199 """Extract substring or subsequence starting at offset"""
11200 return Extract(s, offset, length)
11204 """Create the empty sequence of the given sort
11205 >>> e = Empty(StringSort())
11206 >>> e2 = StringVal("")
11207 >>> print(e.eq(e2))
11209 >>> e3 = Empty(SeqSort(IntSort()))
11212 >>> e4 = Empty(ReSort(SeqSort(IntSort())))
11214 Empty(ReSort(Seq(Int)))
11216 if isinstance(s, SeqSortRef):
11217 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11218 if isinstance(s, ReSortRef):
11219 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11220 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11224 """Create the regular expression that accepts the universal language
11225 >>> e = Full(ReSort(SeqSort(IntSort())))
11227 Full(ReSort(Seq(Int)))
11228 >>> e1 = Full(ReSort(StringSort()))
11230 Full(ReSort(String))
11232 if isinstance(s, ReSortRef):
11233 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11234 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11239 """Create a singleton sequence"""
11240 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11244 """Check if 'a' is a prefix of 'b'
11245 >>> s1 = PrefixOf("ab", "abc")
11248 >>> s2 = PrefixOf("bc", "abc")
11252 ctx = _get_ctx2(a, b)
11253 a = _coerce_seq(a, ctx)
11254 b = _coerce_seq(b, ctx)
11255 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11259 """Check if 'a' is a suffix of 'b'
11260 >>> s1 = SuffixOf("ab", "abc")
11263 >>> s2 = SuffixOf("bc", "abc")
11267 ctx = _get_ctx2(a, b)
11268 a = _coerce_seq(a, ctx)
11269 b = _coerce_seq(b, ctx)
11270 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11274 """Check if 'a' contains 'b'
11275 >>> s1 = Contains("abc", "ab")
11278 >>> s2 = Contains("abc", "bc")
11281 >>> x, y, z = Strings('x y z')
11282 >>> s3 = Contains(Concat(x,y,z), y)
11286 ctx = _get_ctx2(a, b)
11287 a = _coerce_seq(a, ctx)
11288 b = _coerce_seq(b, ctx)
11289 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11292def Replace(s, src, dst):
11293 """Replace the first occurrence of 'src' by 'dst' in 's'
11294 >>> r = Replace("aaa", "a", "b")
11298 ctx = _get_ctx2(dst, s)
11299 if ctx is None and is_expr(src):
11301 src = _coerce_seq(src, ctx)
11302 dst = _coerce_seq(dst, ctx)
11303 s = _coerce_seq(s, ctx)
11304 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11307def IndexOf(s, substr, offset=None):
11308 """Retrieve the index of substring within a string starting at a specified offset.
11309 >>> simplify(IndexOf("abcabc", "bc", 0))
11311 >>> simplify(IndexOf("abcabc", "bc", 2))
11317 if is_expr(offset):
11319 ctx = _get_ctx2(s, substr, ctx)
11320 s = _coerce_seq(s, ctx)
11321 substr = _coerce_seq(substr, ctx)
11322 if _is_int(offset):
11323 offset = IntVal(offset, ctx)
11324 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11327def LastIndexOf(s, substr):
11328 """Retrieve the last index of substring within a string"""
11330 ctx = _get_ctx2(s, substr, ctx)
11331 s = _coerce_seq(s, ctx)
11332 substr = _coerce_seq(substr, ctx)
11333 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11337 """Obtain the length of a sequence 's'
11338 >>> l = Length(StringVal("abc"))
11343 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11346 """Map function 'f' over sequence 's'"""
11347 ctx = _get_ctx2(f, s)
11348 s = _coerce_seq(s, ctx)
11349 return _to_expr_ref(Z3_mk_seq_map(s.ctx_ref(), f.as_ast(), s.as_ast()), ctx)
11351def SeqMapI(f, i, s):
11352 """Map function 'f' over sequence 's' at index 'i'"""
11353 ctx = _get_ctx2(f, s)
11354 s = _coerce_seq(s, ctx)
11357 return _to_expr_ref(Z3_mk_seq_mapi(s.ctx_ref(), f.as_ast(), i.as_ast(), s.as_ast()), ctx)
11359def SeqFoldLeft(f, a, s):
11360 ctx = _get_ctx2(f, s)
11361 s = _coerce_seq(s, ctx)
11363 return _to_expr_ref(Z3_mk_seq_foldl(s.ctx_ref(), f.as_ast(), a.as_ast(), s.as_ast()), ctx)
11365def SeqFoldLeftI(f, i, a, s):
11366 ctx = _get_ctx2(f, s)
11367 s = _coerce_seq(s, ctx)
11370 return _to_expr_ref(Z3_mk_seq_foldli(s.ctx_ref(), f.as_ast(), i.as_ast(), a.as_ast(), s.as_ast()), ctx)
11373 """Convert string expression to integer
11374 >>> a = StrToInt("1")
11375 >>> simplify(1 == a)
11377 >>> b = StrToInt("2")
11378 >>> simplify(1 == b)
11380 >>> c = StrToInt(IntToStr(2))
11381 >>> simplify(1 == c)
11385 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11389 """Convert integer expression to string"""
11392 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11396 """Convert a unit length string to integer code"""
11399 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11402 """Convert code to a string"""
11405 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11407def Re(s, ctx=None):
11408 """The regular expression that accepts sequence 's'
11410 >>> s2 = Re(StringVal("ab"))
11411 >>> s3 = Re(Unit(BoolVal(True)))
11413 s = _coerce_seq(s, ctx)
11414 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11417# Regular expressions
11419class ReSortRef(SortRef):
11420 """Regular expression sort."""
11423 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11428 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11429 if s is None or isinstance(s, Context):
11431 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11432 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11435class ReRef(ExprRef):
11436 """Regular expressions."""
11438 def __add__(self, other):
11439 return Union(self, other)
11443 return isinstance(s, ReRef)
11447 """Create regular expression membership test
11448 >>> re = Union(Re("a"),Re("b"))
11449 >>> print (simplify(InRe("a", re)))
11451 >>> print (simplify(InRe("b", re)))
11453 >>> print (simplify(InRe("c", re)))
11456 s = _coerce_seq(s, re.ctx)
11457 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11461 """Create union of regular expressions.
11462 >>> re = Union(Re("a"), Re("b"), Re("c"))
11463 >>> print (simplify(InRe("d", re)))
11466 args = _get_args(args)
11469 _z3_assert(sz > 0, "At least one argument expected.")
11470 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11475 for i in range(sz):
11476 v[i] = args[i].as_ast()
11477 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11480def Intersect(*args):
11481 """Create intersection of regular expressions.
11482 >>> re = Intersect(Re("a"), Re("b"), Re("c"))
11484 args = _get_args(args)
11487 _z3_assert(sz > 0, "At least one argument expected.")
11488 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11493 for i in range(sz):
11494 v[i] = args[i].as_ast()
11495 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11499 """Create the regular expression accepting one or more repetitions of argument.
11500 >>> re = Plus(Re("a"))
11501 >>> print(simplify(InRe("aa", re)))
11503 >>> print(simplify(InRe("ab", re)))
11505 >>> print(simplify(InRe("", re)))
11509 _z3_assert(is_expr(re), "expression expected")
11510 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11514 """Create the regular expression that optionally accepts the argument.
11515 >>> re = Option(Re("a"))
11516 >>> print(simplify(InRe("a", re)))
11518 >>> print(simplify(InRe("", re)))
11520 >>> print(simplify(InRe("aa", re)))
11524 _z3_assert(is_expr(re), "expression expected")
11525 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11529 """Create the complement regular expression."""
11530 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11534 """Create the regular expression accepting zero or more repetitions of argument.
11535 >>> re = Star(Re("a"))
11536 >>> print(simplify(InRe("aa", re)))
11538 >>> print(simplify(InRe("ab", re)))
11540 >>> print(simplify(InRe("", re)))
11544 _z3_assert(is_expr(re), "expression expected")
11545 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11548def Loop(re, lo, hi=0):
11549 """Create the regular expression accepting between a lower and upper bound repetitions
11550 >>> re = Loop(Re("a"), 1, 3)
11551 >>> print(simplify(InRe("aa", re)))
11553 >>> print(simplify(InRe("aaaa", re)))
11555 >>> print(simplify(InRe("", re)))
11559 _z3_assert(is_expr(re), "expression expected")
11560 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11563def Range(lo, hi, ctx=None):
11564 """Create the range regular expression over two sequences of length 1
11565 >>> range = Range("a","z")
11566 >>> print(simplify(InRe("b", range)))
11568 >>> print(simplify(InRe("bb", range)))
11571 lo = _coerce_seq(lo, ctx)
11572 hi = _coerce_seq(hi, ctx)
11574 _z3_assert(is_expr(lo), "expression expected")
11575 _z3_assert(is_expr(hi), "expression expected")
11576 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11578def Diff(a, b, ctx=None):
11579 """Create the difference regular expression
11582 _z3_assert(is_expr(a), "expression expected")
11583 _z3_assert(is_expr(b), "expression expected")
11584 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11586def AllChar(regex_sort, ctx=None):
11587 """Create a regular expression that accepts all single character strings
11589 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11594def PartialOrder(a, index):
11595 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11598def LinearOrder(a, index):
11599 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11602def TreeOrder(a, index):
11603 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11606def PiecewiseLinearOrder(a, index):
11607 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11610def TransitiveClosure(f):
11611 """Given a binary relation R, such that the two arguments have the same sort
11612 create the transitive closure relation R+.
11613 The transitive closure R+ is a new relation.
11615 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11619 super(ctypes.c_void_p, ast).__init__(ptr)
11622def to_ContextObj(ptr,):
11623 ctx = ContextObj(ptr)
11624 super(ctypes.c_void_p, ctx).__init__(ptr)
11627def to_AstVectorObj(ptr,):
11628 v = AstVectorObj(ptr)
11629 super(ctypes.c_void_p, v).__init__(ptr)
11632# NB. my-hacky-class only works for a single instance of OnClause
11633# it should be replaced with a proper correlation between OnClause
11634# and object references that can be passed over the FFI.
11635# for UserPropagator we use a global dictionary, which isn't great code.
11637_my_hacky_class = None
11638def on_clause_eh(ctx, p, n, dep, clause):
11639 onc = _my_hacky_class
11640 p = _to_expr_ref(to_Ast(p), onc.ctx)
11641 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11642 deps = [dep[i] for i in range(n)]
11643 onc.on_clause(p, deps, clause)
11645_on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11648 def __init__(self, s, on_clause):
11651 self.on_clause = on_clause
11653 global _my_hacky_class
11654 _my_hacky_class = self
11655 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11659 def __init__(self):
11663 def set_threaded(self):
11664 if self.lock is None:
11666 self.lock = threading.Lock()
11668 def get(self, ctx):
11671 r = self.bases[ctx]
11673 r = self.bases[ctx]
11676 def set(self, ctx, r):
11679 self.bases[ctx] = r
11681 self.bases[ctx] = r
11683 def insert(self, r):
11686 id = len(self.bases) + 3
11689 id = len(self.bases) + 3
11694_prop_closures = None
11697def ensure_prop_closures():
11698 global _prop_closures
11699 if _prop_closures is None:
11700 _prop_closures = PropClosures()
11703def user_prop_push(ctx, cb):
11704 prop = _prop_closures.get(ctx)
11709def user_prop_pop(ctx, cb, num_scopes):
11710 prop = _prop_closures.get(ctx)
11712 prop.pop(num_scopes)
11715def user_prop_fresh(ctx, _new_ctx):
11716 _prop_closures.set_threaded()
11717 prop = _prop_closures.get(ctx)
11719 Z3_del_context(nctx.ctx)
11720 new_ctx = to_ContextObj(_new_ctx)
11722 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11724 new_prop = prop.fresh(nctx)
11725 _prop_closures.set(new_prop.id, new_prop)
11729def user_prop_fixed(ctx, cb, id, value):
11730 prop = _prop_closures.get(ctx)
11733 id = _to_expr_ref(to_Ast(id), prop.ctx())
11734 value = _to_expr_ref(to_Ast(value), prop.ctx())
11735 prop.fixed(id, value)
11738def user_prop_created(ctx, cb, id):
11739 prop = _prop_closures.get(ctx)
11742 id = _to_expr_ref(to_Ast(id), prop.ctx())
11747def user_prop_final(ctx, cb):
11748 prop = _prop_closures.get(ctx)
11754def user_prop_eq(ctx, cb, x, y):
11755 prop = _prop_closures.get(ctx)
11758 x = _to_expr_ref(to_Ast(x), prop.ctx())
11759 y = _to_expr_ref(to_Ast(y), prop.ctx())
11763def user_prop_diseq(ctx, cb, x, y):
11764 prop = _prop_closures.get(ctx)
11767 x = _to_expr_ref(to_Ast(x), prop.ctx())
11768 y = _to_expr_ref(to_Ast(y), prop.ctx())
11772def user_prop_decide(ctx, cb, t_ref, idx, phase):
11773 prop = _prop_closures.get(ctx)
11776 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11777 prop.decide(t, idx, phase)
11781_user_prop_push = Z3_push_eh(user_prop_push)
11782_user_prop_pop = Z3_pop_eh(user_prop_pop)
11783_user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11784_user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11785_user_prop_created = Z3_created_eh(user_prop_created)
11786_user_prop_final = Z3_final_eh(user_prop_final)
11787_user_prop_eq = Z3_eq_eh(user_prop_eq)
11788_user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11789_user_prop_decide = Z3_decide_eh(user_prop_decide)
11792def PropagateFunction(name, *sig):
11793 """Create a function that gets tracked by user propagator.
11794 Every term headed by this function symbol is tracked.
11795 If a term is fixed and the fixed callback is registered a
11796 callback is invoked that the term headed by this function is fixed.
11798 sig = _get_args(sig)
11800 _z3_assert(len(sig) > 0, "At least two arguments expected")
11801 arity = len(sig) - 1
11804 _z3_assert(is_sort(rng), "Z3 sort expected")
11805 dom = (Sort * arity)()
11806 for i in range(arity):
11808 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11809 dom[i] = sig[i].ast
11811 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11815class UserPropagateBase:
11818 # Either solver is set or ctx is set.
11819 # Propagators that are created through callbacks
11820 # to "fresh" inherit the context of that is supplied
11821 # as argument to the callback.
11822 # This context should not be deleted. It is owned by the solver.
11824 def __init__(self, s, ctx=None):
11825 assert s is None or ctx is None
11826 ensure_prop_closures()
11829 self.fresh_ctx = None
11831 self.id = _prop_closures.insert(self)
11837 self.created = None
11839 self.fresh_ctx = ctx
11841 Z3_solver_propagate_init(self.ctx_ref(),
11843 ctypes.c_void_p(self.id),
11850 self._ctx.ctx = None
11854 return self.fresh_ctx
11856 return self.solver.ctx
11859 return self.ctx().ref()
11861 def add_fixed(self, fixed):
11862 assert not self.fixed
11863 assert not self._ctx
11865 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11868 def add_created(self, created):
11869 assert not self.created
11870 assert not self._ctx
11872 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11873 self.created = created
11875 def add_final(self, final):
11876 assert not self.final
11877 assert not self._ctx
11879 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11882 def add_eq(self, eq):
11884 assert not self._ctx
11886 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11889 def add_diseq(self, diseq):
11890 assert not self.diseq
11891 assert not self._ctx
11893 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11896 def add_decide(self, decide):
11897 assert not self.decide
11898 assert not self._ctx
11900 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11901 self.decide = decide
11904 raise Z3Exception("push needs to be overwritten")
11906 def pop(self, num_scopes):
11907 raise Z3Exception("pop needs to be overwritten")
11909 def fresh(self, new_ctx):
11910 raise Z3Exception("fresh needs to be overwritten")
11913 assert not self._ctx
11915 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11917 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11920 # Tell the solver to perform the next split on a given term
11921 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11922 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11924 def next_split(self, t, idx, phase):
11925 return Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11928 # Propagation can only be invoked as during a fixed or final callback.
11930 def propagate(self, e, ids, eqs=[]):
11931 _ids, num_fixed = _to_ast_array(ids)
11933 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11934 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11935 return Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11936 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11938 def conflict(self, deps = [], eqs = []):
11939 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
approx(self, precision=10)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, m=None, ctx=None)
__deepcopy__(self, memo={})
__init__(self, ast, ctx=None)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__init__(self, v=None, ctx=None)
__rtruediv__(self, other)
__deepcopy__(self, memo={})
__init__(self, *args, **kws)
__deepcopy__(self, memo={})
__init__(self, name, ctx=None)
declare(self, name, *args)
declare_core(self, name, rec_name, *args)
__deepcopy__(self, memo={})
__init__(self, entry, ctx)
__deepcopy__(self, memo={})
translate(self, other_ctx)
__deepcopy__(self, memo={})
assert_exprs(self, *args)
dimacs(self, include_names=True)
simplify(self, *arguments, **keywords)
convert_model(self, model)
__init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
__deepcopy__(self, memo={})
eval(self, t, model_completion=False)
project_with_witness(self, vars, fml)
update_value(self, x, value)
evaluate(self, t, model_completion=False)
__deepcopy__(self, memo={})
__init__(self, descr, ctx=None)
get_documentation(self, n)
__deepcopy__(self, memo={})
__init__(self, ctx=None, params=None)
denominator_as_long(self)
Strings, Sequences and Regular expressions.
__init__(self, solver=None, ctx=None, logFile=None)
assert_and_track(self, a, p)
import_model_converter(self, other)
assert_exprs(self, *args)
check(self, *assumptions)
__exit__(self, *exc_info)
__deepcopy__(self, memo={})
__init__(self, stats, ctx)
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_sort Z3_API Z3_mk_int_sort(Z3_context c)
Create the integer type.
Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const *domain, Z3_sort range)
Create an array type with N arguments.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_denominator(Z3_context c, Z3_ast a)
Return the denominator (as a numeral AST) of a numeral AST of sort Real.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
void Z3_API Z3_solver_assert_and_track(Z3_context c, Z3_solver s, Z3_ast a, Z3_ast p)
Assert a constraint a into the solver, and track it (in the unsat) core using the Boolean constant p.
Z3_ast Z3_API Z3_func_interp_get_else(Z3_context c, Z3_func_interp f)
Return the 'else' value of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsge(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than or equal to.
void Z3_API Z3_ast_map_inc_ref(Z3_context c, Z3_ast_map m)
Increment the reference counter of the given AST map.
Z3_ast Z3_API Z3_mk_const_array(Z3_context c, Z3_sort domain, Z3_ast v)
Create the constant array.
Z3_ast Z3_API Z3_mk_bvsle(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than or equal to.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_ast Z3_API Z3_ast_map_find(Z3_context c, Z3_ast_map m, Z3_ast k)
Return the value associated with the key k.
Z3_string Z3_API Z3_ast_map_to_string(Z3_context c, Z3_ast_map m)
Convert the given map into a string.
Z3_string Z3_API Z3_param_descrs_to_string(Z3_context c, Z3_param_descrs p)
Convert a parameter description set into a string. This function is mainly used for printing the cont...
Z3_ast Z3_API Z3_mk_zero_ext(Z3_context c, unsigned i, Z3_ast t1)
Extend the given bit-vector with zeros to the (unsigned) equivalent bit-vector of size m+i,...
void Z3_API Z3_solver_set_params(Z3_context c, Z3_solver s, Z3_params p)
Set the given solver using the given parameters.
Z3_ast Z3_API Z3_mk_set_intersect(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the intersection of a list of sets.
Z3_params Z3_API Z3_mk_params(Z3_context c)
Create a Z3 (empty) parameter set. Starting at Z3 4.0, parameter sets are used to configure many comp...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
Z3_ast Z3_API Z3_mk_set_subset(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Check for subsetness of sets.
Z3_ast Z3_API Z3_mk_bvule(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than or equal to.
Z3_ast Z3_API Z3_mk_full_set(Z3_context c, Z3_sort domain)
Create the full set.
Z3_param_kind Z3_API Z3_param_descrs_get_kind(Z3_context c, Z3_param_descrs p, Z3_symbol n)
Return the kind associated with the given parameter name n.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
Z3_ast Z3_API Z3_mk_true(Z3_context c)
Create an AST node representing true.
Z3_ast Z3_API Z3_mk_set_union(Z3_context c, unsigned num_args, Z3_ast const args[])
Take the union of a list of sets.
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
Z3_ast Z3_API Z3_mk_bvsdiv_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed division of t1 and t2 does not overflow.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
void Z3_API Z3_ast_vector_set(Z3_context c, Z3_ast_vector v, unsigned i, Z3_ast a)
Update position i of the AST vector v with the AST a.
Z3_ast Z3_API Z3_mk_bvxor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise exclusive-or.
Z3_string Z3_API Z3_stats_to_string(Z3_context c, Z3_stats s)
Convert a statistics into a string.
Z3_sort Z3_API Z3_mk_real_sort(Z3_context c)
Create the real type.
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, unsigned num_bound, Z3_app const bound[], Z3_ast body)
Create a lambda expression using a list of constants that form the set of bound variables.
void Z3_API Z3_solver_dec_ref(Z3_context c, Z3_solver s)
Decrement the reference counter of the given solver.
Z3_ast Z3_API Z3_mk_bvslt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed less than.
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
bool Z3_API Z3_ast_map_contains(Z3_context c, Z3_ast_map m, Z3_ast k)
Return true if the map m contains the AST key k.
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_symbol Z3_API Z3_get_quantifier_skolem_id(Z3_context c, Z3_ast a)
Obtain skolem id of quantifier.
Z3_ast Z3_API Z3_get_numerator(Z3_context c, Z3_ast a)
Return the numerator (as a numeral AST) of a numeral AST of sort Real.
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.
Z3_ast Z3_API Z3_mk_and(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] and ... and args[num_args-1].
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers,...
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
Z3_symbol Z3_API Z3_param_descrs_get_name(Z3_context c, Z3_param_descrs p, unsigned i)
Return the name of the parameter at given index i.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
Z3_ast Z3_API Z3_mk_false(Z3_context c)
Create an AST node representing false.
Z3_ast_vector Z3_API Z3_ast_map_keys(Z3_context c, Z3_ast_map m)
Return the keys stored in the given map.
Z3_ast Z3_API Z3_mk_bvmul(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement multiplication.
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null,...
void Z3_API Z3_del_constructor(Z3_context c, Z3_constructor constr)
Reclaim memory allocated to constructor.
Z3_ast Z3_API Z3_mk_bvsgt(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed greater than.
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context....
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_mk_set_complement(Z3_context c, Z3_ast arg)
Take the complement of a set.
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.
bool Z3_API Z3_stats_is_uint(Z3_context c, Z3_stats s, unsigned idx)
Return true if the given statistical data is a unsigned integer.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_ast Z3_API Z3_mk_extract(Z3_context c, unsigned high, unsigned low, Z3_ast t1)
Extract the bits high down to low from a bit-vector of size m to yield a new bit-vector of size n,...
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.
Z3_ast Z3_API Z3_mk_bvredand(Z3_context c, Z3_ast t1)
Take conjunction of bits in vector, return vector of length 1.
Z3_ast Z3_API Z3_mk_set_add(Z3_context c, Z3_ast set, Z3_ast elem)
Add an element to a set.
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.
Z3_ast Z3_API Z3_mk_bvadd_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed addition of t1 and t2 does not underflow.
Z3_ast Z3_API Z3_mk_bvadd_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise addition of t1 and t2 does not overflow.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
Z3_ast Z3_API Z3_mk_array_default(Z3_context c, Z3_ast array)
Access the array default value. Produces the default range value, for arrays that can be represented ...
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.
Z3_ast_vector Z3_API Z3_ast_vector_translate(Z3_context s, Z3_ast_vector v, Z3_context t)
Translate the AST vector v from context s into an AST vector in context t.
void Z3_API Z3_func_entry_inc_ref(Z3_context c, Z3_func_entry e)
Increment the reference counter of the given Z3_func_entry object.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.
Z3_ast Z3_API Z3_mk_bvsub_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed subtraction of t1 and t2 does not overflow.
void Z3_API Z3_solver_push(Z3_context c, Z3_solver s)
Create a backtracking point.
Z3_ast Z3_API Z3_mk_bvsub_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise subtraction of t1 and t2 does not underflow.
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
Z3_ast Z3_API Z3_mk_bvudiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned division.
Z3_string Z3_API Z3_ast_vector_to_string(Z3_context c, Z3_ast_vector v)
Convert AST vector into a string.
Z3_ast Z3_API Z3_mk_bvshl(Z3_context c, Z3_ast t1, Z3_ast t2)
Shift left.
bool Z3_API Z3_is_numeral_ast(Z3_context c, Z3_ast a)
Z3_ast Z3_API Z3_mk_bvsrem(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows dividend).
bool Z3_API Z3_is_as_array(Z3_context c, Z3_ast a)
The (_ as-array f) AST node is a construct for assigning interpretations for arrays in Z3....
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
Z3_ast Z3_API Z3_mk_is_int(Z3_context c, Z3_ast t1)
Check if a real number is an integer.
void Z3_API Z3_params_set_bool(Z3_context c, Z3_params p, Z3_symbol k, bool v)
Add a Boolean parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.
Z3_ast Z3_API Z3_mk_sign_ext(Z3_context c, unsigned i, Z3_ast t1)
Sign-extend of the given bit-vector to the (signed) equivalent bit-vector of size m+i,...
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
void Z3_API Z3_stats_inc_ref(Z3_context c, Z3_stats s)
Increment the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs)
n-ary Array read. The argument a is the array and idxs are the indices of the array that gets read.
Z3_ast_vector Z3_API Z3_algebraic_get_poly(Z3_context c, Z3_ast a)
Return the coefficients of the defining polynomial.
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
void Z3_API Z3_func_interp_inc_ref(Z3_context c, Z3_func_interp f)
Increment the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_set_double(Z3_context c, Z3_params p, Z3_symbol k, double v)
Add a double parameter k with value v to the parameter set p.
Z3_string Z3_API Z3_param_descrs_get_documentation(Z3_context c, Z3_param_descrs p, Z3_symbol s)
Retrieve documentation string corresponding to parameter name s.
Z3_sort Z3_API Z3_mk_datatype_sort(Z3_context c, Z3_symbol name)
create a forward reference to a recursive datatype being declared. The forward reference can be used ...
Z3_solver Z3_API Z3_mk_solver(Z3_context c)
Create a new solver. This solver is a "combined solver" (see combined_solver module) that internally ...
Z3_model Z3_API Z3_solver_get_model(Z3_context c, Z3_solver s)
Retrieve the model for the last Z3_solver_check or Z3_solver_check_assumptions.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
Z3_func_decl Z3_API Z3_get_as_array_func_decl(Z3_context c, Z3_ast a)
Return the function declaration f associated with a (_ as_array f) node.
Z3_ast Z3_API Z3_mk_ext_rotate_left(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the left t2 times.
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_implies(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 implies t2.
unsigned Z3_API Z3_get_datatype_sort_num_constructors(Z3_context c, Z3_sort t)
Return number of constructors for datatype.
void Z3_API Z3_params_set_uint(Z3_context c, Z3_params p, Z3_symbol k, unsigned v)
Add a unsigned parameter k with value v to the parameter set p.
Z3_lbool Z3_API Z3_solver_check_assumptions(Z3_context c, Z3_solver s, unsigned num_assumptions, Z3_ast const assumptions[])
Check whether the assertions in the given solver and optional assumptions are consistent or not.
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.
Z3_ast Z3_API Z3_mk_bvashr(Z3_context c, Z3_ast t1, Z3_ast t2)
Arithmetic shift right.
Z3_ast Z3_API Z3_mk_bv2int(Z3_context c, Z3_ast t1, bool is_signed)
Create an integer from the bit-vector argument t1. If is_signed is false, then the bit-vector t1 is t...
Z3_sort Z3_API Z3_get_array_sort_domain_n(Z3_context c, Z3_sort t, unsigned idx)
Return the i'th domain sort of an n-dimensional array.
Z3_ast Z3_API Z3_mk_set_del(Z3_context c, Z3_ast set, Z3_ast elem)
Remove an element to a set.
Z3_ast Z3_API Z3_mk_bvmul_no_overflow(Z3_context c, Z3_ast t1, Z3_ast t2, bool is_signed)
Create a predicate that checks that the bit-wise multiplication of t1 and t2 does not overflow.
Z3_ast Z3_API Z3_mk_bvor(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise or.
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th constructor.
void Z3_API Z3_ast_vector_resize(Z3_context c, Z3_ast_vector v, unsigned n)
Resize the AST vector v.
Z3_ast Z3_API Z3_mk_quantifier_const_ex(Z3_context c, bool is_forall, unsigned weight, Z3_symbol quantifier_id, Z3_symbol skolem_id, unsigned num_bound, Z3_app const bound[], unsigned num_patterns, Z3_pattern const patterns[], unsigned num_no_patterns, Z3_ast const no_patterns[], Z3_ast body)
Create a universal or existential quantifier using a list of constants that will form the set of boun...
Z3_pattern Z3_API Z3_mk_pattern(Z3_context c, unsigned num_patterns, Z3_ast const terms[])
Create a pattern for quantifier instantiation.
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.
unsigned Z3_API Z3_stats_get_uint_value(Z3_context c, Z3_stats s, unsigned idx)
Return the unsigned value of the given statistical data.
Z3_sort Z3_API Z3_get_array_sort_domain(Z3_context c, Z3_sort t)
Return the domain of the given array sort. In the case of a multi-dimensional array,...
Z3_ast Z3_API Z3_mk_bvmul_no_underflow(Z3_context c, Z3_ast t1, Z3_ast t2)
Create a predicate that checks that the bit-wise signed multiplication of t1 and t2 does not underflo...
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
Z3_ast Z3_API Z3_mk_bvadd(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement addition.
unsigned Z3_API Z3_algebraic_get_i(Z3_context c, Z3_ast a)
Return which root of the polynomial the algebraic number represents.
void Z3_API Z3_params_dec_ref(Z3_context c, Z3_params p)
Decrement the reference counter of the given parameter set.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
unsigned Z3_API Z3_ast_map_size(Z3_context c, Z3_ast_map m)
Return the size of the given map.
unsigned Z3_API Z3_param_descrs_size(Z3_context c, Z3_param_descrs p)
Return the number of parameters in the given parameter description set.
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
double Z3_API Z3_stats_get_double_value(Z3_context c, Z3_stats s, unsigned idx)
Return the double value of the given statistical data.
Z3_ast Z3_API Z3_mk_bvugt(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than.
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_ast Z3_API Z3_pattern_to_ast(Z3_context c, Z3_pattern p)
Convert a Z3_pattern into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_bvnot(Z3_context c, Z3_ast t1)
Bitwise negation.
Z3_ast Z3_API Z3_mk_bvurem(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned remainder.
void Z3_API Z3_mk_datatypes(Z3_context c, unsigned num_sorts, Z3_symbol const sort_names[], Z3_sort sorts[], Z3_constructor_list constructor_lists[])
Create mutually recursive datatypes.
unsigned Z3_API Z3_func_interp_get_arity(Z3_context c, Z3_func_interp f)
Return the arity (number of arguments) of the given function interpretation.
Z3_ast Z3_API Z3_mk_bvsub(Z3_context c, Z3_ast t1, Z3_ast t2)
Standard two's complement subtraction.
Z3_ast Z3_API Z3_get_algebraic_number_upper(Z3_context c, Z3_ast a, unsigned precision)
Return a upper bound for the given real algebraic number. The interval isolating the number is smalle...
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.
Z3_ast Z3_API Z3_mk_seq_concat(Z3_context c, unsigned n, Z3_ast const args[])
Concatenate sequences.
Z3_sort Z3_API Z3_mk_enumeration_sort(Z3_context c, Z3_symbol name, unsigned n, Z3_symbol const enum_names[], Z3_func_decl enum_consts[], Z3_func_decl enum_testers[])
Create a enumeration sort.
unsigned Z3_API Z3_get_bv_sort_size(Z3_context c, Z3_sort t)
Return the size of the given bit-vector sort.
Z3_ast Z3_API Z3_mk_set_member(Z3_context c, Z3_ast elem, Z3_ast set)
Check for set membership.
void Z3_API Z3_ast_vector_dec_ref(Z3_context c, Z3_ast_vector v)
Decrement the reference counter of the given AST vector.
void Z3_API Z3_func_interp_dec_ref(Z3_context c, Z3_func_interp f)
Decrement the reference counter of the given Z3_func_interp object.
void Z3_API Z3_params_inc_ref(Z3_context c, Z3_params p)
Increment the reference counter of the given parameter set.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
Z3_sort Z3_API Z3_mk_bv_sort(Z3_context c, unsigned sz)
Create a bit-vector type of the given size.
Z3_ast Z3_API Z3_mk_bvult(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned less than.
void Z3_API Z3_ast_map_dec_ref(Z3_context c, Z3_ast_map m)
Decrement the reference counter of the given AST map.
Z3_string Z3_API Z3_params_to_string(Z3_context c, Z3_params p)
Convert a parameter set into a string. This function is mainly used for printing the contents of a pa...
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.
void Z3_API Z3_func_entry_dec_ref(Z3_context c, Z3_func_entry e)
Decrement the reference counter of the given Z3_func_entry object.
unsigned Z3_API Z3_stats_size(Z3_context c, Z3_stats s)
Return the number of statistical data in s.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.
void Z3_API Z3_param_descrs_dec_ref(Z3_context c, Z3_param_descrs p)
Decrement the reference counter of the given parameter description set.
Z3_model Z3_API Z3_mk_model(Z3_context c)
Create a fresh model object. It has reference count 0.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
Z3_ast Z3_API Z3_mk_bvneg_no_overflow(Z3_context c, Z3_ast t1)
Check that bit-wise negation does not overflow when t1 is interpreted as a signed bit-vector.
Z3_string Z3_API Z3_stats_get_key(Z3_context c, Z3_stats s, unsigned idx)
Return the key (a string) for a particular statistical data.
Z3_ast Z3_API Z3_mk_bvand(Z3_context c, Z3_ast t1, Z3_ast t2)
Bitwise and.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
Z3_ast Z3_API Z3_mk_bvsmod(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed remainder (sign follows divisor).
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_ast Z3_API Z3_mk_int2bv(Z3_context c, unsigned n, Z3_ast t1)
Create an n bit bit-vector from the integer argument t1.
void Z3_API Z3_solver_assert(Z3_context c, Z3_solver s, Z3_ast a)
Assert a constraint into the solver.
unsigned Z3_API Z3_ast_vector_size(Z3_context c, Z3_ast_vector v)
Return the size of the given AST vector.
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.
unsigned Z3_API Z3_solver_get_num_scopes(Z3_context c, Z3_solver s)
Return the number of backtracking points.
Z3_sort Z3_API Z3_get_array_sort_range(Z3_context c, Z3_sort t)
Return the range of the given array sort.
void Z3_API Z3_del_constructor_list(Z3_context c, Z3_constructor_list clist)
Reclaim memory allocated for constructor list.
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_ast Z3_API Z3_func_entry_get_arg(Z3_context c, Z3_func_entry e, unsigned i)
Return an argument of a Z3_func_entry object.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
void Z3_API Z3_ast_vector_inc_ref(Z3_context c, Z3_ast_vector v)
Increment the reference counter of the given AST vector.
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast_vector Z3_API Z3_mk_ast_vector(Z3_context c)
Return an empty AST vector.
Z3_ast Z3_API Z3_mk_empty_set(Z3_context c, Z3_sort domain)
Create the empty set.
Z3_ast Z3_API Z3_mk_set_has_size(Z3_context c, Z3_ast set, Z3_ast k)
Create predicate that holds if Boolean array set has k elements set to true.
Z3_ast Z3_API Z3_mk_repeat(Z3_context c, unsigned i, Z3_ast t1)
Repeat the given bit-vector up length i.
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
void Z3_API Z3_solver_pop(Z3_context c, Z3_solver s, unsigned n)
Backtrack n backtracking points.
void Z3_API Z3_ast_map_erase(Z3_context c, Z3_ast_map m, Z3_ast k)
Erase a key from the map.
Z3_ast Z3_API Z3_mk_int2real(Z3_context c, Z3_ast t1)
Coerce an integer to a real.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
void Z3_API Z3_params_validate(Z3_context c, Z3_params p, Z3_param_descrs d)
Validate the parameter set p against the parameter description set d.
Z3_func_decl Z3_API Z3_get_datatype_sort_recognizer(Z3_context c, Z3_sort t, unsigned idx)
Return idx'th recognizer.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.
Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v)
Array update.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_ast_vector_push(Z3_context c, Z3_ast_vector v, Z3_ast a)
Add the AST a in the end of the AST vector v. The size of v is increased by one.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.
Z3_ast_map Z3_API Z3_mk_ast_map(Z3_context c)
Return an empty mapping from AST to AST.
Z3_ast Z3_API Z3_mk_xor(Z3_context c, Z3_ast t1, Z3_ast t2)
Create an AST node representing t1 xor t2.
Z3_ast Z3_API Z3_mk_map(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast const *args)
Map f on the argument arrays.
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
void Z3_API Z3_param_descrs_inc_ref(Z3_context c, Z3_param_descrs p)
Increment the reference counter of the given parameter description set.
void Z3_API Z3_stats_dec_ref(Z3_context c, Z3_stats s)
Decrement the reference counter of the given statistics object.
Z3_ast Z3_API Z3_mk_array_ext(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create array extensionality index given two arrays with the same sort. The meaning is given by the ax...
Z3_ast Z3_API Z3_mk_re_concat(Z3_context c, unsigned n, Z3_ast const args[])
Create the concatenation of the regular languages.
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
Z3_func_entry Z3_API Z3_func_interp_get_entry(Z3_context c, Z3_func_interp f, unsigned i)
Return a "point" of the given function interpretation. It represents the value of f in a particular p...
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....
Z3_ast Z3_API Z3_mk_concat(Z3_context c, Z3_ast t1, Z3_ast t2)
Concatenate the given bit-vectors.
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
Z3_constructor_list Z3_API Z3_mk_constructor_list(Z3_context c, unsigned num_constructors, Z3_constructor const constructors[])
Create list of constructors.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
Z3_ast Z3_API Z3_mk_bvneg(Z3_context c, Z3_ast t1)
Standard two's complement unary minus.
Z3_ast Z3_API Z3_mk_store_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const *idxs, Z3_ast v)
n-ary Array update.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
Z3_sort Z3_API Z3_mk_bool_sort(Z3_context c)
Create the Boolean type.
void Z3_API Z3_params_set_symbol(Z3_context c, Z3_params p, Z3_symbol k, Z3_symbol v)
Add a symbol parameter k with value v to the parameter set p.
Z3_ast Z3_API Z3_ast_vector_get(Z3_context c, Z3_ast_vector v, unsigned i)
Return the AST at position i in the AST vector v.
Z3_func_decl Z3_API Z3_to_func_decl(Z3_context c, Z3_ast a)
Convert an AST into a FUNC_DECL_AST. This is just type casting.
Z3_ast Z3_API Z3_mk_set_difference(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Take the set difference between two sets.
Z3_ast Z3_API Z3_mk_bvsdiv(Z3_context c, Z3_ast t1, Z3_ast t2)
Two's complement signed division.
Z3_ast Z3_API Z3_mk_bvlshr(Z3_context c, Z3_ast t1, Z3_ast t2)
Logical shift right.
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.
Z3_ast Z3_API Z3_mk_not(Z3_context c, Z3_ast a)
Create an AST node representing not(a).
Z3_ast Z3_API Z3_mk_or(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] or ... or args[num_args-1].
Z3_sort Z3_API Z3_mk_array_sort(Z3_context c, Z3_sort domain, Z3_sort range)
Create an array type.
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
Z3_ast Z3_API Z3_mk_seq_extract(Z3_context c, Z3_ast s, Z3_ast offset, Z3_ast length)
Extract subsequence starting at offset of length.
Z3_sort Z3_API Z3_mk_type_variable(Z3_context c, Z3_symbol s)
Create a type variable.
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.
Z3_ast Z3_API Z3_mk_bvuge(Z3_context c, Z3_ast t1, Z3_ast t2)
Unsigned greater than or equal to.
Z3_string Z3_API Z3_get_numeral_binary_string(Z3_context c, Z3_ast a)
Return numeral value, as a binary string of a numeric constant term.
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise.
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
unsigned Z3_API Z3_func_interp_get_num_entries(Z3_context c, Z3_func_interp f)
Return the number of entries in the given function interpretation.
void Z3_API Z3_ast_map_insert(Z3_context c, Z3_ast_map m, Z3_ast k, Z3_ast v)
Store/Replace a new key, value pair in the given map.
Z3_constructor Z3_API Z3_mk_constructor(Z3_context c, Z3_symbol name, Z3_symbol recognizer, unsigned num_fields, Z3_symbol const field_names[], Z3_sort const sorts[], unsigned sort_refs[])
Create a constructor.
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
double Z3_API Z3_get_numeral_double(Z3_context c, Z3_ast a)
Return numeral as a double.
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_real2int(Z3_context c, Z3_ast t1)
Coerce a real to an integer.
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...
void Z3_API Z3_solver_inc_ref(Z3_context c, Z3_solver s)
Increment the reference counter of the given solver.
Z3_symbol Z3_API Z3_get_quantifier_id(Z3_context c, Z3_ast a)
Obtain id of quantifier.
Z3_ast Z3_API Z3_mk_ext_rotate_right(Z3_context c, Z3_ast t1, Z3_ast t2)
Rotate bits of t1 to the right t2 times.
Z3_string Z3_API Z3_get_numeral_decimal_string(Z3_context c, Z3_ast a, unsigned precision)
Return numeral as a string in decimal notation. The result has at most precision decimal places.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_func_decl Z3_API Z3_get_datatype_sort_constructor_accessor(Z3_context c, Z3_sort t, unsigned idx_c, unsigned idx_a)
Return idx_a'th accessor for the idx_c'th constructor.
Z3_ast Z3_API Z3_mk_bvredor(Z3_context c, Z3_ast t1)
Take disjunction of bits in vector, return vector of length 1.
void Z3_API Z3_ast_map_reset(Z3_context c, Z3_ast_map m)
Remove all keys from the given map.
void Z3_API Z3_solver_reset(Z3_context c, Z3_solver s)
Remove all assertions from the solver.
bool Z3_API Z3_is_algebraic_number(Z3_context c, Z3_ast a)
Return true if the given AST is a real algebraic number.
BitVecVal(val, bv, ctx=None)
_coerce_exprs(a, b, ctx=None)
_ctx_from_ast_args(*args)
_to_func_decl_ref(a, ctx)
_valid_accessor(acc)
Datatypes.
BitVec(name, bv, ctx=None)
RecAddDefinition(f, args, body)
DeclareTypeVar(name, ctx=None)
_z3_check_cint_overflow(n, name)
TupleSort(name, sorts, ctx=None)
_coerce_expr_list(alist, ctx=None)
RealVector(prefix, sz, ctx=None)
SortRef _sort(Context ctx, Any a)
ExprRef RealVar(int idx, ctx=None)
bool is_arith_sort(Any s)
BitVecs(names, bv, ctx=None)
BoolVector(prefix, sz, ctx=None)
FreshConst(sort, prefix="c")
EnumSort(name, values, ctx=None)
simplify(a, *arguments, **keywords)
Utils.
BV2Int(a, is_signed=False)
FreshInt(prefix="x", ctx=None)
_to_func_decl_array(args)
args2params(arguments, keywords, ctx=None)
Cond(p, t1, t2, ctx=None)
RealVarVector(int n, ctx=None)
bool eq(AstRef a, AstRef b)
FreshReal(prefix="b", ctx=None)
_reduce(func, sequence, initial)
ExprRef Var(int idx, SortRef s)
BVAddNoOverflow(a, b, signed)
FreshBool(prefix="b", ctx=None)
_ctx_from_ast_arg_list(args, default_ctx=None)
IntVector(prefix, sz, ctx=None)
DisjointSum(name, sorts, ctx=None)
Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
int _ast_kind(Context ctx, Any a)
BVSubNoUnderflow(a, b, signed)
DatatypeSort(name, ctx=None)
SortRef DeclareSort(name, ctx=None)
BVMulNoOverflow(a, b, signed)
_mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])