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Z3
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Z3
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Functions | |
| def | enable_trace (msg) |
| def | disable_trace (msg) |
| def | get_version_string () |
| def | get_version () |
| def | get_full_version () |
| def | open_log (fname) |
| def | append_log (s) |
| def | to_symbol (s, ctx=None) |
| def | main_ctx () |
| def | set_param (*args, **kws) |
| def | reset_params () |
| def | set_option (*args, **kws) |
| def | get_param (name) |
| def | is_ast (a) |
| def | eq (a, b) |
| def | is_sort (s) |
| def | DeclareSort (name, ctx=None) |
| def | is_func_decl (a) |
| def | Function (name, *sig) |
| def | is_expr (a) |
| def | is_app (a) |
| def | is_const (a) |
| def | is_var (a) |
| def | get_var_index (a) |
| def | is_app_of (a, k) |
| def | If (a, b, c, ctx=None) |
| def | Distinct (*args) |
| def | Const (name, sort) |
| def | Consts (names, sort) |
| def | Var (idx, s) |
| def | RealVar (idx, ctx=None) |
| def | RealVarVector (n, ctx=None) |
| def | is_bool (a) |
| def | is_true (a) |
| def | is_false (a) |
| def | is_and (a) |
| def | is_or (a) |
| def | is_not (a) |
| def | is_eq (a) |
| def | is_distinct (a) |
| def | BoolSort (ctx=None) |
| def | BoolVal (val, ctx=None) |
| def | Bool (name, ctx=None) |
| def | Bools (names, ctx=None) |
| def | BoolVector (prefix, sz, ctx=None) |
| def | FreshBool (prefix='b', ctx=None) |
| def | Implies (a, b, ctx=None) |
| def | Xor (a, b, ctx=None) |
| def | Not (a, ctx=None) |
| def | And (*args) |
| def | Or (*args) |
| def | is_pattern (a) |
| def | MultiPattern (*args) |
| def | is_quantifier (a) |
| def | ForAll (vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]) |
| def | Exists (vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]) |
| def | is_arith_sort (s) |
| def | is_arith (a) |
| def | is_int (a) |
| def | is_real (a) |
| def | is_int_value (a) |
| def | is_rational_value (a) |
| def | is_algebraic_value (a) |
| def | is_add (a) |
| def | is_mul (a) |
| def | is_sub (a) |
| def | is_div (a) |
| def | is_idiv (a) |
| def | is_mod (a) |
| def | is_le (a) |
| def | is_lt (a) |
| def | is_ge (a) |
| def | is_gt (a) |
| def | is_is_int (a) |
| def | is_to_real (a) |
| def | is_to_int (a) |
| def | IntSort (ctx=None) |
| def | RealSort (ctx=None) |
| def | IntVal (val, ctx=None) |
| def | RealVal (val, ctx=None) |
| def | RatVal (a, b, ctx=None) |
| def | Q (a, b, ctx=None) |
| def | Int (name, ctx=None) |
| def | Ints (names, ctx=None) |
| def | IntVector (prefix, sz, ctx=None) |
| def | FreshInt (prefix='x', ctx=None) |
| def | Real (name, ctx=None) |
| def | Reals (names, ctx=None) |
| def | RealVector (prefix, sz, ctx=None) |
| def | FreshReal (prefix='b', ctx=None) |
| def | ToReal (a) |
| def | ToInt (a) |
| def | IsInt (a) |
| def | Sqrt (a, ctx=None) |
| def | Cbrt (a, ctx=None) |
| def | is_bv_sort (s) |
| def | is_bv (a) |
| def | is_bv_value (a) |
| def | BV2Int (a, is_signed=False) |
| def | BitVecSort (sz, ctx=None) |
| def | BitVecVal (val, bv, ctx=None) |
| def | BitVec (name, bv, ctx=None) |
| def | BitVecs (names, bv, ctx=None) |
| def | Concat (*args) |
| def | Extract (high, low, a) |
| def | ULE (a, b) |
| def | ULT (a, b) |
| def | UGE (a, b) |
| def | UGT (a, b) |
| def | UDiv (a, b) |
| def | URem (a, b) |
| def | SRem (a, b) |
| def | LShR (a, b) |
| def | RotateLeft (a, b) |
| def | RotateRight (a, b) |
| def | SignExt (n, a) |
| def | ZeroExt (n, a) |
| def | RepeatBitVec (n, a) |
| def | BVRedAnd (a) |
| def | BVRedOr (a) |
| def | is_array (a) |
| def | is_const_array (a) |
| def | is_K (a) |
| def | is_map (a) |
| def | is_default (a) |
| def | get_map_func (a) |
| def | ArraySort (d, r) |
| def | Array (name, dom, rng) |
| def | Update (a, i, v) |
| def | Default (a) |
| def | Store (a, i, v) |
| def | Select (a, i) |
| def | Map (f, *args) |
| def | K (dom, v) |
| def | Ext (a, b) |
| def | is_select (a) |
| def | is_store (a) |
| def | CreateDatatypes (*ds) |
| def | EnumSort (name, values, ctx=None) |
| def | args2params (arguments, keywords, ctx=None) |
| def | is_as_array (n) |
| def | get_as_array_func (n) |
| def | SolverFor (logic, ctx=None) |
| def | SimpleSolver (ctx=None) |
| def | FiniteDomainSort (name, sz, ctx=None) |
| def | is_finite_domain_sort (s) |
| def | is_finite_domain (a) |
| def | FiniteDomainVal (val, sort, ctx=None) |
| def | is_finite_domain_value (a) |
| def | AndThen (*ts, **ks) |
| def | Then (*ts, **ks) |
| def | OrElse (*ts, **ks) |
| def | ParOr (*ts, **ks) |
| def | ParThen (t1, t2, ctx=None) |
| def | ParAndThen (t1, t2, ctx=None) |
| def | With (t, *args, **keys) |
| def | Repeat (t, max=4294967295, ctx=None) |
| def | TryFor (t, ms, ctx=None) |
| def | tactics (ctx=None) |
| def | tactic_description (name, ctx=None) |
| def | describe_tactics () |
| def | is_probe (p) |
| def | probes (ctx=None) |
| def | probe_description (name, ctx=None) |
| def | describe_probes () |
| def | FailIf (p, ctx=None) |
| def | When (p, t, ctx=None) |
| def | Cond (p, t1, t2, ctx=None) |
| def | simplify (a, *arguments, **keywords) |
| Utils. More... | |
| def | help_simplify () |
| def | simplify_param_descrs () |
| def | substitute (t, *m) |
| def | substitute_vars (t, *m) |
| def | Sum (*args) |
| def | Product (*args) |
| def | AtMost (*args) |
| def | AtLeast (*args) |
| def | PbLe (args, k) |
| def | PbEq (args, k) |
| def | solve (*args, **keywords) |
| def | solve_using (s, *args, **keywords) |
| def | prove (claim, **keywords) |
| def | parse_smt2_string (s, sorts={}, decls={}, ctx=None) |
| def | parse_smt2_file (f, sorts={}, decls={}, ctx=None) |
| def | Interpolant (a, ctx=None) |
| def | tree_interpolant (pat, p=None, ctx=None) |
| def | binary_interpolant (a, b, p=None, ctx=None) |
| def | sequence_interpolant (v, p=None, ctx=None) |
| def | get_default_rounding_mode (ctx=None) |
| def | set_default_rounding_mode (rm, ctx=None) |
| def | get_default_fp_sort (ctx=None) |
| def | set_default_fp_sort (ebits, sbits, ctx=None) |
| def | Float16 (ctx=None) |
| def | FloatHalf (ctx=None) |
| def | Float32 (ctx=None) |
| def | FloatSingle (ctx=None) |
| def | Float64 (ctx=None) |
| def | FloatDouble (ctx=None) |
| def | Float128 (ctx=None) |
| def | FloatQuadruple (ctx=None) |
| def | is_fp_sort (s) |
| def | is_fprm_sort (s) |
| def | RoundNearestTiesToEven (ctx=None) |
| def | RNE (ctx=None) |
| def | RoundNearestTiesToAway (ctx=None) |
| def | RNA (ctx=None) |
| def | RoundTowardPositive (ctx=None) |
| def | RTP (ctx=None) |
| def | RoundTowardNegative (ctx=None) |
| def | RTN (ctx=None) |
| def | RoundTowardZero (ctx=None) |
| def | RTZ (ctx=None) |
| def | is_fprm (a) |
| def | is_fprm_value (a) |
| def | is_fp (a) |
| def | is_fp_value (a) |
| def | FPSort (ebits, sbits, ctx=None) |
| def | fpNaN (s) |
| def | fpPlusInfinity (s) |
| def | fpMinusInfinity (s) |
| def | fpInfinity (s, negative) |
| def | fpPlusZero (s) |
| def | fpMinusZero (s) |
| def | fpZero (s, negative) |
| def | FPVal (sig, exp=None, fps=None, ctx=None) |
| def | FP (name, fpsort, ctx=None) |
| def | FPs (names, fpsort, ctx=None) |
| def | fpAbs (a, ctx=None) |
| def | fpNeg (a, ctx=None) |
| def | fpAdd (rm, a, b, ctx=None) |
| def | fpSub (rm, a, b, ctx=None) |
| def | fpMul (rm, a, b, ctx=None) |
| def | fpDiv (rm, a, b, ctx=None) |
| def | fpRem (a, b, ctx=None) |
| def | fpMin (a, b, ctx=None) |
| def | fpMax (a, b, ctx=None) |
| def | fpFMA (rm, a, b, c, ctx=None) |
| def | fpSqrt (rm, a, ctx=None) |
| def | fpRoundToIntegral (rm, a, ctx=None) |
| def | fpIsNaN (a, ctx=None) |
| def | fpIsInf (a, ctx=None) |
| def | fpIsZero (a, ctx=None) |
| def | fpIsNormal (a, ctx=None) |
| def | fpIsSubnormal (a, ctx=None) |
| def | fpIsNegative (a, ctx=None) |
| def | fpIsPositive (a, ctx=None) |
| def | fpLT (a, b, ctx=None) |
| def | fpLEQ (a, b, ctx=None) |
| def | fpGT (a, b, ctx=None) |
| def | fpGEQ (a, b, ctx=None) |
| def | fpEQ (a, b, ctx=None) |
| def | fpNEQ (a, b, ctx=None) |
| def | fpFP (sgn, exp, sig, ctx=None) |
| def | fpToFP (a1, a2=None, a3=None, ctx=None) |
| def | fpBVToFP (v, sort, ctx=None) |
| def | fpFPToFP (rm, v, sort, ctx=None) |
| def | fpRealToFP (rm, v, sort, ctx=None) |
| def | fpSignedToFP (rm, v, sort, ctx=None) |
| def | fpUnsignedToFP (rm, v, sort, ctx=None) |
| def | fpToFPUnsigned (rm, x, s, ctx=None) |
| def | fpToSBV (rm, x, s, ctx=None) |
| def | fpToUBV (rm, x, s, ctx=None) |
| def | fpToReal (x, ctx=None) |
| def | fpToIEEEBV (x, ctx=None) |
| def | StringSort (ctx=None) |
| def | SeqSort (s) |
| def | is_seq (a) |
| def | is_string (a) |
| def | is_string_value (a) |
| def | StringVal (s, ctx=None) |
| def | String (name, ctx=None) |
| def | Strings (names, ctx=None) |
| def | Empty (s) |
| def | Unit (a) |
| def | PrefixOf (a, b) |
| def | SuffixOf (a, b) |
| def | Contains (a, b) |
| def | Replace (s, src, dst) |
| def | IndexOf (s, substr) |
| def | IndexOf (s, substr, offset) |
| def | Length (s) |
| def | Re (s, ctx=None) |
| def | ReSort (s) |
| def | is_re (s) |
| def | InRe (s, re) |
| def | Union (*args) |
| def | Plus (re) |
| def | Option (re) |
| def | Star (re) |
Variables | |
| sat = CheckSatResult(Z3_L_TRUE) | |
| unsat = CheckSatResult(Z3_L_FALSE) | |
| unknown = CheckSatResult(Z3_L_UNDEF) | |
| def z3py.And | ( | * | args | ) |
Create a Z3 and-expression or and-probe.
>>> p, q, r = Bools('p q r')
>>> And(p, q, r)
And(p, q, r)
>>> P = BoolVector('p', 5)
>>> And(P)
And(p__0, p__1, p__2, p__3, p__4)
Definition at line 1550 of file z3py.py.
Referenced by Fixedpoint.add_rule(), Goal.as_expr(), binary_interpolant(), Fixedpoint.query(), sequence_interpolant(), and Fixedpoint.update_rule().
| def z3py.AndThen | ( | * | ts, |
| ** | ks | ||
| ) |
Return a tactic that applies the tactics in `*ts` in sequence.
>>> x, y = Ints('x y')
>>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
>>> t(And(x == 0, y > x + 1))
[[Not(y <= 1)]]
>>> t(And(x == 0, y > x + 1)).as_expr()
Not(y <= 1)
Definition at line 7049 of file z3py.py.
Referenced by Then().
| def z3py.append_log | ( | s | ) |
| def z3py.args2params | ( | arguments, | |
| keywords, | |||
ctx = None |
|||
| ) |
Convert python arguments into a Z3_params object.
A ':' is added to the keywords, and '_' is replaced with '-'
>>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
(params model true relevancy 2 elim_and true)
Definition at line 4644 of file z3py.py.
Referenced by Tactic.apply(), Solver.set(), Fixedpoint.set(), Optimize.set(), simplify(), and With().
| def z3py.Array | ( | name, | |
| dom, | |||
| rng | |||
| ) |
| def z3py.ArraySort | ( | d, | |
| r | |||
| ) |
Return the Z3 array sort with the given domain and range sorts. >>> A = ArraySort(IntSort(), BoolSort()) >>> A Array(Int, Bool) >>> A.domain() Int >>> A.range() Bool >>> AA = ArraySort(IntSort(), A) >>> AA Array(Int, Array(Int, Bool))
Definition at line 4110 of file z3py.py.
Referenced by Array(), Context.mkArraySort(), and Context.MkArraySort().
| def z3py.AtLeast | ( | * | args | ) |
| def z3py.AtMost | ( | * | args | ) |
| def z3py.binary_interpolant | ( | a, | |
| b, | |||
p = None, |
|||
ctx = None |
|||
| ) |
Compute an interpolant for a binary conjunction.
If a & b is unsatisfiable, returns an interpolant for a & b.
This is a formula phi such that
1) a implies phi
2) b implies not phi
3) All the uninterpreted symbols of phi occur in both a and b.
If a & b is satisfiable, raises an object of class ModelRef
that represents a model of a &b.
If neither a proof of unsatisfiability nor a model is obtained
(for example, because of a timeout, or because models are disabled)
then None is returned.
If parameters p are supplied, these are used in creating the
solver that determines satisfiability.
x = Int('x')
print(binary_interpolant(x<0,x>2))
Not(x >= 0)
Definition at line 7968 of file z3py.py.
| def z3py.BitVec | ( | name, | |
| bv, | |||
ctx = None |
|||
| ) |
Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
If `ctx=None`, then the global context is used.
>>> x = BitVec('x', 16)
>>> is_bv(x)
True
>>> x.size()
16
>>> x.sort()
BitVec(16)
>>> word = BitVecSort(16)
>>> x2 = BitVec('x', word)
>>> eq(x, x2)
True
Definition at line 3560 of file z3py.py.
Referenced by BitVecs().
| def z3py.BitVecs | ( | names, | |
| bv, | |||
ctx = None |
|||
| ) |
| def z3py.BitVecSort | ( | sz, | |
ctx = None |
|||
| ) |
Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
>>> Byte = BitVecSort(8)
>>> Word = BitVecSort(16)
>>> Byte
BitVec(8)
>>> x = Const('x', Byte)
>>> eq(x, BitVec('x', 8))
True
Definition at line 3530 of file z3py.py.
Referenced by BitVec(), BitVecVal(), Context.mkBitVecSort(), and Context.MkBitVecSort().
| def z3py.BitVecVal | ( | val, | |
| bv, | |||
ctx = None |
|||
| ) |
Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
>>> v = BitVecVal(10, 32)
>>> v
10
>>> print("0x%.8x" % v.as_long())
0x0000000a
| def z3py.Bool | ( | name, | |
ctx = None |
|||
| ) |
Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
>>> p = Bool('p')
>>> q = Bool('q')
>>> And(p, q)
And(p, q)
Definition at line 1442 of file z3py.py.
Referenced by Solver.assert_and_track(), Bools(), and BoolVector().
| def z3py.Bools | ( | names, | |
ctx = None |
|||
| ) |
| def z3py.BoolSort | ( | ctx = None | ) |
Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
>>> BoolSort()
Bool
>>> p = Const('p', BoolSort())
>>> is_bool(p)
True
>>> r = Function('r', IntSort(), IntSort(), BoolSort())
>>> r(0, 1)
r(0, 1)
>>> is_bool(r(0, 1))
True
Definition at line 1407 of file z3py.py.
Referenced by Goal.assert_exprs(), Solver.assert_exprs(), Fixedpoint.assert_exprs(), Bool(), FreshBool(), Context.getBoolSort(), If(), Implies(), Interpolant(), Context.mkBoolSort(), Not(), QuantifierRef.sort(), and Xor().
| def z3py.BoolVal | ( | val, | |
ctx = None |
|||
| ) |
Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used. >>> BoolVal(True) True >>> is_true(BoolVal(True)) True >>> is_true(True) False >>> is_false(BoolVal(False)) True
Definition at line 1424 of file z3py.py.
Referenced by AlgebraicNumRef.as_decimal(), Goal.as_expr(), ApplyResult.as_expr(), BoolSortRef.cast(), and Solver.to_smt2().
| def z3py.BoolVector | ( | prefix, | |
| sz, | |||
ctx = None |
|||
| ) |
| def z3py.BV2Int | ( | a, | |
is_signed = False |
|||
| ) |
Return the Z3 expression BV2Int(a).
>>> b = BitVec('b', 3)
>>> BV2Int(b).sort()
Int
>>> x = Int('x')
>>> x > BV2Int(b)
x > BV2Int(b)
>>> x > BV2Int(b, is_signed=False)
x > BV2Int(b)
>>> x > BV2Int(b, is_signed=True)
x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
>>> solve(x > BV2Int(b), b == 1, x < 3)
[b = 1, x = 2]
Definition at line 3508 of file z3py.py.
| def z3py.BVRedAnd | ( | a | ) |
| def z3py.BVRedOr | ( | a | ) |
| def z3py.Cbrt | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.Concat | ( | * | args | ) |
Create a Z3 bit-vector concatenation expression.
>>> v = BitVecVal(1, 4)
>>> Concat(v, v+1, v)
Concat(Concat(1, 1 + 1), 1)
>>> simplify(Concat(v, v+1, v))
289
>>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
121
Definition at line 3603 of file z3py.py.
Referenced by SeqRef.__add__(), and SeqRef.__radd__().
| def z3py.Cond | ( | p, | |
| t1, | |||
| t2, | |||
ctx = None |
|||
| ) |
Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
>>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
Definition at line 7452 of file z3py.py.
Referenced by If().
| def z3py.Const | ( | name, | |
| sort | |||
| ) |
| def z3py.Consts | ( | names, | |
| sort | |||
| ) |
| def z3py.Contains | ( | a, | |
| b | |||
| ) |
| def z3py.CreateDatatypes | ( | * | ds | ) |
Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
In the following example we define a Tree-List using two mutually recursive datatypes.
>>> TreeList = Datatype('TreeList')
>>> Tree = Datatype('Tree')
>>> # Tree has two constructors: leaf and node
>>> Tree.declare('leaf', ('val', IntSort()))
>>> # a node contains a list of trees
>>> Tree.declare('node', ('children', TreeList))
>>> TreeList.declare('nil')
>>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
>>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
>>> Tree.val(Tree.leaf(10))
val(leaf(10))
>>> simplify(Tree.val(Tree.leaf(10)))
10
>>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
>>> n1
node(cons(leaf(10), cons(leaf(20), nil)))
>>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
>>> simplify(n2 == n1)
False
>>> simplify(TreeList.car(Tree.children(n2)) == n1)
True
Definition at line 4385 of file z3py.py.
Referenced by Datatype.create().
| def z3py.DeclareSort | ( | name, | |
ctx = None |
|||
| ) |
Create a new uninterpred sort named `name`.
If `ctx=None`, then the new sort is declared in the global Z3Py context.
>>> A = DeclareSort('A')
>>> a = Const('a', A)
>>> b = Const('b', A)
>>> a.sort() == A
True
>>> b.sort() == A
True
>>> a == b
a == b
Definition at line 600 of file z3py.py.
| def z3py.Default | ( | a | ) |
| def z3py.describe_probes | ( | ) |
| def z3py.describe_tactics | ( | ) |
| def z3py.disable_trace | ( | msg | ) |
| def z3py.Distinct | ( | * | args | ) |
Create a Z3 distinct expression.
>>> x = Int('x')
>>> y = Int('y')
>>> Distinct(x, y)
x != y
>>> z = Int('z')
>>> Distinct(x, y, z)
Distinct(x, y, z)
>>> simplify(Distinct(x, y, z))
Distinct(x, y, z)
>>> simplify(Distinct(x, y, z), blast_distinct=True)
And(Not(x == y), Not(x == z), Not(y == z))
Definition at line 1162 of file z3py.py.
| def z3py.Empty | ( | s | ) |
| def z3py.enable_trace | ( | msg | ) |
| def z3py.EnumSort | ( | name, | |
| values, | |||
ctx = None |
|||
| ) |
Return a new enumeration sort named `name` containing the given values.
The result is a pair (sort, list of constants).
Example:
>>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
Definition at line 4574 of file z3py.py.
Referenced by Context.mkEnumSort(), and Context.MkEnumSort().
| def z3py.eq | ( | a, | |
| b | |||
| ) |
Return `True` if `a` and `b` are structurally identical AST nodes.
>>> x = Int('x')
>>> y = Int('y')
>>> eq(x, y)
False
>>> eq(x + 1, x + 1)
True
>>> eq(x + 1, 1 + x)
False
>>> eq(simplify(x + 1), simplify(1 + x))
True
Definition at line 400 of file z3py.py.
Referenced by substitute().
| def z3py.Exists | ( | vs, | |
| body, | |||
weight = 1, |
|||
qid = "", |
|||
skid = "", |
|||
patterns = [], |
|||
no_patterns = [] |
|||
| ) |
Create a Z3 exists formula.
The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
See http://rise4fun.com/Z3Py/tutorial/advanced for more details.
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = Exists([x, y], f(x, y) >= x, skid="foo")
>>> q
Exists([x, y], f(x, y) >= x)
>>> is_quantifier(q)
True
>>> r = Tactic('nnf')(q).as_expr()
>>> is_quantifier(r)
False
Definition at line 1895 of file z3py.py.
Referenced by Fixedpoint.abstract().
| def z3py.Ext | ( | a, | |
| b | |||
| ) |
| def z3py.Extract | ( | high, | |
| low, | |||
| a | |||
| ) |
Create a Z3 bit-vector extraction expression, or create a string extraction expression.
>>> x = BitVec('x', 8)
>>> Extract(6, 2, x)
Extract(6, 2, x)
>>> Extract(6, 2, x).sort()
BitVec(5)
>>> simplify(Extract(StringVal("abcd"),2,1))
"c"
Definition at line 3648 of file z3py.py.
| def z3py.FailIf | ( | p, | |
ctx = None |
|||
| ) |
Return a tactic that fails if the probe `p` evaluates to true. Otherwise, it returns the input goal unmodified.
In the following example, the tactic applies 'simplify' if and only if there are more than 2 constraints in the goal.
>>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.add(x > 0)
>>> g.add(y > 0)
>>> t(g)
[[x > 0, y > 0]]
>>> g.add(x == y + 1)
>>> t(g)
[[Not(x <= 0), Not(y <= 0), x == 1 + y]]
Definition at line 7415 of file z3py.py.
| def z3py.FiniteDomainSort | ( | name, | |
| sz, | |||
ctx = None |
|||
| ) |
Create a named finite domain sort of a given size sz
Definition at line 6563 of file z3py.py.
Referenced by Context.mkFiniteDomainSort(), and Context.MkFiniteDomainSort().
| def z3py.FiniteDomainVal | ( | val, | |
| sort, | |||
ctx = None |
|||
| ) |
| def z3py.Float128 | ( | ctx = None | ) |
| def z3py.Float16 | ( | ctx = None | ) |
| def z3py.Float32 | ( | ctx = None | ) |
| def z3py.Float64 | ( | ctx = None | ) |
| def z3py.FloatDouble | ( | ctx = None | ) |
| def z3py.FloatHalf | ( | ctx = None | ) |
| def z3py.FloatQuadruple | ( | ctx = None | ) |
| def z3py.FloatSingle | ( | ctx = None | ) |
| def z3py.ForAll | ( | vs, | |
| body, | |||
weight = 1, |
|||
qid = "", |
|||
skid = "", |
|||
patterns = [], |
|||
no_patterns = [] |
|||
| ) |
Create a Z3 forall formula.
The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
See http://rise4fun.com/Z3Py/tutorial/advanced for more details.
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> ForAll([x, y], f(x, y) >= x)
ForAll([x, y], f(x, y) >= x)
>>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
ForAll([x, y], f(x, y) >= x)
>>> ForAll([x, y], f(x, y) >= x, weight=10)
ForAll([x, y], f(x, y) >= x)
Definition at line 1876 of file z3py.py.
Referenced by Fixedpoint.abstract().
| def z3py.FP | ( | name, | |
| fpsort, | |||
ctx = None |
|||
| ) |
Return a floating-point constant named `name`.
`fpsort` is the floating-point sort.
If `ctx=None`, then the global context is used.
>>> x = FP('x', FPSort(8, 24))
>>> is_fp(x)
True
>>> x.ebits()
8
>>> x.sort()
FPSort(8, 24)
>>> word = FPSort(8, 24)
>>> x2 = FP('x', word)
>>> eq(x, x2)
True
Definition at line 8717 of file z3py.py.
Referenced by FPs().
| def z3py.fpAbs | ( | a, | |
ctx = None |
|||
| ) |
Create a Z3 floating-point absolute value expression. >>> s = FPSort(8, 24) >>> rm = RNE() >>> x = FPVal(1.0, s) >>> fpAbs(x) fpAbs(1) >>> y = FPVal(-20.0, s) >>> y -1.25*(2**4) >>> fpAbs(y) fpAbs(-1.25*(2**4)) >>> fpAbs(-1.25*(2**4)) fpAbs(-1.25*(2**4)) >>> fpAbs(x).sort() FPSort(8, 24)
Definition at line 8758 of file z3py.py.
| def z3py.fpAdd | ( | rm, | |
| a, | |||
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point addition expression.
>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpAdd(rm, x, y)
fpAdd(RNE(), x, y)
>>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
x + y
>>> fpAdd(rm, x, y).sort()
FPSort(8, 24)
Definition at line 8847 of file z3py.py.
Referenced by FPRef.__add__(), and FPRef.__radd__().
| def z3py.fpBVToFP | ( | v, | |
| sort, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression that represents the conversion from a bit-vector term to a floating-point term. >>> x_bv = BitVecVal(0x3F800000, 32) >>> x_fp = fpBVToFP(x_bv, Float32()) >>> x_fp fpToFP(1065353216) >>> simplify(x_fp) 1
Definition at line 9144 of file z3py.py.
| def z3py.fpDiv | ( | rm, | |
| a, | |||
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point divison expression.
>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpDiv(rm, x, y)
fpDiv(RNE(), x, y)
>>> fpDiv(rm, x, y).sort()
FPSort(8, 24)
Definition at line 8891 of file z3py.py.
Referenced by FPRef.__div__(), and FPRef.__rdiv__().
| def z3py.fpEQ | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.fpFMA | ( | rm, | |
| a, | |||
| b, | |||
| c, | |||
ctx = None |
|||
| ) |
| def z3py.fpFP | ( | sgn, | |
| exp, | |||
| sig, | |||
ctx = None |
|||
| ) |
Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp. >>> s = FPSort(8, 24) >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23)) >>> print(x) fpFP(1, 127, 4194304) >>> xv = FPVal(-1.5, s) >>> print(xv) -1.5 >>> slvr = Solver() >>> slvr.add(fpEQ(x, xv)) >>> slvr.check() sat >>> xv = FPVal(+1.5, s) >>> print(xv) 1.5 >>> slvr = Solver() >>> slvr.add(fpEQ(x, xv)) >>> slvr.check() unsat
| def z3py.fpFPToFP | ( | rm, | |
| v, | |||
| sort, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression that represents the conversion from a floating-point term to a floating-point term of different precision. >>> x_sgl = FPVal(1.0, Float32()) >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64()) >>> x_dbl fpToFP(RNE(), 1) >>> simplify(x_dbl) 1 >>> x_dbl.sort() FPSort(11, 53)
Definition at line 9160 of file z3py.py.
| def z3py.fpGEQ | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create the Z3 floating-point expression `other >= self`.
>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpGEQ(x, y)
x >= y
>>> (x >= y).sexpr()
'(fp.geq x y)'
Definition at line 9045 of file z3py.py.
Referenced by FPRef.__ge__().
| def z3py.fpGT | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create the Z3 floating-point expression `other > self`.
>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpGT(x, y)
x > y
>>> (x > y).sexpr()
'(fp.gt x y)'
Definition at line 9034 of file z3py.py.
Referenced by FPRef.__gt__().
| def z3py.fpInfinity | ( | s, | |
| negative | |||
| ) |
| def z3py.fpIsInf | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsNaN | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsNegative | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsNormal | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsPositive | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsSubnormal | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpIsZero | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.fpLEQ | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create the Z3 floating-point expression `other <= self`.
>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpLEQ(x, y)
x <= y
>>> (x <= y).sexpr()
'(fp.leq x y)'
Definition at line 9023 of file z3py.py.
Referenced by FPRef.__le__().
| def z3py.fpLT | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create the Z3 floating-point expression `other < self`.
>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpLT(x, y)
x < y
>>> (x < y).sexpr()
'(fp.lt x y)'
Definition at line 9012 of file z3py.py.
Referenced by FPRef.__lt__().
| def z3py.fpMax | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.fpMin | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.fpMinusInfinity | ( | s | ) |
| def z3py.fpMinusZero | ( | s | ) |
| def z3py.fpMul | ( | rm, | |
| a, | |||
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point multiplication expression.
>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpMul(rm, x, y)
fpMul(RNE(), x, y)
>>> fpMul(rm, x, y).sort()
FPSort(8, 24)
Definition at line 8877 of file z3py.py.
Referenced by FPRef.__mul__(), and FPRef.__rmul__().
| def z3py.fpNaN | ( | s | ) |
Create a Z3 floating-point NaN term. >>> s = FPSort(8, 24) >>> set_fpa_pretty(True) >>> fpNaN(s) NaN >>> pb = get_fpa_pretty() >>> set_fpa_pretty(False) >>> fpNaN(s) fpNaN(FPSort(8, 24)) >>> set_fpa_pretty(pb)
Definition at line 8614 of file z3py.py.
Referenced by FPVal().
| def z3py.fpNeg | ( | a, | |
ctx = None |
|||
| ) |
Create a Z3 floating-point addition expression.
>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> fpNeg(x)
-x
>>> fpNeg(x).sort()
FPSort(8, 24)
Definition at line 8780 of file z3py.py.
Referenced by FPRef.__neg__().
| def z3py.fpNEQ | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.fpPlusInfinity | ( | s | ) |
Create a Z3 floating-point +oo term. >>> s = FPSort(8, 24) >>> pb = get_fpa_pretty() >>> set_fpa_pretty(True) >>> fpPlusInfinity(s) +oo >>> set_fpa_pretty(False) >>> fpPlusInfinity(s) fpPlusInfinity(FPSort(8, 24)) >>> set_fpa_pretty(pb)
Definition at line 8630 of file z3py.py.
Referenced by FPVal().
| def z3py.fpPlusZero | ( | s | ) |
| def z3py.fpRealToFP | ( | rm, | |
| v, | |||
| sort, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression that represents the conversion from a real term to a floating-point term. >>> x_r = RealVal(1.5) >>> x_fp = fpRealToFP(RNE(), x_r, Float32()) >>> x_fp fpToFP(RNE(), 3/2) >>> simplify(x_fp) 1.5
Definition at line 9179 of file z3py.py.
| def z3py.fpRem | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point remainder expression.
>>> s = FPSort(8, 24)
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpRem(x, y)
fpRem(x, y)
>>> fpRem(x, y).sort()
FPSort(8, 24)
Definition at line 8905 of file z3py.py.
Referenced by FPRef.__mod__(), and FPRef.__rmod__().
| def z3py.fpRoundToIntegral | ( | rm, | |
| a, | |||
ctx = None |
|||
| ) |
| def z3py.FPs | ( | names, | |
| fpsort, | |||
ctx = None |
|||
| ) |
| def z3py.fpSignedToFP | ( | rm, | |
| v, | |||
| sort, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression that represents the conversion from a signed bit-vector term (encoding an integer) to a floating-point term. >>> x_signed = BitVecVal(-5, BitVecSort(32)) >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32()) >>> x_fp fpToFP(RNE(), 4294967291) >>> simplify(x_fp) -1.25*(2**2)
Definition at line 9196 of file z3py.py.
| def z3py.FPSort | ( | ebits, | |
| sbits, | |||
ctx = None |
|||
| ) |
Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
>>> Single = FPSort(8, 24)
>>> Double = FPSort(11, 53)
>>> Single
FPSort(8, 24)
>>> x = Const('x', Single)
>>> eq(x, FP('x', FPSort(8, 24)))
True
Definition at line 8556 of file z3py.py.
Referenced by get_default_fp_sort(), Context.mkFPSort(), Context.mkFPSort128(), Context.MkFPSort128(), Context.mkFPSort16(), Context.MkFPSort16(), Context.mkFPSort32(), Context.MkFPSort32(), Context.mkFPSort64(), Context.MkFPSort64(), Context.mkFPSortDouble(), Context.MkFPSortDouble(), Context.mkFPSortHalf(), Context.MkFPSortHalf(), Context.mkFPSortQuadruple(), Context.MkFPSortQuadruple(), Context.mkFPSortSingle(), and Context.MkFPSortSingle().
| def z3py.fpSqrt | ( | rm, | |
| a, | |||
ctx = None |
|||
| ) |
| def z3py.fpSub | ( | rm, | |
| a, | |||
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point subtraction expression.
>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpSub(rm, x, y)
fpSub(RNE(), x, y)
>>> fpSub(rm, x, y).sort()
FPSort(8, 24)
Definition at line 8863 of file z3py.py.
Referenced by FPRef.__rsub__(), and FPRef.__sub__().
| def z3py.fpToFP | ( | a1, | |
a2 = None, |
|||
a3 = None, |
|||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression from other term sorts to floating-point. From a bit-vector term in IEEE 754-2008 format: >>> x = FPVal(1.0, Float32()) >>> x_bv = fpToIEEEBV(x) >>> simplify(fpToFP(x_bv, Float32())) 1 From a floating-point term with different precision: >>> x = FPVal(1.0, Float32()) >>> x_db = fpToFP(RNE(), x, Float64()) >>> x_db.sort() FPSort(11, 53) From a real term: >>> x_r = RealVal(1.5) >>> simplify(fpToFP(RNE(), x_r, Float32())) 1.5 From a signed bit-vector term: >>> x_signed = BitVecVal(-5, BitVecSort(32)) >>> simplify(fpToFP(RNE(), x_signed, Float32())) -1.25*(2**2)
Definition at line 9106 of file z3py.py.
| def z3py.fpToFPUnsigned | ( | rm, | |
| x, | |||
| s, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression.
| def z3py.fpToIEEEBV | ( | x, | |
ctx = None |
|||
| ) |
\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
The size of the resulting bit-vector is automatically determined.
Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
knows only one NaN and it will always produce the same bit-vector represenatation of
that NaN.
>>> x = FP('x', FPSort(8, 24))
>>> y = fpToIEEEBV(x)
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False
Definition at line 9300 of file z3py.py.
| def z3py.fpToReal | ( | x, | |
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression, from floating-point expression to real.
>>> x = FP('x', FPSort(8, 24))
>>> y = fpToReal(x)
>>> print(is_fp(x))
True
>>> print(is_real(y))
True
>>> print(is_fp(y))
False
>>> print(is_real(x))
False
Definition at line 9281 of file z3py.py.
| def z3py.fpToSBV | ( | rm, | |
| x, | |||
| s, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
>>> x = FP('x', FPSort(8, 24))
>>> y = fpToSBV(RTZ(), x, BitVecSort(32))
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False
| def z3py.fpToUBV | ( | rm, | |
| x, | |||
| s, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
>>> x = FP('x', FPSort(8, 24))
>>> y = fpToUBV(RTZ(), x, BitVecSort(32))
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False
| def z3py.fpUnsignedToFP | ( | rm, | |
| v, | |||
| sort, | |||
ctx = None |
|||
| ) |
Create a Z3 floating-point conversion expression that represents the conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term. >>> x_signed = BitVecVal(-5, BitVecSort(32)) >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32()) >>> x_fp fpToFPUnsigned(RNE(), 4294967291) >>> simplify(x_fp) 1*(2**32)
Definition at line 9213 of file z3py.py.
| def z3py.FPVal | ( | sig, | |
exp = None, |
|||
fps = None, |
|||
ctx = None |
|||
| ) |
Return a floating-point value of value `val` and sort `fps`. If `ctx=None`, then the global context is used.
>>> v = FPVal(20.0, FPSort(8, 24))
>>> v
1.25*(2**4)
>>> print("0x%.8x" % v.exponent_as_long())
0x00000004
>>> v = FPVal(2.25, FPSort(8, 24))
>>> v
1.125*(2**1)
>>> v = FPVal(-2.25, FPSort(8, 24))
>>> v
-1.125*(2**1)
>>> FPVal(-0.0, FPSort(8, 24))
-0.0
>>> FPVal(0.0, FPSort(8, 24))
+0.0
>>> FPVal(+0.0, FPSort(8, 24))
+0.0
Definition at line 8673 of file z3py.py.
Referenced by set_default_fp_sort().
| def z3py.fpZero | ( | s, | |
| negative | |||
| ) |
| def z3py.FreshBool | ( | prefix = 'b', |
|
ctx = None |
|||
| ) |
Return a fresh Boolean constant in the given context using the given prefix. If `ctx=None`, then the global context is used. >>> b1 = FreshBool() >>> b2 = FreshBool() >>> eq(b1, b2) False
Definition at line 1482 of file z3py.py.
| def z3py.FreshInt | ( | prefix = 'x', |
|
ctx = None |
|||
| ) |
Return a fresh integer constant in the given context using the given prefix. >>> x = FreshInt() >>> y = FreshInt() >>> eq(x, y) False >>> x.sort() Int
Definition at line 2843 of file z3py.py.
| def z3py.FreshReal | ( | prefix = 'b', |
|
ctx = None |
|||
| ) |
Return a fresh real constant in the given context using the given prefix. >>> x = FreshReal() >>> y = FreshReal() >>> eq(x, y) False >>> x.sort() Real
Definition at line 2895 of file z3py.py.
| def z3py.Function | ( | name, | |
| * | sig | ||
| ) |
Create a new Z3 uninterpreted function with the given sorts.
>>> f = Function('f', IntSort(), IntSort())
>>> f(f(0))
f(f(0))
Definition at line 738 of file z3py.py.
| def z3py.get_as_array_func | ( | n | ) |
Return the function declaration f associated with a Z3 expression of the form (_ as-array f).
Definition at line 5721 of file z3py.py.
Referenced by ModelRef.get_interp().
| def z3py.get_default_fp_sort | ( | ctx = None | ) |
| def z3py.get_default_rounding_mode | ( | ctx = None | ) |
Retrieves the global default rounding mode.
Definition at line 8042 of file z3py.py.
Referenced by set_default_fp_sort().
| def z3py.get_full_version | ( | ) |
| def z3py.get_map_func | ( | a | ) |
Return the function declaration associated with a Z3 map array expression.
>>> f = Function('f', IntSort(), IntSort())
>>> b = Array('b', IntSort(), IntSort())
>>> a = Map(f, b)
>>> eq(f, get_map_func(a))
True
>>> get_map_func(a)
f
>>> get_map_func(a)(0)
f(0)
Definition at line 4093 of file z3py.py.
| def z3py.get_param | ( | name | ) |
| def z3py.get_var_index | ( | a | ) |
Return the de-Bruijn index of the Z3 bounded variable `a`.
>>> x = Int('x')
>>> y = Int('y')
>>> is_var(x)
False
>>> is_const(x)
True
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> # Z3 replaces x and y with bound variables when ForAll is executed.
>>> q = ForAll([x, y], f(x, y) == x + y)
>>> q.body()
f(Var(1), Var(0)) == Var(1) + Var(0)
>>> b = q.body()
>>> b.arg(0)
f(Var(1), Var(0))
>>> v1 = b.arg(0).arg(0)
>>> v2 = b.arg(0).arg(1)
>>> v1
Var(1)
>>> v2
Var(0)
>>> get_var_index(v1)
1
>>> get_var_index(v2)
0
Definition at line 1096 of file z3py.py.
| def z3py.get_version | ( | ) |
| def z3py.get_version_string | ( | ) |
| def z3py.help_simplify | ( | ) |
| def z3py.If | ( | a, | |
| b, | |||
| c, | |||
ctx = None |
|||
| ) |
Create a Z3 if-then-else expression.
>>> x = Int('x')
>>> y = Int('y')
>>> max = If(x > y, x, y)
>>> max
If(x > y, x, y)
>>> simplify(max)
If(x <= y, y, x)
Definition at line 1140 of file z3py.py.
Referenced by BoolRef.__mul__().
| def z3py.Implies | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Create a Z3 implies expression.
>>> p, q = Bools('p q')
>>> Implies(p, q)
Implies(p, q)
>>> simplify(Implies(p, q))
Or(Not(p), q)
Definition at line 1495 of file z3py.py.
Referenced by Fixedpoint.add_rule(), and Fixedpoint.update_rule().
| def z3py.IndexOf | ( | s, | |
| substr, | |||
| offset | |||
| ) |
Retrieve the index of substring within a string starting at a specified offset.
>>> simplify(IndexOf("abcabc", "bc", 0))
1
>>> simplify(IndexOf("abcabc", "bc", 2))
4
| def z3py.InRe | ( | s, | |
| re | |||
| ) |
| def z3py.Int | ( | name, | |
ctx = None |
|||
| ) |
Return an integer constant named `name`. If `ctx=None`, then the global context is used.
>>> x = Int('x')
>>> is_int(x)
True
>>> is_int(x + 1)
True
Definition at line 2808 of file z3py.py.
Referenced by Ints(), and IntVector().
| def z3py.Interpolant | ( | a, | |
ctx = None |
|||
| ) |
Create an interpolation operator.
The argument is an interpolation pattern (see tree_interpolant).
>>> x = Int('x')
>>> print(Interpolant(x>0))
interp(x > 0)
Definition at line 7889 of file z3py.py.
Referenced by binary_interpolant(), and sequence_interpolant().
| def z3py.Ints | ( | names, | |
ctx = None |
|||
| ) |
| def z3py.IntSort | ( | ctx = None | ) |
Return the integer sort in the given context. If `ctx=None`, then the global context is used.
>>> IntSort()
Int
>>> x = Const('x', IntSort())
>>> is_int(x)
True
>>> x.sort() == IntSort()
True
>>> x.sort() == BoolSort()
False
Definition at line 2705 of file z3py.py.
Referenced by FreshInt(), Context.getIntSort(), Int(), IntVal(), and Context.mkIntSort().
| def z3py.IntVal | ( | val, | |
ctx = None |
|||
| ) |
Return a Z3 integer value. If `ctx=None`, then the global context is used.
>>> IntVal(1)
1
>>> IntVal("100")
100
Definition at line 2752 of file z3py.py.
Referenced by SeqRef.__getitem__(), AlgebraicNumRef.as_decimal(), and IndexOf().
| def z3py.IntVector | ( | prefix, | |
| sz, | |||
ctx = None |
|||
| ) |
| def z3py.is_add | ( | a | ) |
| def z3py.is_algebraic_value | ( | a | ) |
| def z3py.is_and | ( | a | ) |
| def z3py.is_app | ( | a | ) |
Return `True` if `a` is a Z3 function application.
Note that, constants are function applications with 0 arguments.
>>> a = Int('a')
>>> is_app(a)
True
>>> is_app(a + 1)
True
>>> is_app(IntSort())
False
>>> is_app(1)
False
>>> is_app(IntVal(1))
True
>>> x = Int('x')
>>> is_app(ForAll(x, x >= 0))
False
Definition at line 1029 of file z3py.py.
Referenced by ExprRef.arg(), ExprRef.children(), ExprRef.decl(), is_app_of(), is_const(), is_quantifier(), and ExprRef.num_args().
| def z3py.is_app_of | ( | a, | |
| k | |||
| ) |
Return `True` if `a` is an application of the given kind `k`.
>>> x = Int('x')
>>> n = x + 1
>>> is_app_of(n, Z3_OP_ADD)
True
>>> is_app_of(n, Z3_OP_MUL)
False
Definition at line 1128 of file z3py.py.
Referenced by is_add(), is_and(), is_const_array(), is_default(), is_distinct(), is_div(), is_eq(), is_false(), is_ge(), is_gt(), is_idiv(), is_is_int(), is_K(), is_le(), is_lt(), is_map(), is_mod(), is_mul(), is_not(), is_or(), is_select(), is_store(), is_sub(), is_to_int(), is_to_real(), and is_true().
| def z3py.is_arith | ( | a | ) |
Return `True` if `a` is an arithmetical expression.
>>> x = Int('x')
>>> is_arith(x)
True
>>> is_arith(x + 1)
True
>>> is_arith(1)
False
>>> is_arith(IntVal(1))
True
>>> y = Real('y')
>>> is_arith(y)
True
>>> is_arith(y + 1)
True
Definition at line 2290 of file z3py.py.
Referenced by is_algebraic_value(), is_int(), is_int_value(), is_rational_value(), and is_real().
| def z3py.is_arith_sort | ( | s | ) |
Return `True` if s is an arithmetical sort (type).
>>> is_arith_sort(IntSort())
True
>>> is_arith_sort(RealSort())
True
>>> is_arith_sort(BoolSort())
False
>>> n = Int('x') + 1
>>> is_arith_sort(n.sort())
True
Definition at line 1993 of file z3py.py.
Referenced by ArithSortRef.subsort().
| def z3py.is_array | ( | a | ) |
| def z3py.is_as_array | ( | n | ) |
Return true if n is a Z3 expression of the form (_ as-array f).
Definition at line 5717 of file z3py.py.
Referenced by get_as_array_func(), and ModelRef.get_interp().
| def z3py.is_ast | ( | a | ) |
Return `True` if `a` is an AST node.
>>> is_ast(10)
False
>>> is_ast(IntVal(10))
True
>>> is_ast(Int('x'))
True
>>> is_ast(BoolSort())
True
>>> is_ast(Function('f', IntSort(), IntSort()))
True
>>> is_ast("x")
False
>>> is_ast(Solver())
False
Definition at line 380 of file z3py.py.
Referenced by AstRef.eq(), and eq().
| def z3py.is_bool | ( | a | ) |
Return `True` if `a` is a Z3 Boolean expression.
>>> p = Bool('p')
>>> is_bool(p)
True
>>> q = Bool('q')
>>> is_bool(And(p, q))
True
>>> x = Real('x')
>>> is_bool(x)
False
>>> is_bool(x == 0)
True
Definition at line 1307 of file z3py.py.
Referenced by is_quantifier(), and prove().
| def z3py.is_bv | ( | a | ) |
Return `True` if `a` is a Z3 bit-vector expression.
>>> b = BitVec('b', 32)
>>> is_bv(b)
True
>>> is_bv(b + 10)
True
>>> is_bv(Int('x'))
False
Definition at line 3481 of file z3py.py.
Referenced by BV2Int(), BVRedAnd(), BVRedOr(), Concat(), Extract(), fpBVToFP(), fpFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpUnsignedToFP(), is_bv_value(), Product(), RepeatBitVec(), SignExt(), Sum(), and ZeroExt().
| def z3py.is_bv_sort | ( | s | ) |
Return True if `s` is a Z3 bit-vector sort. >>> is_bv_sort(BitVecSort(32)) True >>> is_bv_sort(IntSort()) False
Definition at line 3020 of file z3py.py.
Referenced by BitVecVal(), fpToSBV(), fpToUBV(), and BitVecSortRef.subsort().
| def z3py.is_bv_value | ( | a | ) |
| def z3py.is_const | ( | a | ) |
Return `True` if `a` is Z3 constant/variable expression.
>>> a = Int('a')
>>> is_const(a)
True
>>> is_const(a + 1)
False
>>> is_const(1)
False
>>> is_const(IntVal(1))
True
>>> x = Int('x')
>>> is_const(ForAll(x, x >= 0))
False
Definition at line 1054 of file z3py.py.
Referenced by ModelRef.__getitem__(), Solver.assert_and_track(), ModelRef.get_interp(), is_quantifier(), and prove().
| def z3py.is_const_array | ( | a | ) |
| def z3py.is_default | ( | a | ) |
| def z3py.is_distinct | ( | a | ) |
| def z3py.is_div | ( | a | ) |
| def z3py.is_eq | ( | a | ) |
Return `True` if `a` is a Z3 equality expression.
>>> x, y = Ints('x y')
>>> is_eq(x == y)
True
Definition at line 1387 of file z3py.py.
Referenced by AstRef.__bool__().
| def z3py.is_expr | ( | a | ) |
Return `True` if `a` is a Z3 expression.
>>> a = Int('a')
>>> is_expr(a)
True
>>> is_expr(a + 1)
True
>>> is_expr(IntSort())
False
>>> is_expr(1)
False
>>> is_expr(IntVal(1))
True
>>> x = Int('x')
>>> is_expr(ForAll(x, x >= 0))
True
>>> is_expr(FPVal(1.0))
True
Definition at line 1007 of file z3py.py.
Referenced by SeqRef.as_string(), SortRef.cast(), BoolSortRef.cast(), ArithSortRef.cast(), BitVecSortRef.cast(), FPSortRef.cast(), Cbrt(), ExprRef.children(), Concat(), IndexOf(), is_quantifier(), is_var(), K(), MultiPattern(), Replace(), simplify(), Sqrt(), substitute(), and substitute_vars().
| def z3py.is_false | ( | a | ) |
Return `True` if `a` is the Z3 false expression.
>>> p = Bool('p')
>>> is_false(p)
False
>>> is_false(False)
False
>>> is_false(BoolVal(False))
True
Definition at line 1341 of file z3py.py.
Referenced by AstRef.__bool__().
| def z3py.is_finite_domain | ( | a | ) |
Return `True` if `a` is a Z3 finite-domain expression.
>>> s = FiniteDomainSort('S', 100)
>>> b = Const('b', s)
>>> is_finite_domain(b)
True
>>> is_finite_domain(Int('x'))
False
Definition at line 6592 of file z3py.py.
Referenced by is_finite_domain_value().
| def z3py.is_finite_domain_sort | ( | s | ) |
Return True if `s` is a Z3 finite-domain sort.
>>> is_finite_domain_sort(FiniteDomainSort('S', 100))
True
>>> is_finite_domain_sort(IntSort())
False
Definition at line 6570 of file z3py.py.
Referenced by FiniteDomainVal().
| def z3py.is_finite_domain_value | ( | a | ) |
| def z3py.is_fp | ( | a | ) |
Return `True` if `a` is a Z3 floating-point expression.
>>> b = FP('b', FPSort(8, 24))
>>> is_fp(b)
True
>>> is_fp(b + 1.0)
True
>>> is_fp(Int('x'))
False
Definition at line 8529 of file z3py.py.
Referenced by fpFPToFP(), fpIsPositive(), fpNeg(), fpToFP(), fpToIEEEBV(), fpToReal(), fpToSBV(), fpToUBV(), is_fp_value(), and set_default_fp_sort().
| def z3py.is_fp_sort | ( | s | ) |
Return True if `s` is a Z3 floating-point sort. >>> is_fp_sort(FPSort(8, 24)) True >>> is_fp_sort(IntSort()) False
Definition at line 8189 of file z3py.py.
Referenced by fpBVToFP(), fpFPToFP(), fpRealToFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpUnsignedToFP(), and FPVal().
| def z3py.is_fp_value | ( | a | ) |
| def z3py.is_fprm | ( | a | ) |
Return `True` if `a` is a Z3 floating-point rounding mode expression. >>> rm = RNE() >>> is_fprm(rm) True >>> rm = 1.0 >>> is_fprm(rm) False
Definition at line 8437 of file z3py.py.
Referenced by fpFPToFP(), fpNeg(), fpRealToFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpToSBV(), fpToUBV(), fpUnsignedToFP(), and is_fprm_value().
| def z3py.is_fprm_sort | ( | s | ) |
| def z3py.is_fprm_value | ( | a | ) |
Return `True` if `a` is a Z3 floating-point rounding mode numeral value.
Definition at line 8449 of file z3py.py.
Referenced by set_default_rounding_mode().
| def z3py.is_func_decl | ( | a | ) |
| def z3py.is_ge | ( | a | ) |
| def z3py.is_gt | ( | a | ) |
| def z3py.is_idiv | ( | a | ) |
| def z3py.is_int | ( | a | ) |
| def z3py.is_int_value | ( | a | ) |
Return `True` if `a` is an integer value of sort Int.
>>> is_int_value(IntVal(1))
True
>>> is_int_value(1)
False
>>> is_int_value(Int('x'))
False
>>> n = Int('x') + 1
>>> n
x + 1
>>> n.arg(1)
1
>>> is_int_value(n.arg(1))
True
>>> is_int_value(RealVal("1/3"))
False
>>> is_int_value(RealVal(1))
False
Definition at line 2352 of file z3py.py.
| def z3py.is_is_int | ( | a | ) |
| def z3py.is_K | ( | a | ) |
| def z3py.is_le | ( | a | ) |
| def z3py.is_lt | ( | a | ) |
| def z3py.is_map | ( | a | ) |
Return `True` if `a` is a Z3 map array expression.
>>> f = Function('f', IntSort(), IntSort())
>>> b = Array('b', IntSort(), IntSort())
>>> a = Map(f, b)
>>> a
Map(f, b)
>>> is_map(a)
True
>>> is_map(b)
False
Definition at line 4070 of file z3py.py.
Referenced by get_map_func().
| def z3py.is_mod | ( | a | ) |
| def z3py.is_mul | ( | a | ) |
| def z3py.is_not | ( | a | ) |
| def z3py.is_or | ( | a | ) |
| def z3py.is_pattern | ( | a | ) |
Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
See http://rise4fun.com/Z3Py/tutorial/advanced for more details.
>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
>>> q
ForAll(x, f(x) == 0)
>>> q.num_patterns()
1
>>> is_pattern(q.pattern(0))
True
>>> q.pattern(0)
f(Var(0))
Definition at line 1630 of file z3py.py.
Referenced by is_quantifier(), and MultiPattern().
| def z3py.is_probe | ( | p | ) |
| def z3py.is_quantifier | ( | a | ) |
| def z3py.is_rational_value | ( | a | ) |
Return `True` if `a` is rational value of sort Real.
>>> is_rational_value(RealVal(1))
True
>>> is_rational_value(RealVal("3/5"))
True
>>> is_rational_value(IntVal(1))
False
>>> is_rational_value(1)
False
>>> n = Real('x') + 1
>>> n.arg(1)
1
>>> is_rational_value(n.arg(1))
True
>>> is_rational_value(Real('x'))
False
Definition at line 2375 of file z3py.py.
| def z3py.is_real | ( | a | ) |
Return `True` if `a` is a real expression.
>>> x = Int('x')
>>> is_real(x + 1)
False
>>> y = Real('y')
>>> is_real(y)
True
>>> is_real(y + 1)
True
>>> is_real(1)
False
>>> is_real(RealVal(1))
True
Definition at line 2328 of file z3py.py.
Referenced by fpRealToFP(), and fpToFP().
| def z3py.is_select | ( | a | ) |
| def z3py.is_seq | ( | a | ) |
Return `True` if `a` is a Z3 sequence expression.
>>> print (is_seq(Unit(IntVal(0))))
True
>>> print (is_seq(StringVal("abc")))
True
Definition at line 9412 of file z3py.py.
Referenced by SeqRef.as_string(), Concat(), and Extract().
| def z3py.is_sort | ( | s | ) |
Return `True` if `s` is a Z3 sort.
>>> is_sort(IntSort())
True
>>> is_sort(Int('x'))
False
>>> is_expr(Int('x'))
True
Definition at line 563 of file z3py.py.
Referenced by ArraySort(), CreateDatatypes(), Function(), is_store(), K(), prove(), and Var().
| def z3py.is_store | ( | a | ) |
| def z3py.is_string | ( | a | ) |
| def z3py.is_string_value | ( | a | ) |
| def z3py.is_sub | ( | a | ) |
| def z3py.is_to_int | ( | a | ) |
| def z3py.is_to_real | ( | a | ) |
| def z3py.is_true | ( | a | ) |
Return `True` if `a` is the Z3 true expression.
>>> p = Bool('p')
>>> is_true(p)
False
>>> is_true(simplify(p == p))
True
>>> x = Real('x')
>>> is_true(x == 0)
False
>>> # True is a Python Boolean expression
>>> is_true(True)
False
Definition at line 1324 of file z3py.py.
Referenced by AstRef.__bool__().
| def z3py.is_var | ( | a | ) |
Return `True` if `a` is variable.
Z3 uses de-Bruijn indices for representing bound variables in
quantifiers.
>>> x = Int('x')
>>> is_var(x)
False
>>> is_const(x)
True
>>> f = Function('f', IntSort(), IntSort())
>>> # Z3 replaces x with bound variables when ForAll is executed.
>>> q = ForAll(x, f(x) == x)
>>> b = q.body()
>>> b
f(Var(0)) == Var(0)
>>> b.arg(1)
Var(0)
>>> is_var(b.arg(1))
True
Definition at line 1072 of file z3py.py.
Referenced by get_var_index().
| def z3py.IsInt | ( | a | ) |
Return the Z3 predicate IsInt(a).
>>> x = Real('x')
>>> IsInt(x + "1/2")
IsInt(x + 1/2)
>>> solve(IsInt(x + "1/2"), x > 0, x < 1)
[x = 1/2]
>>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
no solution
Definition at line 2942 of file z3py.py.
| def z3py.K | ( | dom, | |
| v | |||
| ) |
Return a Z3 constant array expression.
>>> a = K(IntSort(), 10)
>>> a
K(Int, 10)
>>> a.sort()
Array(Int, Int)
>>> i = Int('i')
>>> a[i]
K(Int, 10)[i]
>>> simplify(a[i])
10
Definition at line 4229 of file z3py.py.
| def z3py.Length | ( | s | ) |
| def z3py.LShR | ( | a, | |
| b | |||
| ) |
Create the Z3 expression logical right shift.
Use the operator >> for the arithmetical right shift.
>>> x, y = BitVecs('x y', 32)
>>> LShR(x, y)
LShR(x, y)
>>> (x >> y).sexpr()
'(bvashr x y)'
>>> LShR(x, y).sexpr()
'(bvlshr x y)'
>>> BitVecVal(4, 3)
4
>>> BitVecVal(4, 3).as_signed_long()
-4
>>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
-2
>>> simplify(BitVecVal(4, 3) >> 1)
6
>>> simplify(LShR(BitVecVal(4, 3), 1))
2
>>> simplify(BitVecVal(2, 3) >> 1)
1
>>> simplify(LShR(BitVecVal(2, 3), 1))
1
Definition at line 3807 of file z3py.py.
| def z3py.main_ctx | ( | ) |
Return a reference to the global Z3 context.
>>> x = Real('x')
>>> x.ctx == main_ctx()
True
>>> c = Context()
>>> c == main_ctx()
False
>>> x2 = Real('x', c)
>>> x2.ctx == c
True
>>> eq(x, x2)
False
Definition at line 197 of file z3py.py.
Referenced by And(), SeqRef.as_string(), help_simplify(), Or(), and simplify_param_descrs().
| def z3py.Map | ( | f, | |
| * | args | ||
| ) |
Return a Z3 map array expression.
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> a1 = Array('a1', IntSort(), IntSort())
>>> a2 = Array('a2', IntSort(), IntSort())
>>> b = Map(f, a1, a2)
>>> b
Map(f, a1, a2)
>>> prove(b[0] == f(a1[0], a2[0]))
proved
Definition at line 4207 of file z3py.py.
Referenced by Context.Context(), and InterpolationContext.mkContext().
| def z3py.MultiPattern | ( | * | args | ) |
Create a Z3 multi-pattern using the given expressions `*args`
See http://rise4fun.com/Z3Py/tutorial/advanced for more details.
>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
>>> q
ForAll(x, f(x) != g(x))
>>> q.num_patterns()
1
>>> is_pattern(q.pattern(0))
True
>>> q.pattern(0)
MultiPattern(f(Var(0)), g(Var(0)))
Definition at line 1649 of file z3py.py.
| def z3py.Not | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.open_log | ( | fname | ) |
| def z3py.Option | ( | re | ) |
| def z3py.Or | ( | * | args | ) |
Create a Z3 or-expression or or-probe.
>>> p, q, r = Bools('p q r')
>>> Or(p, q, r)
Or(p, q, r)
>>> P = BoolVector('p', 5)
>>> Or(P)
Or(p__0, p__1, p__2, p__3, p__4)
Definition at line 1583 of file z3py.py.
Referenced by ApplyResult.as_expr().
| def z3py.OrElse | ( | * | ts, |
| ** | ks | ||
| ) |
Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
>>> x = Int('x')
>>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
>>> # Tactic split-clause fails if there is no clause in the given goal.
>>> t(x == 0)
[[x == 0]]
>>> t(Or(x == 0, x == 1))
[[x == 0], [x == 1]]
| def z3py.ParAndThen | ( | t1, | |
| t2, | |||
ctx = None |
|||
| ) |
| def z3py.ParOr | ( | * | ts, |
| ** | ks | ||
| ) |
Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
>>> x = Int('x')
>>> t = ParOr(Tactic('simplify'), Tactic('fail'))
>>> t(x + 1 == 2)
[[x == 1]]
| def z3py.parse_smt2_file | ( | f, | |
sorts = {}, |
|||
decls = {}, |
|||
ctx = None |
|||
| ) |
Parse a file in SMT 2.0 format using the given sorts and decls. This function is similar to parse_smt2_string().
Definition at line 7879 of file z3py.py.
| def z3py.parse_smt2_string | ( | s, | |
sorts = {}, |
|||
decls = {}, |
|||
ctx = None |
|||
| ) |
Parse a string in SMT 2.0 format using the given sorts and decls.
The arguments sorts and decls are Python dictionaries used to initialize
the symbol table used for the SMT 2.0 parser.
>>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
And(x > 0, x < 10)
>>> x, y = Ints('x y')
>>> f = Function('f', IntSort(), IntSort())
>>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
x + f(y) > 0
>>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
a > 0
Definition at line 7859 of file z3py.py.
| def z3py.ParThen | ( | t1, | |
| t2, | |||
ctx = None |
|||
| ) |
Return a tactic that applies t1 and then t2 to every subgoal produced by t1. The subgoals are processed in parallel.
>>> x, y = Ints('x y')
>>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
>>> t(And(Or(x == 1, x == 2), y == x + 1))
[[x == 1, y == 2], [x == 2, y == 3]]
Definition at line 7118 of file z3py.py.
Referenced by ParAndThen().
| def z3py.PbEq | ( | args, | |
| k | |||
| ) |
| def z3py.PbLe | ( | args, | |
| k | |||
| ) |
| def z3py.Plus | ( | re | ) |
| def z3py.PrefixOf | ( | a, | |
| b | |||
| ) |
| def z3py.probe_description | ( | name, | |
ctx = None |
|||
| ) |
Return a short description for the probe named `name`.
>>> d = probe_description('memory')
Definition at line 7374 of file z3py.py.
Referenced by describe_probes().
| def z3py.probes | ( | ctx = None | ) |
Return a list of all available probes in Z3.
>>> l = probes()
>>> l.count('memory') == 1
True
Definition at line 7364 of file z3py.py.
Referenced by describe_probes().
| def z3py.Product | ( | * | args | ) |
Create the product of the Z3 expressions.
>>> a, b, c = Ints('a b c')
>>> Product(a, b, c)
a*b*c
>>> Product([a, b, c])
a*b*c
>>> A = IntVector('a', 5)
>>> Product(A)
a__0*a__1*a__2*a__3*a__4
Definition at line 7572 of file z3py.py.
| def z3py.prove | ( | claim, | |
| ** | keywords | ||
| ) |
| def z3py.Q | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.RatVal | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
Return a Z3 rational a/b. If `ctx=None`, then the global context is used. >>> RatVal(3,5) 3/5 >>> RatVal(3,5).sort() Real
Definition at line 2781 of file z3py.py.
Referenced by Q().
| def z3py.Re | ( | s, | |
ctx = None |
|||
| ) |
| def z3py.Real | ( | name, | |
ctx = None |
|||
| ) |
Return a real constant named `name`. If `ctx=None`, then the global context is used.
>>> x = Real('x')
>>> is_real(x)
True
>>> is_real(x + 1)
True
Definition at line 2856 of file z3py.py.
Referenced by Reals(), and RealVector().
| def z3py.Reals | ( | names, | |
ctx = None |
|||
| ) |
| def z3py.RealSort | ( | ctx = None | ) |
Return the real sort in the given context. If `ctx=None`, then the global context is used.
>>> RealSort()
Real
>>> x = Const('x', RealSort())
>>> is_real(x)
True
>>> is_int(x)
False
>>> x.sort() == RealSort()
True
Definition at line 2721 of file z3py.py.
Referenced by FreshReal(), Context.getRealSort(), Context.mkRealSort(), Real(), RealVal(), and RealVar().
| def z3py.RealVal | ( | val, | |
ctx = None |
|||
| ) |
Return a Z3 real value.
`val` may be a Python int, long, float or string representing a number in decimal or rational notation.
If `ctx=None`, then the global context is used.
>>> RealVal(1)
1
>>> RealVal(1).sort()
Real
>>> RealVal("3/5")
3/5
>>> RealVal("1.5")
3/2
Definition at line 2763 of file z3py.py.
Referenced by AlgebraicNumRef.as_decimal(), Cbrt(), RatVal(), and Sqrt().
| def z3py.RealVar | ( | idx, | |
ctx = None |
|||
| ) |
Create a real free variable. Free variables are used to create quantified formulas. They are also used to create polynomials. >>> RealVar(0) Var(0)
Definition at line 1230 of file z3py.py.
Referenced by RealVarVector().
| def z3py.RealVarVector | ( | n, | |
ctx = None |
|||
| ) |
| def z3py.RealVector | ( | prefix, | |
| sz, | |||
ctx = None |
|||
| ) |
| def z3py.Repeat | ( | t, | |
max = 4294967295, |
|||
ctx = None |
|||
| ) |
Return a tactic that keeps applying `t` until the goal is not modified anymore or the maximum number of iterations `max` is reached.
>>> x, y = Ints('x y')
>>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
>>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
>>> r = t(c)
>>> for subgoal in r: print(subgoal)
[x == 0, y == 0, x > y]
[x == 0, y == 1, x > y]
[x == 1, y == 0, x > y]
[x == 1, y == 1, x > y]
>>> t = Then(t, Tactic('propagate-values'))
>>> t(c)
[[x == 1, y == 0]]
Definition at line 7149 of file z3py.py.
| def z3py.RepeatBitVec | ( | n, | |
| a | |||
| ) |
Return an expression representing `n` copies of `a`.
>>> x = BitVec('x', 8)
>>> n = RepeatBitVec(4, x)
>>> n
RepeatBitVec(4, x)
>>> n.size()
32
>>> v0 = BitVecVal(10, 4)
>>> print("%.x" % v0.as_long())
a
>>> v = simplify(RepeatBitVec(4, v0))
>>> v.size()
16
>>> print("%.x" % v.as_long())
aaaa
Definition at line 3924 of file z3py.py.
| def z3py.Replace | ( | s, | |
| src, | |||
| dst | |||
| ) |
| def z3py.reset_params | ( | ) |
| def z3py.ReSort | ( | s | ) |
Definition at line 9584 of file z3py.py.
Referenced by Context.mkReSort(), and Context.MkReSort().
| def z3py.RNA | ( | ctx = None | ) |
Definition at line 8409 of file z3py.py.
Referenced by get_default_rounding_mode().
| def z3py.RNE | ( | ctx = None | ) |
Definition at line 8401 of file z3py.py.
Referenced by get_default_rounding_mode().
| def z3py.RotateLeft | ( | a, | |
| b | |||
| ) |
Return an expression representing `a` rotated to the left `b` times.
>>> a, b = BitVecs('a b', 16)
>>> RotateLeft(a, b)
RotateLeft(a, b)
>>> simplify(RotateLeft(a, 0))
a
>>> simplify(RotateLeft(a, 16))
a
Definition at line 3838 of file z3py.py.
| def z3py.RotateRight | ( | a, | |
| b | |||
| ) |
Return an expression representing `a` rotated to the right `b` times.
>>> a, b = BitVecs('a b', 16)
>>> RotateRight(a, b)
RotateRight(a, b)
>>> simplify(RotateRight(a, 0))
a
>>> simplify(RotateRight(a, 16))
a
Definition at line 3853 of file z3py.py.
| def z3py.RoundNearestTiesToAway | ( | ctx = None | ) |
| def z3py.RoundNearestTiesToEven | ( | ctx = None | ) |
| def z3py.RoundTowardNegative | ( | ctx = None | ) |
| def z3py.RoundTowardPositive | ( | ctx = None | ) |
| def z3py.RoundTowardZero | ( | ctx = None | ) |
| def z3py.RTN | ( | ctx = None | ) |
Definition at line 8425 of file z3py.py.
Referenced by get_default_rounding_mode().
| def z3py.RTP | ( | ctx = None | ) |
Definition at line 8417 of file z3py.py.
Referenced by get_default_rounding_mode().
| def z3py.RTZ | ( | ctx = None | ) |
Definition at line 8433 of file z3py.py.
Referenced by get_default_rounding_mode().
| def z3py.Select | ( | a, | |
| i | |||
| ) |
| def z3py.SeqSort | ( | s | ) |
Create a sequence sort over elements provided in the argument >>> s = SeqSort(IntSort()) >>> s == Unit(IntVal(1)).sort() True
Definition at line 9357 of file z3py.py.
Referenced by Context.mkSeqSort(), Context.MkSeqSort(), and Context.mkStringSort().
| def z3py.sequence_interpolant | ( | v, | |
p = None, |
|||
ctx = None |
|||
| ) |
Compute interpolant for a sequence of formulas.
If len(v) == N, and if the conjunction of the formulas in v is
unsatisfiable, the interpolant is a sequence of formulas w
such that len(w) = N-1 and v[0] implies w[0] and for i in 0..N-1:
1) w[i] & v[i+1] implies w[i+1] (or false if i+1 = N)
2) All uninterpreted symbols in w[i] occur in both v[0]..v[i]
and v[i+1]..v[n]
Requires len(v) >= 1.
If a & b is satisfiable, raises an object of class ModelRef
that represents a model of a & b.
If neither a proof of unsatisfiability nor a model is obtained
(for example, because of a timeout, or because models are disabled)
then None is returned.
If parameters p are supplied, these are used in creating the
solver that determines satisfiability.
>>> x = Int('x')
>>> y = Int('y')
>>> print(sequence_interpolant([x < 0, y == x , y > 2]))
[Not(x >= 0), Not(y >= 0)]
Definition at line 7996 of file z3py.py.
| def z3py.set_option | ( | * | args, |
| ** | kws | ||
| ) |
| def z3py.set_param | ( | * | args, |
| ** | kws | ||
| ) |
Set Z3 global (or module) parameters. >>> set_param(precision=10)
Definition at line 223 of file z3py.py.
Referenced by set_option().
| def z3py.SignExt | ( | n, | |
| a | |||
| ) |
Return a bit-vector expression with `n` extra sign-bits.
>>> x = BitVec('x', 16)
>>> n = SignExt(8, x)
>>> n.size()
24
>>> n
SignExt(8, x)
>>> n.sort()
BitVec(24)
>>> v0 = BitVecVal(2, 2)
>>> v0
2
>>> v0.size()
2
>>> v = simplify(SignExt(6, v0))
>>> v
254
>>> v.size()
8
>>> print("%.x" % v.as_long())
fe
Definition at line 3868 of file z3py.py.
| def z3py.SimpleSolver | ( | ctx = None | ) |
| def z3py.simplify | ( | a, | |
| * | arguments, | ||
| ** | keywords | ||
| ) |
Utils.
Simplify the expression `a` using the given options.
This function has many options. Use `help_simplify` to obtain the complete list.
>>> x = Int('x')
>>> y = Int('y')
>>> simplify(x + 1 + y + x + 1)
2 + 2*x + y
>>> simplify((x + 1)*(y + 1), som=True)
1 + x + y + x*y
>>> simplify(Distinct(x, y, 1), blast_distinct=True)
And(Not(x == y), Not(x == 1), Not(y == 1))
>>> simplify(And(x == 0, y == 1), elim_and=True)
Not(Or(Not(x == 0), Not(y == 1)))
Definition at line 7468 of file z3py.py.
| def z3py.simplify_param_descrs | ( | ) |
| def z3py.solve | ( | * | args, |
| ** | keywords | ||
| ) |
| def z3py.solve_using | ( | s, | |
| * | args, | ||
| ** | keywords | ||
| ) |
Solve the constraints `*args` using solver `s`. This is a simple function for creating demonstrations. It is similar to `solve`, but it uses the given solver `s`. It configures solver `s` using the options in `keywords`, adds the constraints in `args`, and invokes check.
Definition at line 7706 of file z3py.py.
| def z3py.SolverFor | ( | logic, | |
ctx = None |
|||
| ) |
Create a solver customized for the given logic.
The parameter `logic` is a string. It should be contains
the name of a SMT-LIB logic.
See http://www.smtlib.org/ for the name of all available logics.
>>> s = SolverFor("QF_LIA")
>>> x = Int('x')
>>> s.add(x > 0)
>>> s.add(x < 2)
>>> s.check()
sat
>>> s.model()
[x = 1]
Definition at line 6281 of file z3py.py.
| def z3py.Sqrt | ( | a, | |
ctx = None |
|||
| ) |
| def z3py.SRem | ( | a, | |
| b | |||
| ) |
Create the Z3 expression signed remainder.
Use the operator % for signed modulus, and URem() for unsigned remainder.
>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> SRem(x, y)
SRem(x, y)
>>> SRem(x, y).sort()
BitVec(32)
>>> (x % y).sexpr()
'(bvsmod x y)'
>>> SRem(x, y).sexpr()
'(bvsrem x y)'
Definition at line 3787 of file z3py.py.
| def z3py.Star | ( | re | ) |
| def z3py.Store | ( | a, | |
| i, | |||
| v | |||
| ) |
| def z3py.String | ( | name, | |
ctx = None |
|||
| ) |
Return a string constant named `name`. If `ctx=None`, then the global context is used.
>>> x = String('x')
Definition at line 9443 of file z3py.py.
Referenced by Context.Context(), Statistics.getEntries(), Statistics.getKeys(), Context.getProbeNames(), Context.getTacticNames(), InterpolationContext.mkContext(), Strings(), and FuncInterp.toString().
| def z3py.Strings | ( | names, | |
ctx = None |
|||
| ) |
| def z3py.StringSort | ( | ctx = None | ) |
| def z3py.StringVal | ( | s, | |
ctx = None |
|||
| ) |
create a string expression
Definition at line 9438 of file z3py.py.
Referenced by SeqRef.as_string(), and Extract().
| def z3py.substitute | ( | t, | |
| * | m | ||
| ) |
Apply substitution m on t, m is a list of pairs of the form (from, to). Every occurrence in t of from is replaced with to.
>>> x = Int('x')
>>> y = Int('y')
>>> substitute(x + 1, (x, y + 1))
y + 1 + 1
>>> f = Function('f', IntSort(), IntSort())
>>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
1 + 1
Definition at line 7500 of file z3py.py.
| def z3py.substitute_vars | ( | t, | |
| * | m | ||
| ) |
Substitute the free variables in t with the expression in m.
>>> v0 = Var(0, IntSort())
>>> v1 = Var(1, IntSort())
>>> x = Int('x')
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> # replace v0 with x+1 and v1 with x
>>> substitute_vars(f(v0, v1), x + 1, x)
f(x + 1, x)
Definition at line 7526 of file z3py.py.
| def z3py.SuffixOf | ( | a, | |
| b | |||
| ) |
| def z3py.Sum | ( | * | args | ) |
Create the sum of the Z3 expressions.
>>> a, b, c = Ints('a b c')
>>> Sum(a, b, c)
a + b + c
>>> Sum([a, b, c])
a + b + c
>>> A = IntVector('a', 5)
>>> Sum(A)
a__0 + a__1 + a__2 + a__3 + a__4
Definition at line 7546 of file z3py.py.
| def z3py.tactic_description | ( | name, | |
ctx = None |
|||
| ) |
Return a short description for the tactic named `name`.
>>> d = tactic_description('simplify')
Definition at line 7186 of file z3py.py.
Referenced by describe_tactics().
| def z3py.tactics | ( | ctx = None | ) |
Return a list of all available tactics in Z3.
>>> l = tactics()
>>> l.count('simplify') == 1
True
Definition at line 7176 of file z3py.py.
Referenced by describe_tactics().
| def z3py.Then | ( | * | ts, |
| ** | ks | ||
| ) |
Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
>>> x, y = Ints('x y')
>>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
>>> t(And(x == 0, y > x + 1))
[[Not(y <= 1)]]
>>> t(And(x == 0, y > x + 1)).as_expr()
Not(y <= 1)
| def z3py.to_symbol | ( | s, | |
ctx = None |
|||
| ) |
Convert an integer or string into a Z3 symbol.
Definition at line 100 of file z3py.py.
Referenced by Fixedpoint.add_rule(), Optimize.add_soft(), Array(), BitVec(), Bool(), Const(), CreateDatatypes(), DeclareSort(), EnumSort(), FiniteDomainSort(), FP(), Function(), ParamDescrsRef.get_documentation(), ParamDescrsRef.get_kind(), Int(), is_quantifier(), prove(), Real(), ParamsRef.set(), Fixedpoint.set_predicate_representation(), SolverFor(), String(), and Fixedpoint.update_rule().
| def z3py.ToInt | ( | a | ) |
| def z3py.ToReal | ( | a | ) |
| def z3py.tree_interpolant | ( | pat, | |
p = None, |
|||
ctx = None |
|||
| ) |
Compute interpolant for a tree of formulas.
The input is an interpolation pattern over a set of formulas C.
The pattern pat is a formula combining the formulas in C using
logical conjunction and the "interp" operator (see Interp). This
interp operator is logically the identity operator. It marks the
sub-formulas of the pattern for which interpolants should be
computed. The interpolant is a map sigma from marked subformulas
to formulas, such that, for each marked subformula phi of pat
(where phi sigma is phi with sigma(psi) substituted for each
subformula psi of phi such that psi in dom(sigma)):
1) phi sigma implies sigma(phi), and
2) sigma(phi) is in the common uninterpreted vocabulary between
the formulas of C occurring in phi and those not occurring in
phi
and moreover pat sigma implies false. In the simplest case
an interpolant for the pattern "(and (interp A) B)" maps A
to an interpolant for A /\ B.
The return value is a vector of formulas representing sigma. This
vector contains sigma(phi) for each marked subformula of pat, in
pre-order traversal. This means that subformulas of phi occur before phi
in the vector. Also, subformulas that occur multiply in pat will
occur multiply in the result vector.
If pat is satisfiable, raises an object of class ModelRef
that represents a model of pat.
If neither a proof of unsatisfiability nor a model is obtained
(for example, because of a timeout, or because models are disabled)
then None is returned.
If parameters p are supplied, these are used in creating the
solver that determines satisfiability.
>>> x = Int('x')
>>> y = Int('y')
>>> print(tree_interpolant(And(Interpolant(x < 0), Interpolant(y > 2), x == y)))
[Not(x >= 0), Not(y <= 2)]
# >>> g = And(Interpolant(x<0),x<2)
# >>> try:
# ... print tree_interpolant(g).sexpr()
# ... except ModelRef as m:
# ... print m.sexpr()
(define-fun x () Int
(- 1))
Definition at line 7903 of file z3py.py.
Referenced by binary_interpolant(), and sequence_interpolant().
| def z3py.TryFor | ( | t, | |
| ms, | |||
ctx = None |
|||
| ) |
Return a tactic that applies `t` to a given goal for `ms` milliseconds. If `t` does not terminate in `ms` milliseconds, then it fails.
Definition at line 7168 of file z3py.py.
| def z3py.UDiv | ( | a, | |
| b | |||
| ) |
Create the Z3 expression (unsigned) division `self / other`.
Use the operator / for signed division.
>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> UDiv(x, y)
UDiv(x, y)
>>> UDiv(x, y).sort()
BitVec(32)
>>> (x / y).sexpr()
'(bvsdiv x y)'
>>> UDiv(x, y).sexpr()
'(bvudiv x y)'
Definition at line 3747 of file z3py.py.
| def z3py.UGE | ( | a, | |
| b | |||
| ) |
Create the Z3 expression (unsigned) `other >= self`.
Use the operator >= for signed greater than or equal to.
>>> x, y = BitVecs('x y', 32)
>>> UGE(x, y)
UGE(x, y)
>>> (x >= y).sexpr()
'(bvsge x y)'
>>> UGE(x, y).sexpr()
'(bvuge x y)'
Definition at line 3713 of file z3py.py.
| def z3py.UGT | ( | a, | |
| b | |||
| ) |
| def z3py.ULE | ( | a, | |
| b | |||
| ) |
Create the Z3 expression (unsigned) `other <= self`.
Use the operator <= for signed less than or equal to.
>>> x, y = BitVecs('x y', 32)
>>> ULE(x, y)
ULE(x, y)
>>> (x <= y).sexpr()
'(bvsle x y)'
>>> ULE(x, y).sexpr()
'(bvule x y)'
Definition at line 3679 of file z3py.py.
| def z3py.ULT | ( | a, | |
| b | |||
| ) |
| def z3py.Union | ( | * | args | ) |
Create union of regular expressions.
>>> re = Union(Re("a"), Re("b"), Re("c"))
>>> print (simplify(InRe("d", re)))
False
Definition at line 9617 of file z3py.py.
Referenced by ReRef.__add__().
| def z3py.Update | ( | a, | |
| i, | |||
| v | |||
| ) |
Return a Z3 store array expression.
>>> a = Array('a', IntSort(), IntSort())
>>> i, v = Ints('i v')
>>> s = Update(a, i, v)
>>> s.sort()
Array(Int, Int)
>>> prove(s[i] == v)
proved
>>> j = Int('j')
>>> prove(Implies(i != j, s[j] == a[j]))
proved
Definition at line 4144 of file z3py.py.
Referenced by Store().
| def z3py.URem | ( | a, | |
| b | |||
| ) |
Create the Z3 expression (unsigned) remainder `self % other`.
Use the operator % for signed modulus, and SRem() for signed remainder.
>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> URem(x, y)
URem(x, y)
>>> URem(x, y).sort()
BitVec(32)
>>> (x % y).sexpr()
'(bvsmod x y)'
>>> URem(x, y).sexpr()
'(bvurem x y)'
Definition at line 3767 of file z3py.py.
| def z3py.Var | ( | idx, | |
| s | |||
| ) |
| def z3py.When | ( | p, | |
| t, | |||
ctx = None |
|||
| ) |
Return a tactic that applies tactic `t` only if probe `p` evaluates to true. Otherwise, it returns the input goal unmodified.
>>> t = When(Probe('size') > 2, Tactic('simplify'))
>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.add(x > 0)
>>> g.add(y > 0)
>>> t(g)
[[x > 0, y > 0]]
>>> g.add(x == y + 1)
>>> t(g)
[[Not(x <= 0), Not(y <= 0), x == 1 + y]]
Definition at line 7434 of file z3py.py.
| def z3py.With | ( | t, | |
| * | args, | ||
| ** | keys | ||
| ) |
Return a tactic that applies tactic `t` using the given configuration options.
>>> x, y = Ints('x y')
>>> t = With(Tactic('simplify'), som=True)
>>> t((x + 1)*(y + 2) == 0)
[[2*x + y + x*y == -2]]
Definition at line 7136 of file z3py.py.
| def z3py.Xor | ( | a, | |
| b, | |||
ctx = None |
|||
| ) |
| def z3py.ZeroExt | ( | n, | |
| a | |||
| ) |
Return a bit-vector expression with `n` extra zero-bits.
>>> x = BitVec('x', 16)
>>> n = ZeroExt(8, x)
>>> n.size()
24
>>> n
ZeroExt(8, x)
>>> n.sort()
BitVec(24)
>>> v0 = BitVecVal(2, 2)
>>> v0
2
>>> v0.size()
2
>>> v = simplify(ZeroExt(6, v0))
>>> v
2
>>> v.size()
8
Definition at line 3897 of file z3py.py.
| sat = CheckSatResult(Z3_L_TRUE) |
| unknown = CheckSatResult(Z3_L_UNDEF) |
| unsat = CheckSatResult(Z3_L_FALSE) |
1.8.15