Public Member Functions | |
Expr | simplify () |
Expr | simplify (Params p) |
FuncDecl | getFuncDecl () |
Z3_lbool | getBoolValue () |
int | getNumArgs () |
Expr [] | getArgs () |
Expr | update (Expr[] args) |
Expr | substitute (Expr[] from, Expr[] to) |
Expr | substitute (Expr from, Expr to) |
Expr | substituteVars (Expr[] to) |
Expr | translate (Context ctx) |
String | toString () |
boolean | isNumeral () |
boolean | isWellSorted () |
Sort | getSort () |
boolean | isConst () |
boolean | isIntNum () |
boolean | isRatNum () |
boolean | isAlgebraicNumber () |
boolean | isBool () |
boolean | isTrue () |
boolean | isFalse () |
boolean | isEq () |
boolean | isDistinct () |
boolean | isITE () |
boolean | isAnd () |
boolean | isOr () |
boolean | isIff () |
boolean | isXor () |
boolean | isNot () |
boolean | isImplies () |
boolean | isInt () |
boolean | isReal () |
boolean | isArithmeticNumeral () |
boolean | isLE () |
boolean | isGE () |
boolean | isLT () |
boolean | isGT () |
boolean | isAdd () |
boolean | isSub () |
boolean | isUMinus () |
boolean | isMul () |
boolean | isDiv () |
boolean | isIDiv () |
boolean | isRemainder () |
boolean | isModulus () |
boolean | isIntToReal () |
boolean | isRealToInt () |
boolean | isRealIsInt () |
boolean | isArray () |
boolean | isStore () |
boolean | isSelect () |
boolean | isConstantArray () |
boolean | isDefaultArray () |
boolean | isArrayMap () |
boolean | isAsArray () |
boolean | isSetUnion () |
boolean | isSetIntersect () |
boolean | isSetDifference () |
boolean | isSetComplement () |
boolean | isSetSubset () |
boolean | isBV () |
boolean | isBVNumeral () |
boolean | isBVBitOne () |
boolean | isBVBitZero () |
boolean | isBVUMinus () |
boolean | isBVAdd () |
boolean | isBVSub () |
boolean | isBVMul () |
boolean | isBVSDiv () |
boolean | isBVUDiv () |
boolean | isBVSRem () |
boolean | isBVURem () |
boolean | isBVSMod () |
boolean | isBVULE () |
boolean | isBVSLE () |
boolean | isBVUGE () |
boolean | isBVSGE () |
boolean | isBVULT () |
boolean | isBVSLT () |
boolean | isBVUGT () |
boolean | isBVSGT () |
boolean | isBVAND () |
boolean | isBVOR () |
boolean | isBVNOT () |
boolean | isBVXOR () |
boolean | isBVNAND () |
boolean | isBVNOR () |
boolean | isBVXNOR () |
boolean | isBVConcat () |
boolean | isBVSignExtension () |
boolean | isBVZeroExtension () |
boolean | isBVExtract () |
boolean | isBVRepeat () |
boolean | isBVReduceOR () |
boolean | isBVReduceAND () |
boolean | isBVComp () |
boolean | isBVShiftLeft () |
boolean | isBVShiftRightLogical () |
boolean | isBVShiftRightArithmetic () |
boolean | isBVRotateLeft () |
boolean | isBVRotateRight () |
boolean | isBVRotateLeftExtended () |
boolean | isBVRotateRightExtended () |
boolean | isIntToBV () |
boolean | isBVToInt () |
boolean | isBVCarry () |
boolean | isBVXOR3 () |
boolean | isLabel () |
boolean | isLabelLit () |
boolean | isOEQ () |
boolean | isProofTrue () |
boolean | isProofAsserted () |
boolean | isProofGoal () |
boolean | isProofModusPonens () |
boolean | isProofReflexivity () |
boolean | isProofSymmetry () |
boolean | isProofTransitivity () |
boolean | isProofTransitivityStar () |
boolean | isProofMonotonicity () |
boolean | isProofQuantIntro () |
boolean | isProofDistributivity () |
boolean | isProofAndElimination () |
boolean | isProofOrElimination () |
boolean | isProofRewrite () |
boolean | isProofRewriteStar () |
boolean | isProofPullQuant () |
boolean | isProofPullQuantStar () |
boolean | isProofPushQuant () |
boolean | isProofElimUnusedVars () |
boolean | isProofDER () |
boolean | isProofQuantInst () |
boolean | isProofHypothesis () |
boolean | isProofLemma () |
boolean | isProofUnitResolution () |
boolean | isProofIFFTrue () |
boolean | isProofIFFFalse () |
boolean | isProofCommutativity () |
boolean | isProofDefAxiom () |
boolean | isProofDefIntro () |
boolean | isProofApplyDef () |
boolean | isProofIFFOEQ () |
boolean | isProofNNFPos () |
boolean | isProofNNFNeg () |
boolean | isProofNNFStar () |
boolean | isProofCNFStar () |
boolean | isProofSkolemize () |
boolean | isProofModusPonensOEQ () |
boolean | isProofTheoryLemma () |
boolean | isRelation () |
boolean | isRelationStore () |
boolean | isEmptyRelation () |
boolean | isIsEmptyRelation () |
boolean | isRelationalJoin () |
boolean | isRelationUnion () |
boolean | isRelationWiden () |
boolean | isRelationProject () |
boolean | isRelationFilter () |
boolean | isRelationNegationFilter () |
boolean | isRelationRename () |
boolean | isRelationComplement () |
boolean | isRelationSelect () |
boolean | isRelationClone () |
boolean | isFiniteDomain () |
boolean | isFiniteDomainLT () |
int | getIndex () |
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boolean | equals (Object o) |
int | compareTo (AST other) |
int | hashCode () |
int | getId () |
AST | translate (Context ctx) |
Z3_ast_kind | getASTKind () |
boolean | isExpr () |
boolean | isApp () |
boolean | isVar () |
boolean | isQuantifier () |
boolean | isSort () |
boolean | isFuncDecl () |
String | toString () |
String | getSExpr () |
Protected Member Functions | |
Expr (Context ctx, long obj) | |
Constructor for Expr
Z3Exception | on error |
Definition at line 2105 of file Expr.java.
Referenced by Expr.update().
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The arguments of the expression.
Z3Exception | on error |
Definition at line 105 of file Expr.java.
Referenced by FuncInterp.toString().
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Indicates whether the expression is the true or false expression or something else (Z3_L_UNDEF).
Z3Exception | on error |
Definition at line 84 of file Expr.java.
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The function declaration of the function that is applied in this expression.
Z3Exception | on error |
Definition at line 72 of file Expr.java.
Referenced by Model.getConstInterp(), Expr.isAdd(), Expr.isAnd(), Expr.isArithmeticNumeral(), Expr.isArrayMap(), Expr.isAsArray(), Expr.isBVAdd(), Expr.isBVAND(), Expr.isBVBitOne(), Expr.isBVBitZero(), Expr.isBVCarry(), Expr.isBVComp(), Expr.isBVConcat(), Expr.isBVExtract(), Expr.isBVMul(), Expr.isBVNAND(), Expr.isBVNOR(), Expr.isBVNOT(), Expr.isBVNumeral(), Expr.isBVOR(), Expr.isBVReduceAND(), Expr.isBVReduceOR(), Expr.isBVRepeat(), Expr.isBVRotateLeft(), Expr.isBVRotateLeftExtended(), Expr.isBVRotateRight(), Expr.isBVRotateRightExtended(), Expr.isBVSDiv(), Expr.isBVSGE(), Expr.isBVSGT(), Expr.isBVShiftLeft(), Expr.isBVShiftRightArithmetic(), Expr.isBVShiftRightLogical(), Expr.isBVSignExtension(), Expr.isBVSLE(), Expr.isBVSLT(), Expr.isBVSMod(), Expr.isBVSRem(), Expr.isBVSub(), Expr.isBVToInt(), Expr.isBVUDiv(), Expr.isBVUGE(), Expr.isBVUGT(), Expr.isBVULE(), Expr.isBVULT(), Expr.isBVUMinus(), Expr.isBVURem(), Expr.isBVXNOR(), Expr.isBVXOR(), Expr.isBVXOR3(), Expr.isBVZeroExtension(), Expr.isConst(), Expr.isConstantArray(), Expr.isDefaultArray(), Expr.isDistinct(), Expr.isDiv(), Expr.isEmptyRelation(), Expr.isEq(), Expr.isFalse(), Expr.isFiniteDomainLT(), Expr.isGE(), Expr.isGT(), Expr.isIDiv(), Expr.isIff(), Expr.isImplies(), Expr.isIntToBV(), Expr.isIntToReal(), Expr.isIsEmptyRelation(), Expr.isITE(), Expr.isLabel(), Expr.isLabelLit(), Expr.isLE(), Expr.isLT(), Expr.isModulus(), Expr.isMul(), Expr.isNot(), Expr.isOEQ(), Expr.isOr(), Expr.isProofAndElimination(), Expr.isProofApplyDef(), Expr.isProofAsserted(), Expr.isProofCNFStar(), Expr.isProofCommutativity(), Expr.isProofDefAxiom(), Expr.isProofDefIntro(), Expr.isProofDER(), Expr.isProofDistributivity(), Expr.isProofElimUnusedVars(), Expr.isProofGoal(), Expr.isProofHypothesis(), Expr.isProofIFFFalse(), Expr.isProofIFFOEQ(), Expr.isProofIFFTrue(), Expr.isProofLemma(), Expr.isProofModusPonens(), Expr.isProofModusPonensOEQ(), Expr.isProofMonotonicity(), Expr.isProofNNFNeg(), Expr.isProofNNFPos(), Expr.isProofNNFStar(), Expr.isProofOrElimination(), Expr.isProofPullQuant(), Expr.isProofPullQuantStar(), Expr.isProofPushQuant(), Expr.isProofQuantInst(), Expr.isProofQuantIntro(), Expr.isProofReflexivity(), Expr.isProofRewrite(), Expr.isProofRewriteStar(), Expr.isProofSkolemize(), Expr.isProofSymmetry(), Expr.isProofTheoryLemma(), Expr.isProofTransitivity(), Expr.isProofTransitivityStar(), Expr.isProofTrue(), Expr.isProofUnitResolution(), Expr.isRealIsInt(), Expr.isRealToInt(), Expr.isRelationalJoin(), Expr.isRelationClone(), Expr.isRelationComplement(), Expr.isRelationFilter(), Expr.isRelationNegationFilter(), Expr.isRelationProject(), Expr.isRelationRename(), Expr.isRelationSelect(), Expr.isRelationStore(), Expr.isRelationUnion(), Expr.isRelationWiden(), Expr.isRemainder(), FPRMNum.isRNA(), FPRMNum.isRNE(), FPRMNum.isRoundNearestTiesToAway(), FPRMNum.isRoundNearestTiesToEven(), FPRMNum.isRoundTowardNegative(), FPRMNum.isRoundTowardPositive(), FPRMNum.isRoundTowardZero(), FPRMNum.isRTN(), FPRMNum.isRTP(), FPRMNum.isRTZ(), Expr.isSelect(), Expr.isSetComplement(), Expr.isSetDifference(), Expr.isSetIntersect(), Expr.isSetSubset(), Expr.isSetUnion(), Expr.isStore(), Expr.isSub(), Expr.isTrue(), Expr.isUMinus(), and Expr.isXor().
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The de-Burijn index of a bound variable. Remarks: Bound variables are indexed by de-Bruijn indices. It is perhaps easiest to explain the meaning of de-Bruijn indices by indicating the compilation process from non-de-Bruijn formulas to de-Bruijn format.
The last line is significant: the index of a bound variable is different depending on the scope in which it appears. The deeper x appears, the higher is its index.
Z3Exception | on error |
Definition at line 2092 of file Expr.java.
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The number of arguments of the expression.
Z3Exception | on error |
Definition at line 95 of file Expr.java.
Referenced by Expr.getArgs(), Expr.isConst(), and Expr.update().
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The Sort of the term.
Z3Exception | on error |
Definition at line 242 of file Expr.java.
Referenced by FPExpr.getEBits(), FPExpr.getSBits(), and BitVecExpr.getSortSize().
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Indicates whether the term is addition (binary)
Z3Exception | on error |
Definition at line 487 of file Expr.java.
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Indicates whether the term is an n-ary conjunction
Z3Exception | on error |
Definition at line 356 of file Expr.java.
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Indicates whether the term is an arithmetic numeral.
Z3Exception | on error |
Definition at line 437 of file Expr.java.
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Indicates whether the term is of an array sort.
Z3Exception | on error |
Definition at line 598 of file Expr.java.
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Indicates whether the term is an array map. Remarks: It satisfies mapf[i] = f(a1[i],...,a_n[i]) for every i.
Z3Exception | on error |
Definition at line 655 of file Expr.java.
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Indicates whether the term is an as-array term. Remarks: An as-array term * is n array value that behaves as the function graph of the function * passed as parameter.
Z3Exception | on error |
Definition at line 666 of file Expr.java.
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Indicates whether the term has Boolean sort.
Z3Exception | on error |
Definition at line 293 of file Expr.java.
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Indicates whether the terms is of bit-vector sort.
Z3Exception | on error |
Definition at line 726 of file Expr.java.
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Indicates whether the term is a bit-vector addition (binary)
Z3Exception | on error |
Definition at line 778 of file Expr.java.
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Indicates whether the term is a bit-wise AND
Z3Exception | on error |
Definition at line 989 of file Expr.java.
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Indicates whether the term is a one-bit bit-vector with value one
Z3Exception | on error |
Definition at line 748 of file Expr.java.
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Indicates whether the term is a one-bit bit-vector with value zero
Z3Exception | on error |
Definition at line 758 of file Expr.java.
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Indicates whether the term is a bit-vector carry Remarks: Compute the * carry bit in a full-adder. The meaning is given by the equivalence (carry * l1 l2 l3) <=> (or (and l1 l2) (and l1 l3) (and l2 l3)))
Z3Exception | on error |
Definition at line 1238 of file Expr.java.
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Indicates whether the term is a bit-vector comparison
Z3Exception | on error |
Definition at line 1129 of file Expr.java.
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Indicates whether the term is a bit-vector concatenation (binary)
Z3Exception | on error |
Definition at line 1059 of file Expr.java.
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Indicates whether the term is a bit-vector extraction
Z3Exception | on error |
Definition at line 1089 of file Expr.java.
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Indicates whether the term is a bit-vector multiplication (binary)
Z3Exception | on error |
Definition at line 798 of file Expr.java.
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Indicates whether the term is a bit-wise NAND
Z3Exception | on error |
Definition at line 1029 of file Expr.java.
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Indicates whether the term is a bit-wise NOR
Z3Exception | on error |
Definition at line 1039 of file Expr.java.
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Indicates whether the term is a bit-wise NOT
Z3Exception | on error |
Definition at line 1009 of file Expr.java.
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Indicates whether the term is a bit-vector numeral
Z3Exception | on error |
Definition at line 738 of file Expr.java.
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Indicates whether the term is a bit-wise OR
Z3Exception | on error |
Definition at line 999 of file Expr.java.
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Indicates whether the term is a bit-vector reduce AND
Z3Exception | on error |
Definition at line 1119 of file Expr.java.
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Indicates whether the term is a bit-vector reduce OR
Z3Exception | on error |
Definition at line 1109 of file Expr.java.
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Indicates whether the term is a bit-vector repetition
Z3Exception | on error |
Definition at line 1099 of file Expr.java.
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Indicates whether the term is a bit-vector rotate left
Z3Exception | on error |
Definition at line 1169 of file Expr.java.
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Indicates whether the term is a bit-vector rotate left (extended) Remarks: Similar to Z3_OP_ROTATE_LEFT, but it is a binary operator instead of a parametric one.
Z3Exception | on error |
Definition at line 1191 of file Expr.java.
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Indicates whether the term is a bit-vector rotate right
Z3Exception | on error |
Definition at line 1179 of file Expr.java.
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Indicates whether the term is a bit-vector rotate right (extended) Remarks: Similar to Z3_OP_ROTATE_RIGHT, but it is a binary operator instead of a parametric one.
Z3Exception | on error |
Definition at line 1203 of file Expr.java.
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Indicates whether the term is a bit-vector signed division (binary)
Z3Exception | on error |
Definition at line 808 of file Expr.java.
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Indicates whether the term is a signed bit-vector greater-than-or-equal
Z3Exception | on error |
Definition at line 939 of file Expr.java.
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Indicates whether the term is a signed bit-vector greater-than
Z3Exception | on error |
Definition at line 979 of file Expr.java.
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Indicates whether the term is a bit-vector shift left
Z3Exception | on error |
Definition at line 1139 of file Expr.java.
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Indicates whether the term is a bit-vector arithmetic shift left
Z3Exception | on error |
Definition at line 1159 of file Expr.java.
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Indicates whether the term is a bit-vector logical shift right
Z3Exception | on error |
Definition at line 1149 of file Expr.java.
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Indicates whether the term is a bit-vector sign extension
Z3Exception | on error |
Definition at line 1069 of file Expr.java.
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Indicates whether the term is a signed bit-vector less-than-or-equal
Z3Exception | on error |
Definition at line 918 of file Expr.java.
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Indicates whether the term is a signed bit-vector less-than
Z3Exception | on error |
Definition at line 959 of file Expr.java.
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Indicates whether the term is a bit-vector signed modulus
Z3Exception | on error |
Definition at line 848 of file Expr.java.
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Indicates whether the term is a bit-vector signed remainder (binary)
Z3Exception | on error |
Definition at line 828 of file Expr.java.
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Indicates whether the term is a bit-vector subtraction (binary)
Z3Exception | on error |
Definition at line 788 of file Expr.java.
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Indicates whether the term is a coercion from bit-vector to integer
Remarks: This function is not supported by the decision procedures. Only * the most rudimentary simplification rules are applied to this * function.
Z3Exception | on error |
Definition at line 1227 of file Expr.java.
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Indicates whether the term is a bit-vector unsigned division (binary)
Z3Exception | on error |
Definition at line 818 of file Expr.java.
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Indicates whether the term is an unsigned bit-vector greater-than-or-equal
Z3Exception | on error |
Definition at line 929 of file Expr.java.
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Indicates whether the term is an unsigned bit-vector greater-than
Z3Exception | on error |
Definition at line 969 of file Expr.java.
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Indicates whether the term is an unsigned bit-vector less-than-or-equal
Z3Exception | on error |
Definition at line 908 of file Expr.java.
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Indicates whether the term is an unsigned bit-vector less-than
Z3Exception | on error |
Definition at line 949 of file Expr.java.
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Indicates whether the term is a bit-vector unary minus
Z3Exception | on error |
Definition at line 768 of file Expr.java.
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Indicates whether the term is a bit-vector unsigned remainder (binary)
Z3Exception | on error |
Definition at line 838 of file Expr.java.
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Indicates whether the term is a bit-wise XNOR
Z3Exception | on error |
Definition at line 1049 of file Expr.java.
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Indicates whether the term is a bit-wise XOR
Z3Exception | on error |
Definition at line 1019 of file Expr.java.
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Indicates whether the term is a bit-vector ternary XOR Remarks: The * meaning is given by the equivalence (xor3 l1 l2 l3) <=> (xor (xor * l1 l2) l3)
Z3Exception | on error |
Definition at line 1249 of file Expr.java.
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Indicates whether the term is a bit-vector zero extension
Z3Exception | on error |
Definition at line 1079 of file Expr.java.
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Indicates whether the term represents a constant.
Z3Exception | on error |
Definition at line 253 of file Expr.java.
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Indicates whether the term is a constant array. Remarks: For example, * select(const(v),i) = v holds for every v and i. The function is * unary.
Z3Exception | on error |
Definition at line 632 of file Expr.java.
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Indicates whether the term is a default array. Remarks: For example default(const(v)) = v. The function is unary.
Z3Exception | on error |
Definition at line 643 of file Expr.java.
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Indicates whether the term is an n-ary distinct predicate (every argument is mutually distinct).
Z3Exception | on error |
Definition at line 336 of file Expr.java.
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Indicates whether the term is division (binary)
Z3Exception | on error |
Definition at line 527 of file Expr.java.
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Indicates whether the term is an empty relation
Z3Exception | on error |
Definition at line 1902 of file Expr.java.
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Indicates whether the term is an equality predicate.
Z3Exception | on error |
Definition at line 325 of file Expr.java.
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Indicates whether the term is the constant false.
Z3Exception | on error |
Definition at line 315 of file Expr.java.
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Indicates whether the term is of an array sort.
Z3Exception | on error |
Definition at line 2056 of file Expr.java.
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Indicates whether the term is a less than predicate over a finite domain.
Z3Exception | on error |
Definition at line 2069 of file Expr.java.
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Indicates whether the term is a greater-than-or-equal
Z3Exception | on error |
Definition at line 457 of file Expr.java.
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Indicates whether the term is a greater-than
Z3Exception | on error |
Definition at line 477 of file Expr.java.
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Indicates whether the term is integer division (binary)
Z3Exception | on error |
Definition at line 537 of file Expr.java.
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Indicates whether the term is an if-and-only-if (Boolean equivalence, binary)
Z3Exception | on error |
Definition at line 377 of file Expr.java.
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Indicates whether the term is an implication
Z3Exception | on error |
Definition at line 407 of file Expr.java.
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Indicates whether the term is of integer sort.
Z3Exception | on error |
Definition at line 417 of file Expr.java.
Referenced by Expr.isIntNum().
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Indicates whether the term is an integer numeral.
Z3Exception | on error |
Definition at line 263 of file Expr.java.
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Indicates whether the term is a coercion from integer to bit-vector
Remarks: This function is not supported by the decision procedures. Only * the most rudimentary simplification rules are applied to this * function.
Z3Exception | on error |
Definition at line 1215 of file Expr.java.
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Indicates whether the term is a coercion of integer to real (unary)
Z3Exception | on error |
Definition at line 567 of file Expr.java.
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Indicates whether the term is a test for the emptiness of a relation
Z3Exception | on error |
Definition at line 1912 of file Expr.java.
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Indicates whether the term is a ternary if-then-else term
Z3Exception | on error |
Definition at line 346 of file Expr.java.
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Indicates whether the term is a label (used by the Boogie Verification condition generator). Remarks: The label has two parameters, a string and a Boolean polarity. It takes one argument, a formula.
Z3Exception | on error |
Definition at line 1262 of file Expr.java.
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Indicates whether the term is a label literal (used by the Boogie Verification condition generator). Remarks: A label literal has a set of string parameters. It takes no arguments.
Z3Exception | on error |
Definition at line 1275 of file Expr.java.
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Indicates whether the term is a less-than-or-equal
Z3Exception | on error |
Definition at line 447 of file Expr.java.
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Indicates whether the term is a less-than
Z3Exception | on error |
Definition at line 467 of file Expr.java.
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Indicates whether the term is modulus (binary)
Z3Exception | on error |
Definition at line 557 of file Expr.java.
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Indicates whether the term is multiplication (binary)
Z3Exception | on error |
Definition at line 517 of file Expr.java.
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Indicates whether the term is a negation
Z3Exception | on error |
Definition at line 397 of file Expr.java.
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Indicates whether the term is a numeral
Z3Exception | on error |
Definition at line 221 of file Expr.java.
Referenced by Expr.isIntNum(), and Expr.isRatNum().
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Indicates whether the term is a binary equivalence modulo namings. Remarks: This binary predicate is used in proof terms. It captures equisatisfiability and equivalence modulo renamings.
Z3Exception | on error |
Definition at line 1287 of file Expr.java.
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Indicates whether the term is an n-ary disjunction
Z3Exception | on error |
Definition at line 366 of file Expr.java.
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Indicates whether the term is a proof by elimination of AND Remarks: * Given a proof for (and l_1 ... l_n), produces a proof for l_i T1: (and * l_1 ... l_n) [and-elim T1]: l_i
Z3Exception | on error |
Definition at line 1448 of file Expr.java.
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Indicates whether the term is a proof for application of a definition Remarks: [apply-def T1]: F ~ n F is 'equivalent' to n, given that T1 is a proof that n is a name for F.
Z3Exception | on error |
Definition at line 1721 of file Expr.java.
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Indicates whether the term is a proof for a fact asserted by the user.
Z3Exception | on error |
Definition at line 1307 of file Expr.java.
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Indicates whether the term is a proof for (~ P Q) where Q is in conjunctive normal form. Remarks: A proof for (~ P Q) where Q is in conjunctive normal form. This proof object is only used if the parameter PROOF_MODE is 1. This proof object may have n antecedents. Each antecedent is a PR_DEF_INTRO.
Z3Exception | on error |
Definition at line 1813 of file Expr.java.
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Indicates whether the term is a proof by commutativity Remarks: [comm]: (= (f a b) (f b a))
f is a commutative operator.
This proof object has no antecedents. Remark: if f is bool, then = is iff.
Z3Exception | on error |
Definition at line 1660 of file Expr.java.
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Indicates whether the term is a proof for Tseitin-like axioms Remarks: Proof object used to justify Tseitin's like axioms:
(or (not (and p q)) p) (or (not (and p q)) q) (or (not (and p q r)) p) (or (not (and p q r)) q) (or (not (and p q r)) r) ... (or (and p q) (not p) (not q)) (or (not (or p q)) p q) (or (or p q) (not p)) (or (or p q) (not q)) (or (not (iff p q)) (not p) q) (or (not (iff p q)) p (not q)) (or (iff p q) (not p) (not q)) (or (iff p q) p q) (or (not (ite a b c)) (not a) b) (or (not (ite a b c)) a c) (or (ite a b c) (not a) (not b)) (or (ite a b c) a (not c)) (or (not (not a)) (not a)) (or (not a) a)
This proof object has no antecedents. Note: all axioms are propositional tautologies. Note also that 'and' and 'or' can take multiple arguments. You can recover the propositional tautologies by unfolding the Boolean connectives in the axioms a small bounded number of steps (=3).
Z3Exception | on error |
Definition at line 1686 of file Expr.java.
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Indicates whether the term is a proof for introduction of a name Remarks: Introduces a name for a formula/term. Suppose e is an expression with free variables x, and def-intro introduces the name n(x). The possible cases are:
When e is of Boolean type: [def-intro]: (and (or n (not e)) (or (not n) e))
or: [def-intro]: (or (not n) e) when e only occurs positively.
When e is of the form (ite cond th el): [def-intro]: (and (or (not cond) (= n th)) (or cond (= n el)))
Otherwise: [def-intro]: (= n e)
Z3Exception | on error |
Definition at line 1709 of file Expr.java.
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Indicates whether the term is a proof for destructive equality resolution Remarks: A proof for destructive equality resolution: (iff (forall (x) (or (not (= x t)) P[x])) P[t]) if x does not occur in t.
This proof object has no antecedents.
Several variables can be eliminated simultaneously.
Z3Exception | on error |
Definition at line 1568 of file Expr.java.
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Indicates whether the term is a distributivity proof object. Remarks: Given that f (= or) distributes over g (= and), produces a proof for (= (f a (g c d)) (g (f a c) (f a d))) If f and g are associative, this proof also justifies the following equality: (= (f (g a b) (g c d)) (g (f a c) (f a d) (f b c) (f b d))) where each f and g can have arbitrary number of arguments.
This proof object has no antecedents. Remark. This rule is used by the CNF conversion pass and instantiated by f = or, and g = and.
Z3Exception | on error |
Definition at line 1437 of file Expr.java.
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Indicates whether the term is a proof for elimination of unused variables. Remarks: A proof for (iff (forall (x_1 ... x_n y_1 ... y_m) p[x_1 ... x_n]) (forall (x_1 ... x_n) p[x_1 ... x_n]))
It is used to justify the elimination of unused variables. This proof object has no antecedents.
Z3Exception | on error |
Definition at line 1552 of file Expr.java.
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Indicates whether the term is a proof for a fact (tagged as goal) asserted by the user.
Z3Exception | on error |
Definition at line 1318 of file Expr.java.
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Indicates whether the term is a hypthesis marker. Remarks: Mark a hypothesis in a natural deduction style proof.
Z3Exception | on error |
Definition at line 1592 of file Expr.java.
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Indicates whether the term is a proof by iff-false Remarks: T1: (not p) [iff-false T1]: (iff p false)
Z3Exception | on error |
Definition at line 1643 of file Expr.java.
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Indicates whether the term is a proof iff-oeq Remarks: T1: (iff p q) [iff~ T1]: (~ p q)
Z3Exception | on error |
Definition at line 1733 of file Expr.java.
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Indicates whether the term is a proof by iff-true Remarks: T1: p [iff-true T1]: (iff p true)
Z3Exception | on error |
Definition at line 1631 of file Expr.java.
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Indicates whether the term is a proof by lemma Remarks: T1: false [lemma T1]: (or (not l_1) ... (not l_n))
This proof object has one antecedent: a hypothetical proof for false. It converts the proof in a proof for (or (not l_1) ... (not l_n)), when T1 contains the hypotheses: l_1, ..., l_n.
Z3Exception | on error |
Definition at line 1608 of file Expr.java.
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Indicates whether the term is proof via modus ponens Remarks: Given a proof for p and a proof for (implies p q), produces a proof for q. T1: p T2: (implies p q) [mp T1 T2]: q The second antecedents may also be a proof for (iff p q).
Z3Exception | on error |
Definition at line 1332 of file Expr.java.
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Indicates whether the term is a proof by modus ponens for equi-satisfiability. Remarks: Modus ponens style rule for equi-satisfiability. T1: p T2: (~ p q) [mp~ T1 T2]: q
Z3Exception | on error |
Definition at line 1843 of file Expr.java.
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Indicates whether the term is a monotonicity proof object. Remarks: T1: (R t_1 s_1) ... Tn: (R t_n s_n) [monotonicity T1 ... Tn]: (R (f t_1 ... t_n) (f s_1 ... s_n)) Remark: if t_i == s_i, then the antecedent Ti is suppressed. That is, reflexivity proofs are supressed to save space.
Z3Exception | on error |
Definition at line 1407 of file Expr.java.
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Indicates whether the term is a proof for a negative NNF step Remarks: Proof for a (negative) NNF step. Examples:
T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ r_n [nnf-neg T1 ... Tn]: (not (and s_1 ... s_n)) ~ (or r_1 ... r_n) and T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ r_n [nnf-neg T1 ... Tn]: (not (or s_1 ... s_n)) ~ (and r_1 ... r_n) and T1: (not s_1) ~ r_1 T2: (not s_2) ~ r_2 T3: s_1 ~ r_1' T4: s_2 ~ r_2' [nnf-neg T1 T2 T3 T4]: (~ (not (iff s_1 s_2)) (and (or r_1 r_2) (or r_1' r_2')))
Z3Exception | on error |
Definition at line 1780 of file Expr.java.
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Indicates whether the term is a proof for a positive NNF step Remarks: Proof for a (positive) NNF step. Example:
T1: (not s_1) ~ r_1 T2: (not s_2) ~ r_2 T3: s_1 ~ r_1' T4: s_2 ~ r_2'
r_2)))
The negation normal form steps NNF_POS and NNF_NEG are used in the following cases: (a) When creating the NNF of a positive force quantifier. The quantifier is retained (unless the bound variables are eliminated). Example T1: q ~ q_new [nnf-pos T1]: (~ (forall (x T) q) (forall (x T) q_new))
(b) When recursively creating NNF over Boolean formulas, where the top-level connective is changed during NNF conversion. The relevant Boolean connectives for NNF_POS are 'implies', 'iff', 'xor', 'ite'. NNF_NEG furthermore handles the case where negation is pushed over Boolean connectives 'and' and 'or'.
Z3Exception | on error |
Definition at line 1761 of file Expr.java.
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Indicates whether the term is a proof for (~ P Q) here Q is in negation normal form. Remarks: A proof for (~ P Q) where Q is in negation normal form.
This proof object is only used if the parameter PROOF_MODE is 1.
This proof object may have n antecedents. Each antecedent is a PR_DEF_INTRO.
Z3Exception | on error |
Definition at line 1798 of file Expr.java.
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Indicates whether the term is a proof by eliminiation of not-or Remarks: * Given a proof for (not (or l_1 ... l_n)), produces a proof for (not l_i). * T1: (not (or l_1 ... l_n)) [not-or-elim T1]: (not l_i)
Z3Exception | on error |
Definition at line 1459 of file Expr.java.
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Indicates whether the term is a proof for pulling quantifiers out. Remarks: A proof for (iff (f (forall (x) q(x)) r) (forall (x) (f (q x) r))). This proof object has no antecedents.
Z3Exception | on error |
Definition at line 1510 of file Expr.java.
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Indicates whether the term is a proof for pulling quantifiers out.
Remarks: A proof for (iff P Q) where Q is in prenex normal form. This * proof object is only used if the parameter PROOF_MODE is 1. This proof * object has no antecedents
Z3Exception | on error |
Definition at line 1522 of file Expr.java.
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Indicates whether the term is a proof for pushing quantifiers in. Remarks: A proof for: (iff (forall (x_1 ... x_m) (and p_1[x_1 ... x_m] ... p_n[x_1 ... x_m])) (and (forall (x_1 ... x_m) p_1[x_1 ... x_m]) ... (forall (x_1 ... x_m) p_n[x_1 ... x_m]))) This proof object has no antecedents
Z3Exception | on error |
Definition at line 1536 of file Expr.java.
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Indicates whether the term is a proof for quantifier instantiation
Remarks: A proof of (or (not (forall (x) (P x))) (P a))
Z3Exception | on error |
Definition at line 1580 of file Expr.java.
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Indicates whether the term is a quant-intro proof Remarks: Given a proof * for (~ p q), produces a proof for (~ (forall (x) p) (forall (x) q)). T1: * (~ p q) [quant-intro T1]: (~ (forall (x) p) (forall (x) q))
Z3Exception | on error |
Definition at line 1418 of file Expr.java.
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Indicates whether the term is a proof for (R t t), where R is a reflexive relation. Remarks: This proof object has no antecedents. The only reflexive relations that are used are equivalence modulo namings, equality and equivalence. That is, R is either '~', '=' or 'iff'.
Z3Exception | on error |
Definition at line 1347 of file Expr.java.
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Indicates whether the term is a proof by rewriting Remarks: A proof for a local rewriting step (= t s). The head function symbol of t is interpreted.
This proof object has no antecedents. The conclusion of a rewrite rule is either an equality (= t s), an equivalence (iff t s), or equi-satisfiability (~ t s). Remark: if f is bool, then = is iff.
Examples: (= (+ x 0) x) (= (+ x 1 2) (+ 3 x)) (iff (or x false) x)
Z3Exception | on error |
Definition at line 1479 of file Expr.java.
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Indicates whether the term is a proof by rewriting Remarks: A proof for rewriting an expression t into an expression s. This proof object is used if the parameter PROOF_MODE is 1. This proof object can have n antecedents. The antecedents are proofs for equalities used as substitution rules. The object is also used in a few cases if the parameter PROOF_MODE is 2. The cases are: - When applying contextual simplification (CONTEXT_SIMPLIFIER=true) - When converting bit-vectors to Booleans (BIT2BOOL=true) - When pulling ite expression up (PULL_CHEAP_ITE_TREES=true)
Z3Exception | on error |
Definition at line 1498 of file Expr.java.
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Indicates whether the term is a proof for a Skolemization step Remarks: Proof for:
(p x y)) (p (sk y) y))
This proof object has no antecedents.
Z3Exception | on error |
Definition at line 1830 of file Expr.java.
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Indicates whether the term is proof by symmetricity of a relation
Remarks: Given an symmetric relation R and a proof for (R t s), produces * a proof for (R s t). T1: (R t s) [symmetry T1]: (R s t) T1 is the * antecedent of this proof object.
Z3Exception | on error |
Definition at line 1359 of file Expr.java.
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Indicates whether the term is a proof for theory lemma Remarks: Generic proof for theory lemmas.
The theory lemma function comes with one or more parameters. The first parameter indicates the name of the theory. For the theory of arithmetic, additional parameters provide hints for checking the theory lemma. The hints for arithmetic are: - farkas - followed by rational coefficients. Multiply the coefficients to the inequalities in the lemma, add the (negated) inequalities and obtain a contradiction. - triangle-eq - Indicates a lemma related to the equivalence: (iff (= t1 t2) (and (<= t1 t2) (<= t2 t1))) - gcd-test - Indicates an integer linear arithmetic lemma that uses a gcd test.
Z3Exception | on error |
Definition at line 1865 of file Expr.java.
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Indicates whether the term is a proof by transitivity of a relation
Remarks: Given a transitive relation R, and proofs for (R t s) and (R s * u), produces a proof for (R t u). T1: (R t s) T2: (R s u) [trans T1 T2]: * (R t u)
Z3Exception | on error |
Definition at line 1371 of file Expr.java.
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Indicates whether the term is a proof by condensed transitivity of a relation Remarks: Condensed transitivity proof. This proof object is only used if the parameter PROOF_MODE is 1. It combines several symmetry and transitivity proofs. Example: T1: (R a b) T2: (R c b) T3: (R c d) [trans* T1 T2 T3]: (R a d) R must be a symmetric and transitive relation.
Assuming that this proof object is a proof for (R s t), then a proof checker must check if it is possible to prove (R s t) using the antecedents, symmetry and transitivity. That is, if there is a path from s to t, if we view every antecedent (R a b) as an edge between a and b.
Z3Exception | on error |
Definition at line 1392 of file Expr.java.
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Indicates whether the term is a Proof for the expression 'true'.
Z3Exception | on error |
Definition at line 1297 of file Expr.java.
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Indicates whether the term is a proof by unit resolution Remarks: T1: * (or l_1 ... l_n l_1' ... l_m') T2: (not l_1) ... T(n+1): (not l_n) * [unit-resolution T1 ... T(n+1)]: (or l_1' ... l_m')
Z3Exception | on error |
Definition at line 1619 of file Expr.java.
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Indicates whether the term is a real numeral.
Z3Exception | on error |
Definition at line 273 of file Expr.java.
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Indicates whether the term is of sort real.
Z3Exception | on error |
Definition at line 427 of file Expr.java.
Referenced by Expr.isRatNum().
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Indicates whether the term is a check that tests whether a real is integral (unary)
Z3Exception | on error |
Definition at line 588 of file Expr.java.
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Indicates whether the term is a coercion of real to integer (unary)
Z3Exception | on error |
Definition at line 577 of file Expr.java.
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Indicates whether the term is of an array sort.
Z3Exception | on error |
Definition at line 1875 of file Expr.java.
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Indicates whether the term is a relational join
Z3Exception | on error |
Definition at line 1922 of file Expr.java.
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Indicates whether the term is a relational clone (copy) Remarks: Create a fresh copy (clone) of a relation. The function is logically the identity, but in the context of a register machine allows for terms of kind
to perform destructive updates to the first argument.
Z3Exception | on error |
Definition at line 2046 of file Expr.java.
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Indicates whether the term is the complement of a relation
Z3Exception | on error |
Definition at line 2016 of file Expr.java.
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Indicates whether the term is a relation filter Remarks: Filter (restrict) a relation with respect to a predicate. The first argument is a relation. The second argument is a predicate with free de-Brujin indices corresponding to the columns of the relation. So the first column in the relation has index 0.
Z3Exception | on error |
Definition at line 1974 of file Expr.java.
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Indicates whether the term is an intersection of a relation with the negation of another. Remarks: Intersect the first relation with respect to negation of the second relation (the function takes two arguments). Logically, the specification can be described by a function
target = filter_by_negation(pos, neg, columns)
where columns are pairs c1, d1, .., cN, dN of columns from pos and neg, such that target are elements in x in pos, such that there is no y in neg that agrees with x on the columns c1, d1, .., cN, dN.
Z3Exception | on error |
Definition at line 1994 of file Expr.java.
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Indicates whether the term is a projection of columns (provided as numbers in the parameters). Remarks: The function takes one argument.
Z3Exception | on error |
Definition at line 1959 of file Expr.java.
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Indicates whether the term is the renaming of a column in a relation Remarks: The function takes one argument. The parameters contain the renaming as a cycle.
Z3Exception | on error |
Definition at line 2006 of file Expr.java.
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Indicates whether the term is a relational select Remarks: Check if a record is an element of the relation. The function takes
arguments, where the first argument is a relation, and the remaining
arguments correspond to a record.
Z3Exception | on error |
Definition at line 2030 of file Expr.java.
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Indicates whether the term is an relation store Remarks: Insert a record into a relation. The function takes
arguments, where the first argument is the relation and the remaining
elements correspond to the
columns of the relation.
Z3Exception | on error |
Definition at line 1892 of file Expr.java.
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Indicates whether the term is the union or convex hull of two relations.
Remarks: The function takes two arguments.
Z3Exception | on error |
Definition at line 1934 of file Expr.java.
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Indicates whether the term is the widening of two relations Remarks: The function takes two arguments.
Z3Exception | on error |
Definition at line 1946 of file Expr.java.
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Indicates whether the term is remainder (binary)
Z3Exception | on error |
Definition at line 547 of file Expr.java.
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Indicates whether the term is an array select.
Z3Exception | on error |
Definition at line 621 of file Expr.java.
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Indicates whether the term is set complement
Z3Exception | on error |
Definition at line 706 of file Expr.java.
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Indicates whether the term is set difference
Z3Exception | on error |
Definition at line 696 of file Expr.java.
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Indicates whether the term is set intersection
Z3Exception | on error |
Definition at line 686 of file Expr.java.
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Indicates whether the term is set subset
Z3Exception | on error |
Definition at line 716 of file Expr.java.
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Indicates whether the term is set union
Z3Exception | on error |
Definition at line 676 of file Expr.java.
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Indicates whether the term is an array store. Remarks: It satisfies * select(store(a,i,v),j) = if i = j then v else select(a,j). Array store * takes at least 3 arguments.
Z3Exception | on error |
Definition at line 611 of file Expr.java.
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Indicates whether the term is subtraction (binary)
Z3Exception | on error |
Definition at line 497 of file Expr.java.
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Indicates whether the term is the constant true.
Z3Exception | on error |
Definition at line 305 of file Expr.java.
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Indicates whether the term is a unary minus
Z3Exception | on error |
Definition at line 507 of file Expr.java.
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Indicates whether the term is well-sorted.
Z3Exception | on error |
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Indicates whether the term is an exclusive or
Z3Exception | on error |
Definition at line 387 of file Expr.java.
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Returns a simplified version of the expression
Z3Exception | on error |
Definition at line 37 of file Expr.java.
Returns a simplified version of the expression A set of parameters
p | a Params object to configure the simplifier |
Z3Exception | on error |
Definition at line 51 of file Expr.java.
Substitute every occurrence of
in the expression with
, for
smaller than
. Remarks: The result is the new expression. The arrays
and
must have size
. For every
smaller than
, we must have that sort of
must be equal to sort of
.
Z3Exception | on error |
Definition at line 145 of file Expr.java.
Referenced by Expr.substitute().
Substitute every occurrence of
in the expression with
.
Z3Exception | on error |
Definition at line 164 of file Expr.java.
Substitute the free variables in the expression with the expressions in
Remarks: For every
smaller than *
, the variable with de-Bruijn index
* is replaced with term
.
Z3Exception | on error |
Z3Exception | on error |
Definition at line 179 of file Expr.java.
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Returns a string representation of the expression.
Definition at line 211 of file Expr.java.
Referenced by Optimize.Handle.toString().
Translates (copies) the term to the Context
.
ctx | A context |
Z3Exception | on error |
Definition at line 195 of file Expr.java.
Update the arguments of the expression using the arguments
The number of new arguments should coincide with the current number of arguments.
args | arguments |
Z3Exception | on error |
Definition at line 123 of file Expr.java.