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Public Member Functions | Protected Member Functions | Properties
Expr Class Reference

Expressions are terms. More...

+ Inheritance diagram for Expr:

Public Member Functions

Expr Simplify (Params p=null)
 Returns a simplified version of the expression. More...
 
void Update (Expr[] args)
 Update the arguments of the expression using the arguments args The number of new arguments should coincide with the current number of arguments. More...
 
Expr Substitute (Expr[] from, Expr[] to)
 Substitute every occurrence of from[i] in the expression with to[i], for i smaller than num_exprs. More...
 
Expr Substitute (Expr from, Expr to)
 Substitute every occurrence of from in the expression with to. More...
 
Expr SubstituteVars (Expr[] to)
 Substitute the free variables in the expression with the expressions in to More...
 
new Expr Translate (Context ctx)
 Translates (copies) the term to the Context ctx . More...
 
override string ToString ()
 Returns a string representation of the expression. More...
 
- Public Member Functions inherited from AST
override bool Equals (object o)
 Object comparison. More...
 
virtual int CompareTo (object other)
 Object Comparison. More...
 
override int GetHashCode ()
 The AST's hash code. More...
 
AST Translate (Context ctx)
 Translates (copies) the AST to the Context ctx . More...
 
override string ToString ()
 A string representation of the AST. More...
 
string SExpr ()
 A string representation of the AST in s-expression notation. More...
 
- Public Member Functions inherited from Z3Object
void Dispose ()
 Disposes of the underlying native Z3 object. More...
 

Protected Member Functions

 Expr (Context ctx)
 Constructor for Expr More...
 
 Expr (Context ctx, IntPtr obj)
 Constructor for Expr More...
 

Properties

FuncDecl FuncDecl [get]
 The function declaration of the function that is applied in this expression. More...
 
Z3_lbool BoolValue [get]
 Indicates whether the expression is the true or false expression or something else (Z3_L_UNDEF). More...
 
uint NumArgs [get]
 The number of arguments of the expression. More...
 
Expr[] Args [get]
 The arguments of the expression. More...
 
bool IsNumeral [get]
 Indicates whether the term is a numeral More...
 
bool IsWellSorted [get]
 Indicates whether the term is well-sorted. More...
 
Sort Sort [get]
 The Sort of the term. More...
 
bool IsConst [get]
 Indicates whether the term represents a constant. More...
 
bool IsIntNum [get]
 Indicates whether the term is an integer numeral. More...
 
bool IsRatNum [get]
 Indicates whether the term is a real numeral. More...
 
bool IsAlgebraicNumber [get]
 Indicates whether the term is an algebraic number More...
 
bool IsBool [get]
 Indicates whether the term has Boolean sort. More...
 
bool IsTrue [get]
 Indicates whether the term is the constant true. More...
 
bool IsFalse [get]
 Indicates whether the term is the constant false. More...
 
bool IsEq [get]
 Indicates whether the term is an equality predicate. More...
 
bool IsDistinct [get]
 Indicates whether the term is an n-ary distinct predicate (every argument is mutually distinct). More...
 
bool IsITE [get]
 Indicates whether the term is a ternary if-then-else term More...
 
bool IsAnd [get]
 Indicates whether the term is an n-ary conjunction More...
 
bool IsOr [get]
 Indicates whether the term is an n-ary disjunction More...
 
bool IsIff [get]
 Indicates whether the term is an if-and-only-if (Boolean equivalence, binary) More...
 
bool IsXor [get]
 Indicates whether the term is an exclusive or More...
 
bool IsNot [get]
 Indicates whether the term is a negation More...
 
bool IsImplies [get]
 Indicates whether the term is an implication More...
 
bool IsInterpolant [get]
 Indicates whether the term is marked for interpolation. More...
 
bool IsInt [get]
 Indicates whether the term is of integer sort. More...
 
bool IsReal [get]
 Indicates whether the term is of sort real. More...
 
bool IsArithmeticNumeral [get]
 Indicates whether the term is an arithmetic numeral. More...
 
bool IsLE [get]
 Indicates whether the term is a less-than-or-equal More...
 
bool IsGE [get]
 Indicates whether the term is a greater-than-or-equal More...
 
bool IsLT [get]
 Indicates whether the term is a less-than More...
 
bool IsGT [get]
 Indicates whether the term is a greater-than More...
 
bool IsAdd [get]
 Indicates whether the term is addition (binary) More...
 
bool IsSub [get]
 Indicates whether the term is subtraction (binary) More...
 
bool IsUMinus [get]
 Indicates whether the term is a unary minus More...
 
bool IsMul [get]
 Indicates whether the term is multiplication (binary) More...
 
bool IsDiv [get]
 Indicates whether the term is division (binary) More...
 
bool IsIDiv [get]
 Indicates whether the term is integer division (binary) More...
 
bool IsRemainder [get]
 Indicates whether the term is remainder (binary) More...
 
bool IsModulus [get]
 Indicates whether the term is modulus (binary) More...
 
bool IsIntToReal [get]
 Indicates whether the term is a coercion of integer to real (unary) More...
 
bool IsRealToInt [get]
 Indicates whether the term is a coercion of real to integer (unary) More...
 
bool IsRealIsInt [get]
 Indicates whether the term is a check that tests whether a real is integral (unary) More...
 
bool IsArray [get]
 Indicates whether the term is of an array sort. More...
 
bool IsStore [get]
 Indicates whether the term is an array store. More...
 
bool IsSelect [get]
 Indicates whether the term is an array select. More...
 
bool IsConstantArray [get]
 Indicates whether the term is a constant array. More...
 
bool IsDefaultArray [get]
 Indicates whether the term is a default array. More...
 
bool IsArrayMap [get]
 Indicates whether the term is an array map. More...
 
bool IsAsArray [get]
 Indicates whether the term is an as-array term. More...
 
bool IsSetUnion [get]
 Indicates whether the term is set union More...
 
bool IsSetIntersect [get]
 Indicates whether the term is set intersection More...
 
bool IsSetDifference [get]
 Indicates whether the term is set difference More...
 
bool IsSetComplement [get]
 Indicates whether the term is set complement More...
 
bool IsSetSubset [get]
 Indicates whether the term is set subset More...
 
bool IsBV [get]
 Indicates whether the terms is of bit-vector sort. More...
 
bool IsBVNumeral [get]
 Indicates whether the term is a bit-vector numeral More...
 
bool IsBVBitOne [get]
 Indicates whether the term is a one-bit bit-vector with value one More...
 
bool IsBVBitZero [get]
 Indicates whether the term is a one-bit bit-vector with value zero More...
 
bool IsBVUMinus [get]
 Indicates whether the term is a bit-vector unary minus More...
 
bool IsBVAdd [get]
 Indicates whether the term is a bit-vector addition (binary) More...
 
bool IsBVSub [get]
 Indicates whether the term is a bit-vector subtraction (binary) More...
 
bool IsBVMul [get]
 Indicates whether the term is a bit-vector multiplication (binary) More...
 
bool IsBVSDiv [get]
 Indicates whether the term is a bit-vector signed division (binary) More...
 
bool IsBVUDiv [get]
 Indicates whether the term is a bit-vector unsigned division (binary) More...
 
bool IsBVSRem [get]
 Indicates whether the term is a bit-vector signed remainder (binary) More...
 
bool IsBVURem [get]
 Indicates whether the term is a bit-vector unsigned remainder (binary) More...
 
bool IsBVSMod [get]
 Indicates whether the term is a bit-vector signed modulus More...
 
bool IsBVULE [get]
 Indicates whether the term is an unsigned bit-vector less-than-or-equal More...
 
bool IsBVSLE [get]
 Indicates whether the term is a signed bit-vector less-than-or-equal More...
 
bool IsBVUGE [get]
 Indicates whether the term is an unsigned bit-vector greater-than-or-equal More...
 
bool IsBVSGE [get]
 Indicates whether the term is a signed bit-vector greater-than-or-equal More...
 
bool IsBVULT [get]
 Indicates whether the term is an unsigned bit-vector less-than More...
 
bool IsBVSLT [get]
 Indicates whether the term is a signed bit-vector less-than More...
 
bool IsBVUGT [get]
 Indicates whether the term is an unsigned bit-vector greater-than More...
 
bool IsBVSGT [get]
 Indicates whether the term is a signed bit-vector greater-than More...
 
bool IsBVAND [get]
 Indicates whether the term is a bit-wise AND More...
 
bool IsBVOR [get]
 Indicates whether the term is a bit-wise OR More...
 
bool IsBVNOT [get]
 Indicates whether the term is a bit-wise NOT More...
 
bool IsBVXOR [get]
 Indicates whether the term is a bit-wise XOR More...
 
bool IsBVNAND [get]
 Indicates whether the term is a bit-wise NAND More...
 
bool IsBVNOR [get]
 Indicates whether the term is a bit-wise NOR More...
 
bool IsBVXNOR [get]
 Indicates whether the term is a bit-wise XNOR More...
 
bool IsBVConcat [get]
 Indicates whether the term is a bit-vector concatenation (binary) More...
 
bool IsBVSignExtension [get]
 Indicates whether the term is a bit-vector sign extension More...
 
bool IsBVZeroExtension [get]
 Indicates whether the term is a bit-vector zero extension More...
 
bool IsBVExtract [get]
 Indicates whether the term is a bit-vector extraction More...
 
bool IsBVRepeat [get]
 Indicates whether the term is a bit-vector repetition More...
 
bool IsBVReduceOR [get]
 Indicates whether the term is a bit-vector reduce OR More...
 
bool IsBVReduceAND [get]
 Indicates whether the term is a bit-vector reduce AND More...
 
bool IsBVComp [get]
 Indicates whether the term is a bit-vector comparison More...
 
bool IsBVShiftLeft [get]
 Indicates whether the term is a bit-vector shift left More...
 
bool IsBVShiftRightLogical [get]
 Indicates whether the term is a bit-vector logical shift right More...
 
bool IsBVShiftRightArithmetic [get]
 Indicates whether the term is a bit-vector arithmetic shift left More...
 
bool IsBVRotateLeft [get]
 Indicates whether the term is a bit-vector rotate left More...
 
bool IsBVRotateRight [get]
 Indicates whether the term is a bit-vector rotate right More...
 
bool IsBVRotateLeftExtended [get]
 Indicates whether the term is a bit-vector rotate left (extended) More...
 
bool IsBVRotateRightExtended [get]
 Indicates whether the term is a bit-vector rotate right (extended) More...
 
bool IsIntToBV [get]
 Indicates whether the term is a coercion from integer to bit-vector More...
 
bool IsBVToInt [get]
 Indicates whether the term is a coercion from bit-vector to integer More...
 
bool IsBVCarry [get]
 Indicates whether the term is a bit-vector carry More...
 
bool IsBVXOR3 [get]
 Indicates whether the term is a bit-vector ternary XOR More...
 
bool IsLabel [get]
 Indicates whether the term is a label (used by the Boogie Verification condition generator). More...
 
bool IsLabelLit [get]
 Indicates whether the term is a label literal (used by the Boogie Verification condition generator). More...
 
bool IsOEQ [get]
 Indicates whether the term is a binary equivalence modulo namings. More...
 
bool IsProofTrue [get]
 Indicates whether the term is a Proof for the expression 'true'. More...
 
bool IsProofAsserted [get]
 Indicates whether the term is a proof for a fact asserted by the user. More...
 
bool IsProofGoal [get]
 Indicates whether the term is a proof for a fact (tagged as goal) asserted by the user. More...
 
bool IsProofModusPonens [get]
 Indicates whether the term is proof via modus ponens More...
 
bool IsProofReflexivity [get]
 Indicates whether the term is a proof for (R t t), where R is a reflexive relation. More...
 
bool IsProofSymmetry [get]
 Indicates whether the term is proof by symmetricity of a relation More...
 
bool IsProofTransitivity [get]
 Indicates whether the term is a proof by transitivity of a relation More...
 
bool IsProofTransitivityStar [get]
 Indicates whether the term is a proof by condensed transitivity of a relation More...
 
bool IsProofMonotonicity [get]
 Indicates whether the term is a monotonicity proof object. More...
 
bool IsProofQuantIntro [get]
 Indicates whether the term is a quant-intro proof More...
 
bool IsProofDistributivity [get]
 Indicates whether the term is a distributivity proof object. More...
 
bool IsProofAndElimination [get]
 Indicates whether the term is a proof by elimination of AND More...
 
bool IsProofOrElimination [get]
 Indicates whether the term is a proof by eliminiation of not-or More...
 
bool IsProofRewrite [get]
 Indicates whether the term is a proof by rewriting More...
 
bool IsProofRewriteStar [get]
 Indicates whether the term is a proof by rewriting More...
 
bool IsProofPullQuant [get]
 Indicates whether the term is a proof for pulling quantifiers out. More...
 
bool IsProofPullQuantStar [get]
 Indicates whether the term is a proof for pulling quantifiers out. More...
 
bool IsProofPushQuant [get]
 Indicates whether the term is a proof for pushing quantifiers in. More...
 
bool IsProofElimUnusedVars [get]
 Indicates whether the term is a proof for elimination of unused variables. More...
 
bool IsProofDER [get]
 Indicates whether the term is a proof for destructive equality resolution More...
 
bool IsProofQuantInst [get]
 Indicates whether the term is a proof for quantifier instantiation More...
 
bool IsProofHypothesis [get]
 Indicates whether the term is a hypthesis marker. More...
 
bool IsProofLemma [get]
 Indicates whether the term is a proof by lemma More...
 
bool IsProofUnitResolution [get]
 Indicates whether the term is a proof by unit resolution More...
 
bool IsProofIFFTrue [get]
 Indicates whether the term is a proof by iff-true More...
 
bool IsProofIFFFalse [get]
 Indicates whether the term is a proof by iff-false More...
 
bool IsProofCommutativity [get]
 Indicates whether the term is a proof by commutativity More...
 
bool IsProofDefAxiom [get]
 Indicates whether the term is a proof for Tseitin-like axioms More...
 
bool IsProofDefIntro [get]
 Indicates whether the term is a proof for introduction of a name More...
 
bool IsProofApplyDef [get]
 Indicates whether the term is a proof for application of a definition More...
 
bool IsProofIFFOEQ [get]
 Indicates whether the term is a proof iff-oeq More...
 
bool IsProofNNFPos [get]
 Indicates whether the term is a proof for a positive NNF step More...
 
bool IsProofNNFNeg [get]
 Indicates whether the term is a proof for a negative NNF step More...
 
bool IsProofNNFStar [get]
 Indicates whether the term is a proof for (~ P Q) here Q is in negation normal form. More...
 
bool IsProofCNFStar [get]
 Indicates whether the term is a proof for (~ P Q) where Q is in conjunctive normal form. More...
 
bool IsProofSkolemize [get]
 Indicates whether the term is a proof for a Skolemization step More...
 
bool IsProofModusPonensOEQ [get]
 Indicates whether the term is a proof by modus ponens for equi-satisfiability. More...
 
bool IsProofTheoryLemma [get]
 Indicates whether the term is a proof for theory lemma More...
 
bool IsRelation [get]
 Indicates whether the term is of an array sort. More...
 
bool IsRelationStore [get]
 Indicates whether the term is an relation store More...
 
bool IsEmptyRelation [get]
 Indicates whether the term is an empty relation More...
 
bool IsIsEmptyRelation [get]
 Indicates whether the term is a test for the emptiness of a relation More...
 
bool IsRelationalJoin [get]
 Indicates whether the term is a relational join More...
 
bool IsRelationUnion [get]
 Indicates whether the term is the union or convex hull of two relations. More...
 
bool IsRelationWiden [get]
 Indicates whether the term is the widening of two relations More...
 
bool IsRelationProject [get]
 Indicates whether the term is a projection of columns (provided as numbers in the parameters). More...
 
bool IsRelationFilter [get]
 Indicates whether the term is a relation filter More...
 
bool IsRelationNegationFilter [get]
 Indicates whether the term is an intersection of a relation with the negation of another. More...
 
bool IsRelationRename [get]
 Indicates whether the term is the renaming of a column in a relation More...
 
bool IsRelationComplement [get]
 Indicates whether the term is the complement of a relation More...
 
bool IsRelationSelect [get]
 Indicates whether the term is a relational select More...
 
bool IsRelationClone [get]
 Indicates whether the term is a relational clone (copy) More...
 
bool IsFiniteDomain [get]
 Indicates whether the term is of an array sort. More...
 
bool IsFiniteDomainLT [get]
 Indicates whether the term is a less than predicate over a finite domain. More...
 
uint Index [get]
 The de-Burijn index of a bound variable. More...
 
- Properties inherited from AST
uint Id [get]
 A unique identifier for the AST (unique among all ASTs). More...
 
Z3_ast_kind ASTKind [get]
 The kind of the AST. More...
 
bool IsExpr [get]
 Indicates whether the AST is an Expr More...
 
bool IsApp [get]
 Indicates whether the AST is an application More...
 
bool IsVar [get]
 Indicates whether the AST is a BoundVariable More...
 
bool IsQuantifier [get]
 Indicates whether the AST is a Quantifier More...
 
bool IsSort [get]
 Indicates whether the AST is a Sort More...
 
bool IsFuncDecl [get]
 Indicates whether the AST is a FunctionDeclaration More...
 

Additional Inherited Members

- Static Public Member Functions inherited from AST
static bool operator== (AST a, AST b)
 Comparison operator. More...
 
static bool operator!= (AST a, AST b)
 Comparison operator. More...
 

Detailed Description

Expressions are terms.

Definition at line 29 of file Expr.cs.

Constructor & Destructor Documentation

Expr ( Context  ctx)
inlineprotected

Constructor for Expr

Definition at line 1492 of file Expr.cs.

1492 : base(ctx) { Contract.Requires(ctx != null); }
Expr ( Context  ctx,
IntPtr  obj 
)
inlineprotected

Constructor for Expr

Definition at line 1496 of file Expr.cs.

1496 : base(ctx, obj) { Contract.Requires(ctx != null); }

Member Function Documentation

Expr Simplify ( Params  p = null)
inline

Returns a simplified version of the expression.

Parameters
pA set of parameters to configure the simplifier
See also
Context.SimplifyHelp

Definition at line 36 of file Expr.cs.

37  {
38  Contract.Ensures(Contract.Result<Expr>() != null);
39 
40  if (p == null)
41  return Expr.Create(Context, Native.Z3_simplify(Context.nCtx, NativeObject));
42  else
43  return Expr.Create(Context, Native.Z3_simplify_ex(Context.nCtx, NativeObject, p.NativeObject));
44  }
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
Expr Substitute ( Expr[]  from,
Expr[]  to 
)
inline

Substitute every occurrence of from[i] in the expression with to[i], for i smaller than num_exprs.

The result is the new expression. The arrays from and to must have size num_exprs. For every i smaller than num_exprs, we must have that sort of from[i] must be equal to sort of to[i].

Definition at line 115 of file Expr.cs.

116  {
117  Contract.Requires(from != null);
118  Contract.Requires(to != null);
119  Contract.Requires(Contract.ForAll(from, f => f != null));
120  Contract.Requires(Contract.ForAll(to, t => t != null));
121  Contract.Ensures(Contract.Result<Expr>() != null);
122 
123  Context.CheckContextMatch(from);
124  Context.CheckContextMatch(to);
125  if (from.Length != to.Length)
126  throw new Z3Exception("Argument sizes do not match");
127  return Expr.Create(Context, Native.Z3_substitute(Context.nCtx, NativeObject, (uint)from.Length, Expr.ArrayToNative(from), Expr.ArrayToNative(to)));
128  }
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
Expr Substitute ( Expr  from,
Expr  to 
)
inline

Substitute every occurrence of from in the expression with to.

See also
Substitute(Expr[],Expr[])

Definition at line 134 of file Expr.cs.

135  {
136  Contract.Requires(from != null);
137  Contract.Requires(to != null);
138  Contract.Ensures(Contract.Result<Expr>() != null);
139 
140  return Substitute(new Expr[] { from }, new Expr[] { to });
141  }
Expr Substitute(Expr[] from, Expr[] to)
Substitute every occurrence of from[i] in the expression with to[i], for i smaller than num_exprs...
Definition: Expr.cs:115
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
Expr SubstituteVars ( Expr[]  to)
inline

Substitute the free variables in the expression with the expressions in to

For every i smaller than num_exprs, the variable with de-Bruijn index i is replaced with term to[i].

Definition at line 149 of file Expr.cs.

150  {
151  Contract.Requires(to != null);
152  Contract.Requires(Contract.ForAll(to, t => t != null));
153  Contract.Ensures(Contract.Result<Expr>() != null);
154 
155  Context.CheckContextMatch(to);
156  return Expr.Create(Context, Native.Z3_substitute_vars(Context.nCtx, NativeObject, (uint)to.Length, Expr.ArrayToNative(to)));
157  }
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
override string ToString ( )
inline

Returns a string representation of the expression.

Definition at line 178 of file Expr.cs.

179  {
180  return base.ToString();
181  }
new Expr Translate ( Context  ctx)
inline

Translates (copies) the term to the Context ctx .

Parameters
ctxA context
Returns
A copy of the term which is associated with ctx

Definition at line 164 of file Expr.cs.

165  {
166  Contract.Requires(ctx != null);
167  Contract.Ensures(Contract.Result<Expr>() != null);
168 
169  if (ReferenceEquals(Context, ctx))
170  return this;
171  else
172  return Expr.Create(ctx, Native.Z3_translate(Context.nCtx, NativeObject, ctx.nCtx));
173  }
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
void Update ( Expr[]  args)
inline

Update the arguments of the expression using the arguments args The number of new arguments should coincide with the current number of arguments.

Definition at line 96 of file Expr.cs.

97  {
98  Contract.Requires(args != null);
99  Contract.Requires(Contract.ForAll(args, a => a != null));
100 
101  Context.CheckContextMatch(args);
102  if (IsApp && args.Length != NumArgs)
103  throw new Z3Exception("Number of arguments does not match");
104  NativeObject = Native.Z3_update_term(Context.nCtx, NativeObject, (uint)args.Length, Expr.ArrayToNative(args));
105  }
uint NumArgs
The number of arguments of the expression.
Definition: Expr.cs:71
Expr(Context ctx)
Constructor for Expr
Definition: Expr.cs:1492
bool IsApp
Indicates whether the AST is an application
Definition: AST.cs:156

Property Documentation

Expr [] Args
get

The arguments of the expression.

Definition at line 79 of file Expr.cs.

Z3_lbool BoolValue
get

Indicates whether the expression is the true or false expression or something else (Z3_L_UNDEF).

Definition at line 63 of file Expr.cs.

The function declaration of the function that is applied in this expression.

Definition at line 50 of file Expr.cs.

Referenced by Model.ConstInterp().

uint Index
get

The de-Burijn index of a bound variable.

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.

abs(forall (x1) phi) = forall (x1) abs1(phi, x1, 0)
abs(forall (x1, x2) phi) = abs(forall (x1) abs(forall (x2) phi))
abs1(x, x, n) = b_n
abs1(y, x, n) = y
abs1(f(t1,...,tn), x, n) = f(abs1(t1,x,n), ..., abs1(tn,x,n))
abs1(forall (x1) phi, x, n) = forall (x1) (abs1(phi, x, n+1))

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.

Definition at line 1475 of file Expr.cs.

bool IsAdd
get

Indicates whether the term is addition (binary)

Definition at line 383 of file Expr.cs.

bool IsAlgebraicNumber
get

Indicates whether the term is an algebraic number

Definition at line 247 of file Expr.cs.

bool IsAnd
get

Indicates whether the term is an n-ary conjunction

Definition at line 297 of file Expr.cs.

bool IsArithmeticNumeral
get

Indicates whether the term is an arithmetic numeral.

Definition at line 358 of file Expr.cs.

bool IsArray
get

Indicates whether the term is of an array sort.

Definition at line 441 of file Expr.cs.

bool IsArrayMap
get

Indicates whether the term is an array map.

It satisfies mapf[i] = f(a1[i],...,a_n[i]) for every i.

Definition at line 478 of file Expr.cs.

bool IsAsArray
get

Indicates whether the term is an as-array term.

An as-array term is n array value that behaves as the function graph of the function passed as parameter.

Definition at line 485 of file Expr.cs.

bool IsBool
get

Indicates whether the term has Boolean sort.

Definition at line 259 of file Expr.cs.

bool IsBV
get

Indicates whether the terms is of bit-vector sort.

Definition at line 520 of file Expr.cs.

bool IsBVAdd
get

Indicates whether the term is a bit-vector addition (binary)

Definition at line 547 of file Expr.cs.

bool IsBVAND
get

Indicates whether the term is a bit-wise AND

Definition at line 652 of file Expr.cs.

bool IsBVBitOne
get

Indicates whether the term is a one-bit bit-vector with value one

Definition at line 532 of file Expr.cs.

bool IsBVBitZero
get

Indicates whether the term is a one-bit bit-vector with value zero

Definition at line 537 of file Expr.cs.

bool IsBVCarry
get

Indicates whether the term is a bit-vector carry

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)))

Definition at line 780 of file Expr.cs.

bool IsBVComp
get

Indicates whether the term is a bit-vector comparison

Definition at line 722 of file Expr.cs.

bool IsBVConcat
get

Indicates whether the term is a bit-vector concatenation (binary)

Definition at line 687 of file Expr.cs.

bool IsBVExtract
get

Indicates whether the term is a bit-vector extraction

Definition at line 702 of file Expr.cs.

bool IsBVMul
get

Indicates whether the term is a bit-vector multiplication (binary)

Definition at line 557 of file Expr.cs.

bool IsBVNAND
get

Indicates whether the term is a bit-wise NAND

Definition at line 672 of file Expr.cs.

bool IsBVNOR
get

Indicates whether the term is a bit-wise NOR

Definition at line 677 of file Expr.cs.

bool IsBVNOT
get

Indicates whether the term is a bit-wise NOT

Definition at line 662 of file Expr.cs.

bool IsBVNumeral
get

Indicates whether the term is a bit-vector numeral

Definition at line 527 of file Expr.cs.

bool IsBVOR
get

Indicates whether the term is a bit-wise OR

Definition at line 657 of file Expr.cs.

bool IsBVReduceAND
get

Indicates whether the term is a bit-vector reduce AND

Definition at line 717 of file Expr.cs.

bool IsBVReduceOR
get

Indicates whether the term is a bit-vector reduce OR

Definition at line 712 of file Expr.cs.

bool IsBVRepeat
get

Indicates whether the term is a bit-vector repetition

Definition at line 707 of file Expr.cs.

bool IsBVRotateLeft
get

Indicates whether the term is a bit-vector rotate left

Definition at line 742 of file Expr.cs.

bool IsBVRotateLeftExtended
get

Indicates whether the term is a bit-vector rotate left (extended)

Similar to Z3_OP_ROTATE_LEFT, but it is a binary operator instead of a parametric one.

Definition at line 753 of file Expr.cs.

bool IsBVRotateRight
get

Indicates whether the term is a bit-vector rotate right

Definition at line 747 of file Expr.cs.

bool IsBVRotateRightExtended
get

Indicates whether the term is a bit-vector rotate right (extended)

Similar to Z3_OP_ROTATE_RIGHT, but it is a binary operator instead of a parametric one.

Definition at line 759 of file Expr.cs.

bool IsBVSDiv
get

Indicates whether the term is a bit-vector signed division (binary)

Definition at line 562 of file Expr.cs.

bool IsBVSGE
get

Indicates whether the term is a signed bit-vector greater-than-or-equal

Definition at line 627 of file Expr.cs.

bool IsBVSGT
get

Indicates whether the term is a signed bit-vector greater-than

Definition at line 647 of file Expr.cs.

bool IsBVShiftLeft
get

Indicates whether the term is a bit-vector shift left

Definition at line 727 of file Expr.cs.

bool IsBVShiftRightArithmetic
get

Indicates whether the term is a bit-vector arithmetic shift left

Definition at line 737 of file Expr.cs.

bool IsBVShiftRightLogical
get

Indicates whether the term is a bit-vector logical shift right

Definition at line 732 of file Expr.cs.

bool IsBVSignExtension
get

Indicates whether the term is a bit-vector sign extension

Definition at line 692 of file Expr.cs.

bool IsBVSLE
get

Indicates whether the term is a signed bit-vector less-than-or-equal

Definition at line 617 of file Expr.cs.

bool IsBVSLT
get

Indicates whether the term is a signed bit-vector less-than

Definition at line 637 of file Expr.cs.

bool IsBVSMod
get

Indicates whether the term is a bit-vector signed modulus

Definition at line 582 of file Expr.cs.

bool IsBVSRem
get

Indicates whether the term is a bit-vector signed remainder (binary)

Definition at line 572 of file Expr.cs.

bool IsBVSub
get

Indicates whether the term is a bit-vector subtraction (binary)

Definition at line 552 of file Expr.cs.

bool IsBVToInt
get

Indicates whether the term is a coercion from bit-vector to integer

This function is not supported by the decision procedures. Only the most rudimentary simplification rules are applied to this function.

Definition at line 773 of file Expr.cs.

bool IsBVUDiv
get

Indicates whether the term is a bit-vector unsigned division (binary)

Definition at line 567 of file Expr.cs.

bool IsBVUGE
get

Indicates whether the term is an unsigned bit-vector greater-than-or-equal

Definition at line 622 of file Expr.cs.

bool IsBVUGT
get

Indicates whether the term is an unsigned bit-vector greater-than

Definition at line 642 of file Expr.cs.

bool IsBVULE
get

Indicates whether the term is an unsigned bit-vector less-than-or-equal

Definition at line 612 of file Expr.cs.

bool IsBVULT
get

Indicates whether the term is an unsigned bit-vector less-than

Definition at line 632 of file Expr.cs.

bool IsBVUMinus
get

Indicates whether the term is a bit-vector unary minus

Definition at line 542 of file Expr.cs.

bool IsBVURem
get

Indicates whether the term is a bit-vector unsigned remainder (binary)

Definition at line 577 of file Expr.cs.

bool IsBVXNOR
get

Indicates whether the term is a bit-wise XNOR

Definition at line 682 of file Expr.cs.

bool IsBVXOR
get

Indicates whether the term is a bit-wise XOR

Definition at line 667 of file Expr.cs.

bool IsBVXOR3
get

Indicates whether the term is a bit-vector ternary XOR

The meaning is given by the equivalence (xor3 l1 l2 l3) <=> (xor (xor l1 l2) l3)

Definition at line 786 of file Expr.cs.

bool IsBVZeroExtension
get

Indicates whether the term is a bit-vector zero extension

Definition at line 697 of file Expr.cs.

bool IsConst
get

Indicates whether the term represents a constant.

Definition at line 217 of file Expr.cs.

bool IsConstantArray
get

Indicates whether the term is a constant array.

For example, select(const(v),i) = v holds for every v and i. The function is unary.

Definition at line 466 of file Expr.cs.

bool IsDefaultArray
get

Indicates whether the term is a default array.

For example default(const(v)) = v. The function is unary.

Definition at line 472 of file Expr.cs.

bool IsDistinct
get

Indicates whether the term is an n-ary distinct predicate (every argument is mutually distinct).

Definition at line 287 of file Expr.cs.

bool IsDiv
get

Indicates whether the term is division (binary)

Definition at line 403 of file Expr.cs.

bool IsEmptyRelation
get

Indicates whether the term is an empty relation

Definition at line 1339 of file Expr.cs.

bool IsEq
get

Indicates whether the term is an equality predicate.

Definition at line 282 of file Expr.cs.

bool IsFalse
get

Indicates whether the term is the constant false.

Definition at line 277 of file Expr.cs.

bool IsFiniteDomain
get

Indicates whether the term is of an array sort.

Definition at line 1439 of file Expr.cs.

bool IsFiniteDomainLT
get

Indicates whether the term is a less than predicate over a finite domain.

Definition at line 1450 of file Expr.cs.

bool IsGE
get

Indicates whether the term is a greater-than-or-equal

Definition at line 368 of file Expr.cs.

bool IsGT
get

Indicates whether the term is a greater-than

Definition at line 378 of file Expr.cs.

bool IsIDiv
get

Indicates whether the term is integer division (binary)

Definition at line 408 of file Expr.cs.

bool IsIff
get

Indicates whether the term is an if-and-only-if (Boolean equivalence, binary)

Definition at line 307 of file Expr.cs.

bool IsImplies
get

Indicates whether the term is an implication

Definition at line 322 of file Expr.cs.

bool IsInt
get

Indicates whether the term is of integer sort.

Definition at line 339 of file Expr.cs.

bool IsInterpolant
get

Indicates whether the term is marked for interpolation.

Definition at line 331 of file Expr.cs.

bool IsIntNum
get

Indicates whether the term is an integer numeral.

Definition at line 227 of file Expr.cs.

bool IsIntToBV
get

Indicates whether the term is a coercion from integer to bit-vector

This function is not supported by the decision procedures. Only the most rudimentary simplification rules are applied to this function.

Definition at line 766 of file Expr.cs.

bool IsIntToReal
get

Indicates whether the term is a coercion of integer to real (unary)

Definition at line 423 of file Expr.cs.

bool IsIsEmptyRelation
get

Indicates whether the term is a test for the emptiness of a relation

Definition at line 1344 of file Expr.cs.

bool IsITE
get

Indicates whether the term is a ternary if-then-else term

Definition at line 292 of file Expr.cs.

bool IsLabel
get

Indicates whether the term is a label (used by the Boogie Verification condition generator).

The label has two parameters, a string and a Boolean polarity. It takes one argument, a formula.

Definition at line 795 of file Expr.cs.

bool IsLabelLit
get

Indicates whether the term is a label literal (used by the Boogie Verification condition generator).

A label literal has a set of string parameters. It takes no arguments.

Definition at line 801 of file Expr.cs.

bool IsLE
get

Indicates whether the term is a less-than-or-equal

Definition at line 363 of file Expr.cs.

bool IsLT
get

Indicates whether the term is a less-than

Definition at line 373 of file Expr.cs.

bool IsModulus
get

Indicates whether the term is modulus (binary)

Definition at line 418 of file Expr.cs.

bool IsMul
get

Indicates whether the term is multiplication (binary)

Definition at line 398 of file Expr.cs.

bool IsNot
get

Indicates whether the term is a negation

Definition at line 317 of file Expr.cs.

bool IsNumeral
get

Indicates whether the term is a numeral

Definition at line 187 of file Expr.cs.

bool IsOEQ
get

Indicates whether the term is a binary equivalence modulo namings.

This binary predicate is used in proof terms. It captures equisatisfiability and equivalence modulo renamings.

Definition at line 810 of file Expr.cs.

bool IsOr
get

Indicates whether the term is an n-ary disjunction

Definition at line 302 of file Expr.cs.

bool IsProofAndElimination
get

Indicates whether the term is a proof by elimination of AND

Given a proof for (and l_1 ... l_n), produces a proof for l_i T1: (and l_1 ... l_n)

Definition at line 941 of file Expr.cs.

bool IsProofApplyDef
get

Indicates whether the term is a proof for application of a definition

[apply-def T1]: F ~ n F is 'equivalent' to n, given that T1 is a proof that n is a name for F.

Definition at line 1182 of file Expr.cs.

bool IsProofAsserted
get

Indicates whether the term is a proof for a fact asserted by the user.

Definition at line 820 of file Expr.cs.

bool IsProofCNFStar
get

Indicates whether the term is a proof for (~ P Q) where Q is in conjunctive normal form.

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.

Definition at line 1266 of file Expr.cs.

bool IsProofCommutativity
get

Indicates whether the term is a proof by commutativity

f is a commutative operator.

This proof object has no antecedents. Remark: if f is bool, then = is iff.

Definition at line 1113 of file Expr.cs.

bool IsProofDefAxiom
get

Indicates whether the term is a proof for Tseitin-like axioms

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).

Definition at line 1149 of file Expr.cs.

bool IsProofDefIntro
get

Indicates whether the term is a proof for introduction of a name

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:

or:

when e only occurs positively.

When e is of the form (ite cond th el):

Otherwise: [def-intro]: (= n e)

Definition at line 1172 of file Expr.cs.

bool IsProofDER
get

Indicates whether the term is a proof for destructive equality resolution

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.

Definition at line 1043 of file Expr.cs.

bool IsProofDistributivity
get

Indicates whether the term is a distributivity proof object.

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.

Definition at line 931 of file Expr.cs.

bool IsProofElimUnusedVars
get

Indicates whether the term is a proof for elimination of unused variables.

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.

Definition at line 1029 of file Expr.cs.

bool IsProofGoal
get

Indicates whether the term is a proof for a fact (tagged as goal) asserted by the user.

Definition at line 825 of file Expr.cs.

bool IsProofHypothesis
get

Indicates whether the term is a hypthesis marker.

Mark a hypothesis in a natural deduction style proof.

Definition at line 1057 of file Expr.cs.

bool IsProofIFFFalse
get

Indicates whether the term is a proof by iff-false

T1: (not p) [iff-false T1]: (iff p false)

Definition at line 1100 of file Expr.cs.

bool IsProofIFFOEQ
get

Indicates whether the term is a proof iff-oeq

T1: (iff p q) [iff~ T1]: (~ p q)

Definition at line 1191 of file Expr.cs.

bool IsProofIFFTrue
get

Indicates whether the term is a proof by iff-true

T1: p [iff-true T1]: (iff p true)

Definition at line 1091 of file Expr.cs.

bool IsProofLemma
get

Indicates whether the term is a proof by lemma

T1: false

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.

Definition at line 1070 of file Expr.cs.

bool IsProofModusPonens
get

Indicates whether the term is proof via modus ponens

Given a proof for p and a proof for (implies p q), produces a proof for q. T1: p T2: (implies p q)

The second antecedents may also be a proof for (iff p q).

Definition at line 836 of file Expr.cs.

bool IsProofModusPonensOEQ
get

Indicates whether the term is a proof by modus ponens for equi-satisfiability.

Modus ponens style rule for equi-satisfiability. T1: p T2: (~ p q)

Definition at line 1290 of file Expr.cs.

bool IsProofMonotonicity
get

Indicates whether the term is a monotonicity proof object.

T1: (R t_1 s_1) ... Tn: (R t_n s_n)

Remark: if t_i == s_i, then the antecedent Ti is suppressed. That is, reflexivity proofs are supressed to save space.

Definition at line 903 of file Expr.cs.

bool IsProofNNFNeg
get

Indicates whether the term is a proof for a negative NNF step

Proof for a (negative) NNF step. Examples:

T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ r_n

and T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ 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'

(and (or r_1 r_2) (or r_1' r_2')))

Definition at line 1244 of file Expr.cs.

bool IsProofNNFPos
get

Indicates whether the term is a proof for a positive NNF step

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'

(and (or r_1 r_2') (or r_1' 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

(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'.

Definition at line 1219 of file Expr.cs.

bool IsProofNNFStar
get

Indicates whether the term is a proof for (~ P Q) here Q is in negation normal form.

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.

Definition at line 1256 of file Expr.cs.

bool IsProofOrElimination
get

Indicates whether the term is a proof by eliminiation of not-or

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)

Definition at line 951 of file Expr.cs.

bool IsProofPullQuant
get

Indicates whether the term is a proof for pulling quantifiers out.

A proof for (iff (f (forall (x) q(x)) r) (forall (x) (f (q x) r))). This proof object has no antecedents.

Definition at line 994 of file Expr.cs.

bool IsProofPullQuantStar
get

Indicates whether the term is a proof for pulling quantifiers out.

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

Definition at line 1004 of file Expr.cs.

bool IsProofPushQuant
get

Indicates whether the term is a proof for pushing quantifiers in.

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

Definition at line 1017 of file Expr.cs.

bool IsProofQuantInst
get

Indicates whether the term is a proof for quantifier instantiation

A proof of (or (not (forall (x) (P x))) (P a))

Definition at line 1051 of file Expr.cs.

bool IsProofQuantIntro
get

Indicates whether the term is a quant-intro proof

Given a proof for (~ p q), produces a proof for (~ (forall (x) p) (forall (x) q)). T1: (~ p q)

Definition at line 913 of file Expr.cs.

bool IsProofReflexivity
get

Indicates whether the term is a proof for (R t t), where R is a reflexive relation.

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'.

Definition at line 845 of file Expr.cs.

bool IsProofRewrite
get

Indicates whether the term is a proof by rewriting

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)

Definition at line 970 of file Expr.cs.

bool IsProofRewriteStar
get

Indicates whether the term is a proof by rewriting

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)

Definition at line 986 of file Expr.cs.

bool IsProofSkolemize
get

Indicates whether the term is a proof for a Skolemization step

Proof for:

This proof object has no antecedents.

Definition at line 1279 of file Expr.cs.

bool IsProofSymmetry
get

Indicates whether the term is proof by symmetricity of a relation

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.

Definition at line 856 of file Expr.cs.

bool IsProofTheoryLemma
get

Indicates whether the term is a proof for theory lemma

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.

Definition at line 1309 of file Expr.cs.

bool IsProofTransitivity
get

Indicates whether the term is a proof by transitivity of a relation

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)

Definition at line 868 of file Expr.cs.

bool IsProofTransitivityStar
get

Indicates whether the term is a proof by condensed transitivity of a relation

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.

Definition at line 889 of file Expr.cs.

bool IsProofTrue
get

Indicates whether the term is a Proof for the expression 'true'.

Definition at line 815 of file Expr.cs.

bool IsProofUnitResolution
get

Indicates whether the term is a proof by unit resolution

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')

Definition at line 1082 of file Expr.cs.

bool IsRatNum
get

Indicates whether the term is a real numeral.

Definition at line 237 of file Expr.cs.

bool IsReal
get

Indicates whether the term is of sort real.

Definition at line 351 of file Expr.cs.

bool IsRealIsInt
get

Indicates whether the term is a check that tests whether a real is integral (unary)

Definition at line 433 of file Expr.cs.

bool IsRealToInt
get

Indicates whether the term is a coercion of real to integer (unary)

Definition at line 428 of file Expr.cs.

bool IsRelation
get

Indicates whether the term is of an array sort.

Definition at line 1317 of file Expr.cs.

bool IsRelationalJoin
get

Indicates whether the term is a relational join

Definition at line 1349 of file Expr.cs.

bool IsRelationClone
get

Indicates whether the term is a relational clone (copy)

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

See also
IsRelationUnion

to perform destructive updates to the first argument.

Definition at line 1431 of file Expr.cs.

bool IsRelationComplement
get

Indicates whether the term is the complement of a relation

Definition at line 1409 of file Expr.cs.

bool IsRelationFilter
get

Indicates whether the term is a relation filter

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.

Definition at line 1379 of file Expr.cs.

bool IsRelationNegationFilter
get

Indicates whether the term is an intersection of a relation with the negation of another.

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.

Definition at line 1395 of file Expr.cs.

bool IsRelationProject
get

Indicates whether the term is a projection of columns (provided as numbers in the parameters).

The function takes one argument.

Definition at line 1367 of file Expr.cs.

bool IsRelationRename
get

Indicates whether the term is the renaming of a column in a relation

The function takes one argument. The parameters contain the renaming as a cycle.

Definition at line 1404 of file Expr.cs.

bool IsRelationSelect
get

Indicates whether the term is a relational select

Check if a record is an element of the relation. The function takes n+1 arguments, where the first argument is a relation, and the remaining n arguments correspond to a record.

Definition at line 1419 of file Expr.cs.

bool IsRelationStore
get

Indicates whether the term is an relation store

Insert a record into a relation. The function takes n+1 arguments, where the first argument is the relation and the remaining n elements correspond to the n columns of the relation.

Definition at line 1334 of file Expr.cs.

bool IsRelationUnion
get

Indicates whether the term is the union or convex hull of two relations.

The function takes two arguments.

Definition at line 1355 of file Expr.cs.

bool IsRelationWiden
get

Indicates whether the term is the widening of two relations

The function takes two arguments.

Definition at line 1361 of file Expr.cs.

bool IsRemainder
get

Indicates whether the term is remainder (binary)

Definition at line 413 of file Expr.cs.

bool IsSelect
get

Indicates whether the term is an array select.

Definition at line 460 of file Expr.cs.

bool IsSetComplement
get

Indicates whether the term is set complement

Definition at line 507 of file Expr.cs.

bool IsSetDifference
get

Indicates whether the term is set difference

Definition at line 502 of file Expr.cs.

bool IsSetIntersect
get

Indicates whether the term is set intersection

Definition at line 497 of file Expr.cs.

bool IsSetSubset
get

Indicates whether the term is set subset

Definition at line 512 of file Expr.cs.

bool IsSetUnion
get

Indicates whether the term is set union

Definition at line 492 of file Expr.cs.

bool IsStore
get

Indicates whether the term is an array store.

It satisfies select(store(a,i,v),j) = if i = j then v else select(a,j). Array store takes at least 3 arguments.

Definition at line 455 of file Expr.cs.

bool IsSub
get

Indicates whether the term is subtraction (binary)

Definition at line 388 of file Expr.cs.

bool IsTrue
get

Indicates whether the term is the constant true.

Definition at line 272 of file Expr.cs.

bool IsUMinus
get

Indicates whether the term is a unary minus

Definition at line 393 of file Expr.cs.

bool IsWellSorted
get

Indicates whether the term is well-sorted.

Returns
True if the term is well-sorted, false otherwise.

Definition at line 196 of file Expr.cs.

bool IsXor
get

Indicates whether the term is an exclusive or

Definition at line 312 of file Expr.cs.

uint NumArgs
get

The number of arguments of the expression.

Definition at line 71 of file Expr.cs.

Sort Sort
get

The Sort of the term.

Definition at line 204 of file Expr.cs.