Kind

Every Term has a kind which represents its type, for example whether it is an equality ( Equal ), a conjunction ( And ), or a bit-vector addtion ( BVAdd ). The kinds below directly correspond to the enum values of the C++ Kind enum.

class cvc5. Kind ( value )

The Kind enum

ABS

Absolute value.

ADD

Arithmetic addition.

AND

Logical conjunction.

APPLY_CONSTRUCTOR

Datatype constructor application.

APPLY_SELECTOR

Datatype selector application.

Note

Undefined if misapplied.

APPLY_TESTER

Datatype tester application.

APPLY_UF

Application of an uninterpreted function.

  • Arity: n > 1

    • 1: Function Term

    • 2..n: Function argument instantiation Terms of any first-class Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

APPLY_UPDATER

Datatype update application.

  • Arity: 3

    • 1: Datatype updater Term (see DatatypeSelector.getUpdaterTerm() )

    • 2: Term of Datatype Sort (DatatypeSelector of the updater must belong to a constructor of this Datatype Sort)

    • 3: Term of the codomain Sort of the selector (the Term to update the field of the datatype term with)

  • Create Term of this Kind with:

  • Create Op of this kind with:

Note

Does not change the datatype argument if misapplied.

ARCCOSECANT

Arc cosecant function.

ARCCOSINE

Arc cosine function.

ARCCOTANGENT

Arc cotangent function.

ARCSECANT

Arc secant function.

ARCSINE

Arc sine function.

ARCTANGENT

Arc tangent function.

BAG_CARD

Bag cardinality.

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_CHOOSE

Bag choose.

Select an element from a given bag.

For a bag \(A = \{(x,n)\}\) where \(n\) is the multiplicity, then the term (choose \(A\) ) is equivalent to the term \(x\) . For an empty bag, then it is an arbitrary value. For a bag that contains distinct elements, it will deterministically return an element in \(A\) .

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_COUNT

Bag element multiplicity.

BAG_DIFFERENCE_REMOVE

Bag difference remove.

Removes shared elements in the two bags.

BAG_DIFFERENCE_SUBTRACT

Bag difference subtract.

Subtracts multiplicities of the second from the first.

BAG_DUPLICATE_REMOVAL

Bag duplicate removal.

Eliminate duplicates in a given bag. The returned bag contains exactly the same elements in the given bag, but with multiplicity one.

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_EMPTY

Empty bag.

BAG_FILTER

Bag filter.

This operator filters the elements of a bag. (bag.filter \(p \; B\) ) takes a predicate \(p\) of Sort \((\rightarrow S_1 \; S_2)\) as a first argument, and a bag \(B\) of Sort (Bag \(S\) ) as a second argument, and returns a subbag of Sort (Bag \(T\) ) that includes all elements of \(B\) that satisfy \(p\) with the same multiplicity.

  • Arity: 2

    • 1: Term of function Sort \((\rightarrow S_1 \; S_2)\)

    • 2: Term of bag Sort (Bag \(S_1\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_FOLD

Bag fold.

This operator combines elements of a bag into a single value. (bag.fold \(f \; t \; B\) ) folds the elements of bag \(B\) starting with Term \(t\) and using the combining function \(f\) .

  • Arity: 2

    • 1: Term of function Sort \((\rightarrow S_1 \; S_2 \; S_2)\)

    • 2: Term of Sort \(S_2\) (the initial value)

    • 3: Term of bag Sort (Bag \(S_1\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_FROM_SET

Conversion from set to bag.

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_INTER_MIN

Bag intersection (min).

BAG_IS_SINGLETON

Bag is singleton tester.

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_MAKE

Bag make.

Construct a bag with the given element and given multiplicity.

  • Arity: 2

    • 1: Term of any Sort (the bag element)

    • 2: Term of Sort Int (the multiplicity of the element)

  • Create Term of this Kind with:

  • Create Op of this kind with:

BAG_MAP

Bag map.

This operator applies the first argument, a function of Sort \((\rightarrow S_1 \; S_2)\) , to every element of the second argument, a set of Sort (Bag \(S_1\) ), and returns a set of Sort (Bag \(S_2\) ).

  • Arity: 2

    • 1: Term of function Sort \((\rightarrow S_1 \; S_2)\)

    • 2: Term of bag Sort (Bag \(S_1\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_MEMBER

Bag membership predicate.

  • Arity: 2

    • 1: Term of any Sort (must match the element Sort of the given bag Term)

    • 2: Terms of bag Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

BAG_SUBBAG

Bag inclusion predicate.

Determine if multiplicities of the first bag are less than or equal to multiplicities of the second bag.

BAG_TO_SET

Conversion from bag to set.

Warning

This kind is experimental and may be changed or removed in future versions.

BAG_UNION_DISJOINT

Bag disjoint union (sum).

BAG_UNION_MAX

Bag max union.

BITVECTOR_ADD

Addition of two or more bit-vectors.

BITVECTOR_AND

Bit-wise and.

BITVECTOR_ASHR

Bit-vector arithmetic shift right.

BITVECTOR_COMP

Equality comparison (returns bit-vector of size 1 ).

BITVECTOR_CONCAT

Concatenation of two or more bit-vectors.

BITVECTOR_EXTRACT

Bit-vector extract.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 2

    • 1: The upper bit index.

    • 2: The lower bit index.

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_ITE

Bit-vector if-then-else.

Same semantics as regular ITE, but condition is bit-vector of size 1 .

  • Arity: 3

    • 1: Term of bit-vector Sort of size 1

    • 1..3: Terms of bit-vector sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_LSHR

Bit-vector logical shift right.

BITVECTOR_MULT

Multiplication of two or more bit-vectors.

BITVECTOR_NAND

Bit-wise nand.

BITVECTOR_NEG

Negation of a bit-vector (two’s complement).

BITVECTOR_NOR

Bit-wise nor.

BITVECTOR_NOT

Bit-wise negation.

BITVECTOR_OR

Bit-wise or.

BITVECTOR_REDAND

Bit-vector redand.

BITVECTOR_REDOR

Bit-vector redor.

BITVECTOR_REPEAT

Bit-vector repeat.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 1

    • 1: The number of times to repeat the given term.

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_ROTATE_LEFT

Bit-vector rotate left.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 1

    • 1: The number of bits to rotate the given term left.

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_ROTATE_RIGHT

Bit-vector rotate right.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 1

    • 1: The number of bits to rotate the given term right.

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_SDIV

Signed bit-vector division.

Two’s complement signed division of two bit-vectors. If the divisor is zero and the dividend is positive, the result is all ones. If the divisor is zero and the dividend is negative, the result is one.

BITVECTOR_SGE

Bit-vector signed greater than or equal.

BITVECTOR_SGT

Bit-vector signed greater than.

BITVECTOR_SHL

Bit-vector shift left.

BITVECTOR_SIGN_EXTEND

Bit-vector sign extension.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 1

    • 1: The number of bits (of the value of the sign bit) to extend the given term with.

  • Create Term of this Kind with:

  • Create Op of this kind with:

BITVECTOR_SLE

Bit-vector signed less than or equal.

BITVECTOR_SLT

Bit-vector signed less than.

BITVECTOR_SLTBV

Bit-vector signed less than returning a bit-vector of size 1 .

BITVECTOR_SMOD

Signed bit-vector remainder (sign follows divisor).

Two’s complement signed remainder where the sign follows the divisor. If the modulus is zero, the result is the dividend.

BITVECTOR_SREM

Signed bit-vector remainder (sign follows dividend).

Two’s complement signed remainder of two bit-vectors where the sign follows the dividend. If the modulus is zero, the result is the dividend.

BITVECTOR_SUB

Subtraction of two bit-vectors.

BITVECTOR_TO_NAT

Bit-vector conversion to (non-negative) integer.

BITVECTOR_UDIV

Unsigned bit-vector division.

Truncates towards 0 . If the divisor is zero, the result is all ones.

BITVECTOR_UGE

Bit-vector unsigned greater than or equal.

BITVECTOR_UGT

Bit-vector unsigned greater than.

BITVECTOR_ULE

Bit-vector unsigned less than or equal.

BITVECTOR_ULT

Bit-vector unsigned less than.

BITVECTOR_ULTBV

Bit-vector unsigned less than returning a bit-vector of size 1.

BITVECTOR_UREM

Unsigned bit-vector remainder.

Remainder from unsigned bit-vector division. If the modulus is zero, the result is the dividend.

BITVECTOR_XNOR

Bit-wise xnor, left associative.

BITVECTOR_XOR

Bit-wise xor.

BITVECTOR_ZERO_EXTEND

Bit-vector zero extension.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 1

    • 1: The number of zeroes to extend the given term with.

  • Create Term of this Kind with:

  • Create Op of this kind with:

CARDINALITY_CONSTRAINT

Cardinality constraint on uninterpreted sort.

Interpreted as a predicate that is true when the cardinality of uinterpreted Sort \(S\) is less than or equal to an upper bound.

Warning

This kind is experimental and may be changed or removed in future versions.

CONSTANT

Free constant symbol.

Note

Not permitted in bindings (e.g., FORALL , EXISTS ).

CONST_ARRAY

Constant array.

  • Arity: 2

    • 1: Term of array Sort

    • 2: Term of array element Sort (value)

  • Create Term of this Kind with:

  • Create Op of this kind with:

CONST_BITVECTOR

Fixed-size bit-vector constant.

CONST_BOOLEAN

Boolean constant.

CONST_FLOATINGPOINT

Floating-point constant, created from IEEE-754 bit-vector representation of the floating-point value.

CONST_RATIONAL

Multiple-precision rational constant.

CONST_ROUNDINGMODE

RoundingMode constant.

CONST_SEQUENCE

Constant sequence.

A constant sequence is a term that is equivalent to: 

(seq.++ (seq.unit c1) ... (seq.unit cn))

where \(n \leq 0\) and \(c_1, ..., c_n\) are constants of some sort. The elements can be extracted with Term.getSequenceValue() .

CONST_STRING

Constant string.

COSECANT

Cosecant function.

COSINE

Cosine function.

COTANGENT

Cotangent function.

DISTINCT

Disequality.

DIVISIBLE

Operator for the divisibility-by- \(k\) predicate.

  • Arity: 1

    • 1: Term of Sort Int

  • Indices: 1

    • 1: The integer \(k\) to divide by.

  • Create Term of this Kind with:

  • Create Op of this kind with:

DIVISION

Real division, division by 0 undefined, left associative.

EQUAL

Equality, chainable.

EQ_RANGE

Equality over arrays \(a\) and \(b\) over a given range \([i,j]\) , i.e.,

\[\forall k . i \leq k \leq j \Rightarrow a[k] = b[k]\]

  • Arity: 4

    • 1: Term of array Sort (first array)

    • 2: Term of array Sort (second array)

    • 3: Term of array index Sort (lower bound of range, inclusive)

    • 4: Term of array index Sort (upper bound of range, inclusive)

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

Note

We currently support the creation of array equalities over index Sorts bit-vector, floating-point, Int and Real. Requires to enable option arrays-exp .

EXISTS

Existentially quantified formula.

EXPONENTIAL

Exponential function.

FLOATINGPOINT_ABS

Floating-point absolute value.

FLOATINGPOINT_ADD

Floating-point addition.

  • Arity: 3

    • 1: Term of Sort RoundingMode

    • 2..3: Terms of floating-point Sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_DIV

Floating-point division.

  • Arity: 3

    • 1: Term of Sort RoundingMode

    • 2..3: Terms of floating-point Sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_EQ

Floating-point equality.

FLOATINGPOINT_FMA

Floating-point fused multiply and add.

  • Arity: 4

    • 1: Term of Sort RoundingMode

    • 2..4: Terms of floating-point Sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_FP

Create floating-point literal from bit-vector triple.

  • Arity: 3

    • 1: Term of bit-vector Sort of size 1 (sign bit)

    • 2: Term of bit-vector Sort of exponent size (exponent)

    • 3: Term of bit-vector Sort of significand size - 1 (significand without hidden bit)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_GEQ

Floating-point greater than or equal.

FLOATINGPOINT_GT

Floating-point greater than.

FLOATINGPOINT_IS_INF

Floating-point is infinite tester.

FLOATINGPOINT_IS_NAN

Floating-point is NaN tester.

FLOATINGPOINT_IS_NEG

Floating-point is negative tester.

FLOATINGPOINT_IS_NORMAL

Floating-point is normal tester.

FLOATINGPOINT_IS_POS

Floating-point is positive tester.

FLOATINGPOINT_IS_SUBNORMAL

Floating-point is sub-normal tester.

FLOATINGPOINT_IS_ZERO

Floating-point is zero tester.

FLOATINGPOINT_LEQ

Floating-point less than or equal.

FLOATINGPOINT_LT

Floating-point less than.

FLOATINGPOINT_MAX

Floating-point maximum.

FLOATINGPOINT_MIN

Floating-point minimum.

FLOATINGPOINT_MULT

Floating-point multiply.

  • Arity: 3

    • 1: Term of Sort RoundingMode

    • 2..3: Terms of floating-point Sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_NEG

Floating-point negation.

FLOATINGPOINT_REM

Floating-point remainder.

FLOATINGPOINT_RTI

Floating-point round to integral.

FLOATINGPOINT_SQRT

Floating-point square root.

  • Arity: 2

    • 1: Term of Sort RoundingMode

    • 2: Term of floating-point Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_SUB

Floating-point sutraction.

  • Arity: 3

    • 1: Term of Sort RoundingMode

    • 2..3: Terms of floating-point Sort (sorts must match)

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_FP_FROM_FP

Conversion to floating-point from floating-point.

  • Arity: 2

    • 1: Term of Sort RoundingMode

    • 2: Term of floating-point Sort

  • Indices: 2

    • 1: The exponent size

    • 2: The significand size

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_FP_FROM_IEEE_BV

Conversion to floating-point from IEEE-754 bit-vector.

  • Arity: 1

    • 1: Term of bit-vector Sort

  • Indices: 2

    • 1: The exponent size

    • 2: The significand size

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_FP_FROM_REAL

Conversion to floating-point from Real.

  • Arity: 2

    • 1: Term of Sort RoundingMode

    • 2: Term of Sort Real

  • Indices: 2

    • 1: The exponent size

    • 2: The significand size

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_FP_FROM_SBV

Conversion to floating-point from signed bit-vector.

  • Arity: 2

    • 1: Term of Sort RoundingMode

    • 2: Term of bit-vector Sort

  • Indices: 2

    • 1: The exponent size

    • 2: The significand size

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_FP_FROM_UBV

Conversion to floating-point from unsigned bit-vector.

  • Arity: 2

    • 1: Term of Sort RoundingMode

    • 2: Term of bit-vector Sort

  • Indices: 2

    • 1: The exponent size

    • 2: The significand size

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_REAL

Conversion to Real from floating-point.

FLOATINGPOINT_TO_SBV

Conversion to signed bit-vector from floating-point.

  • Arity: 1

    • 1: Term of floating-point Sort

  • Indices: 1

    • 1: The size of the bit-vector to convert to.

  • Create Term of this Kind with:

  • Create Op of this kind with:

FLOATINGPOINT_TO_UBV

Conversion to unsigned bit-vector from floating-point.

  • Arity: 1

    • 1: Term of floating-point Sort

  • Indices: 1

    • 1: The size of the bit-vector to convert to.

  • Create Term of this Kind with:

  • Create Op of this kind with:

FORALL

Universally quantified formula.

GEQ

Greater than or equal, chainable.

GT

Greater than, chainable.

HO_APPLY

Higher-order applicative encoding of function application, left associative.

  • Arity: n = 2

    • 1: Function Term

    • 2: Argument Term of the domain Sort of the function

  • Create Term of this Kind with:

  • Create Op of this kind with:

IAND

Integer and.

Operator for bit-wise AND over integers, parameterized by a (positive) bit-width \(k\) . 

((_ iand k) i_1 i_2)

is equivalent to 

((_ iand k) i_1 i_2)
(bv2int (bvand ((_ int2bv k) i_1) ((_ int2bv k) i_2)))

for all integers i_1 , i_2 .

IMPLIES

Logical implication.

INST_ADD_TO_POOL

A instantantiation-add-to-pool annotation.

An instantantiation-add-to-pool annotation indicates that when a quantified formula is instantiated, the instantiated version of a term should be added to the given pool.

For example, consider a quantified formula: 

(FORALL (VARIABLE_LIST x) F
        (INST_PATTERN_LIST (INST_ADD_TO_POOL (ADD x 1) p)))

where assume that \(x\) has type Int. When this quantified formula is instantiated with, e.g., the term \(t\) , the term (ADD t 1) is added to pool \(p\) .

  • Arity: 2

    • 1: The Term whose free variables are bound by the quantified formula.

    • 2: The pool to add to, whose Sort should be a set of elements that match the Sort of the first argument.

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

Note

Should only be used as a child of INST_PATTERN_LIST .

INST_ATTRIBUTE

Instantiation attribute.

Specifies a custom property for a quantified formula given by a term that is ascribed a user attribute.

Note

Should only be used as a child of INST_PATTERN_LIST .

INST_NO_PATTERN

Instantiation no-pattern.

Specifies a (list of) terms that should not be used as a pattern for quantifier instantiation.

Note

Should only be used as a child of INST_PATTERN_LIST .

INST_PATTERN

Instantiation pattern.

Specifies a (list of) terms to be used as a pattern for quantifier instantiation.

Note

Should only be used as a child of INST_PATTERN_LIST .

INST_PATTERN_LIST

A list of instantiation patterns, attributes or annotations.

INST_POOL

Instantiation pool annotation.

Specifies an annotation for pool based instantiation.

In detail, pool symbols can be declared via the method

A pool symbol represents a set of terms of a given sort. An instantiation pool annotation should match the types of the quantified formula.

For example, for a quantified formula: 

(FORALL (VARIABLE_LIST x y) F (INST_PATTERN_LIST (INST_POOL p q)))

if \(x\) and \(y\) have Sorts \(S_1\) and \(S_2\) , then pool symbols \(p\) and \(q\) should have Sorts (Set \(S_1\) ) and (Set \(S_2\) ), respectively. This annotation specifies that the quantified formula above should be instantiated with the product of all terms that occur in the sets \(p\) and \(q\) .

  • Arity: n > 0

    • 1..n: Terms that comprise the pools, which are one-to-one with the variables of the quantified formula to be instantiated

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

Note

Should only be used as a child of INST_PATTERN_LIST .

INTERNAL_KIND

Internal kind.

This kind serves as an abstraction for internal kinds that are not exposed via the API but may appear in terms returned by API functions, e.g., when querying the simplified form of a term.

Note

Should never be created via the API.

INTS_DIVISION

Integer division, division by 0 undefined, left associative.

INTS_MODULUS

Integer modulus, modulus by 0 undefined.

INT_TO_BITVECTOR

Conversion from Int to bit-vector.

  • Arity: 1

    • 1: Term of Sort Int

  • Indices: 1

    • 1: The size of the bit-vector to convert to.

  • Create Term of this Kind with:

  • Create Op of this kind with:

IS_INTEGER

Is-integer predicate.

ITE

If-then-else.

  • Arity: 3

    • 1: Term of Sort Bool

    • 2: The ‘then’ term, Term of any Sort

    • 3: The ‘else’ term, Term of the same sort as second argument

  • Create Term of this Kind with:

  • Create Op of this kind with:

LAMBDA

Lambda expression.

LAST_KIND

Marks the upper-bound of this enumeration.

LEQ

Less than or equal, chainable.

LT

Less than, chainable.

MATCH

Match expression.

This kind is primarily used in the parser to support the SMT-LIBv2 match expression.

For example, the SMT-LIBv2 syntax for the following match term 

(match l (((cons h t) h) (nil 0)))

is represented by the AST 

(MATCH l
    (MATCH_BIND_CASE (VARIABLE_LIST h t) (cons h t) h)
    (MATCH_CASE nil 0))

Terms of kind MATCH_CASE are constant case expressions, which are used for nullary constructors. Kind MATCH_BIND_CASE is used for constructors with selectors and variable match patterns. If not all constructors are covered, at least one catch-all variable pattern must be included.

MATCH_BIND_CASE

Match case with binders, for constructors with selectors and variable patterns.

A (non-constant) case expression to be used within a match expression.

  • Arity: 3

    • For variable patterns:

      • 1: Term of kind VARIABLE_LIST (containing the free variable of the case)

      • 2: Term of kind VARIABLE (the pattern expression, the free variable of the case)

      • 3: Term of any Sort (the term the pattern evaluates to)

    • For constructors with selectors:

      • 1: Term of kind VARIABLE_LIST (containing the free variable of the case)

      • 2: Term of kind APPLY_CONSTRUCTOR (the pattern expression, applying the set of variables to the constructor)

      • 3: Term of any Sort (the term the match term evaluates to)

  • Create Term of this Kind with:

  • Create Op of this kind with:

MATCH_CASE

Match case for nullary constructors.

A (constant) case expression to be used within a match expression.

MULT

Arithmetic multiplication.

NEG

Arithmetic negation.

NOT

Logical negation.

NULL_TERM

Null kind.

The kind of a null term ( Term.Term() ).

Note

May not be explicitly created via API functions other than Term.Term() .

OR

Logical disjunction.

PI

Pi constant.

Note

PI is considered a special symbol of Sort Real, but is not a Real value, i.e., Term.isRealValue() will return false .

POW

Arithmetic power.

POW2

Power of two.

Operator for raising 2 to a non-negative integer power.

REGEXP_ALL

Regular expression all.

REGEXP_ALLCHAR

Regular expression all characters.

REGEXP_COMPLEMENT

Regular expression complement.

REGEXP_CONCAT

Regular expression concatenation.

REGEXP_DIFF

Regular expression difference.

REGEXP_INTER

Regular expression intersection.

REGEXP_LOOP

Regular expression loop.

Regular expression loop from lower bound to upper bound number of repetitions.

  • Arity: 1

    • 1: Term of Sort RegLan

  • Indices: 1

    • 1: The lower bound

    • 2: The upper bound

  • Create Term of this Kind with:

  • Create Op of this kind with:

REGEXP_NONE

Regular expression none.

REGEXP_OPT

Regular expression ?.

REGEXP_PLUS

Regular expression +.

REGEXP_RANGE

Regular expression range.

  • Arity: 2

    • 1: Term of Sort String (lower bound character for the range)

    • 2: Term of Sort String (upper bound character for the range)

  • Create Term of this Kind with:

  • Create Op of this kind with:

REGEXP_REPEAT

Operator for regular expression repeat.

  • Arity: 1

    • 1: Term of Sort RegLan

  • Indices: 1

    • 1: The number of repetitions

  • Create Term of this Kind with:

  • Create Op of this kind with:

REGEXP_STAR

Regular expression *.

REGEXP_UNION

Regular expression union.

RELATION_IDEN

Relation identity.

Warning

This kind is experimental and may be changed or removed in future versions.

RELATION_JOIN

Relation join.

RELATION_JOIN_IMAGE

Relation join image.

Warning

This kind is experimental and may be changed or removed in future versions.

RELATION_PRODUCT

Relation cartesian product.

RELATION_TCLOSURE

Relation transitive closure.

RELATION_TRANSPOSE

Relation transpose.

SECANT

Secant function.

SELECT

Array select.

SEP_EMP

Separation logic empty heap.

Warning

This kind is experimental and may be changed or removed in future versions.

SEP_NIL

Separation logic nil.

Warning

This kind is experimental and may be changed or removed in future versions.

SEP_PTO

Separation logic points-to relation.

  • Arity: 2

    • 1: Term denoting the location of the points-to constraint

    • 2: Term denoting the data of the points-to constraint

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

SEP_STAR

Separation logic star.

  • Arity: n > 1

    • 1..n: Terms of sort Bool (the child constraints that hold in

      disjoint (separated) heaps)

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

SEP_WAND

Separation logic magic wand.

  • Arity: 2

    • 1: Terms of Sort Bool (the antecendant of the magic wand constraint)

    • 2: Terms of Sort Bool (conclusion of the magic wand constraint,

      which is asserted to hold in all heaps that are disjoint extensions of the antecedent)

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

SEQ_AT

Sequence element at.

Returns the element at index \(i\) from a sequence \(s\) . If the index is negative or the index is greater or equal to the length of the sequence, the result is the empty sequence. Otherwise the result is a sequence of length 1 .

  • Arity: 2

    • 1: Term of sequence Sort

    • 2: Term of Sort Int (index \(i\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_CONCAT

Sequence concat.

SEQ_CONTAINS

Sequence contains.

Checks whether a sequence \(s_1\) contains another sequence \(s_2\) . If \(s_2\) is empty, the result is always true .

  • Arity: 2

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_EXTRACT

Sequence extract.

Extracts a subsequence, starting at index \(i\) and of length \(l\) , from a sequence \(s\) . If the start index is negative, the start index is greater than the length of the sequence, or the length is negative, the result is the empty sequence.

  • Arity: 3

    • 1: Term of sequence Sort

    • 2: Term of Sort Int (index \(i\) )

    • 3: Term of Sort Int (length \(l\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_INDEXOF

Sequence index-of.

Returns the index of a subsequence \(s_2\) in a sequence \(s_1\) starting at index \(i\) . If the index is negative or greater than the length of sequence \(s_1\) or the subsequence \(s_2\) does not appear in sequence \(s_1\) after index \(i\) , the result is -1.

  • Arity: 3

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

    • 3: Term of Sort Int ( \(i\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_LENGTH

Sequence length.

SEQ_NTH

Sequence nth.

Corresponds to the nth element of a sequence.

SEQ_PREFIX

Sequence prefix-of.

Checks whether a sequence \(s_1\) is a prefix of sequence \(s_2\) . If sequence \(s_1\) is empty, this operator returns true .

  • Arity: 1

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_REPLACE

Sequence replace.

Replaces the first occurrence of a sequence \(s_2\) in a sequence \(s_1\) with sequence \(s_3\) . If \(s_2\) does not appear in \(s_1\) , \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

    • 3: Term of sequence Sort ( \(s_3\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_REPLACE_ALL

Sequence replace all.

Replaces all occurrences of a sequence \(s_2\) in a sequence \(s_1\) with sequence \(s_3\) . If \(s_2\) does not appear in \(s_1\) , sequence \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

    • 3: Term of sequence Sort ( \(s_3\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_REV

Sequence reverse.

SEQ_SUFFIX

Sequence suffix-of.

Checks whether a sequence \(s_1\) is a suffix of sequence \(s_2\) . If sequence \(s_1\) is empty, this operator returns true .

  • Arity: 1

    • 1: Term of sequence Sort ( \(s_1\) )

    • 2: Term of sequence Sort ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SEQ_UNIT

Sequence unit.

Corresponds to a sequence of length one with the given term.

SEQ_UPDATE

Sequence update.

Updates a sequence \(s\) by replacing its context starting at an index with string \(t\) . If the start index is negative, the start index is greater than the length of the sequence, the result is \(s\) . Otherwise, the length of the original sequence is preserved.

  • Arity: 3

    • 1: Term of sequence Sort

    • 2: Term of Sort Int (index \(i\) )

    • 3: Term of sequence Sort (replacement sequence \(t\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SET_CARD

Set cardinality.

SET_CHOOSE

Set choose.

Select an element from a given set. For a set \(A = \{x\}\) , the term (set.choose \(A\) ) is equivalent to the term \(x_1\) . For an empty set, it is an arbitrary value. For a set with cardinality > 1, it will deterministically return an element in \(A\) .

Warning

This kind is experimental and may be changed or removed in future versions.

SET_COMPLEMENT

Set complement with respect to finite universe.

SET_COMPREHENSION

Set comprehension

A set comprehension is specified by a variable list \(x_1 ... x_n\) , a predicate \(P[x_1...x_n]\) , and a term \(t[x_1...x_n]\) . A comprehension \(C\) with the above form has members given by the following semantics:

\[\forall y. ( \exists x_1...x_n. P[x_1...x_n] \wedge t[x_1...x_n] = y ) \Leftrightarrow (set.member \; y \; C)\]

where \(y\) ranges over the element Sort of the (set) Sort of the comprehension. If \(t[x_1..x_n]\) is not provided, it is equivalent to \(y\) in the above formula.

  • Arity: 3

    • 1: Term of Kind VARIABLE_LIST

    • 2: Term of sort Bool (the predicate of the comprehension)

    • 3: (optional) Term denoting the generator for the comprehension

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

SET_EMPTY

Empty set.

SET_INSERT

The set obtained by inserting elements;

  • Arity: n > 0

    • 1..n-1: Terms of any Sort (must match the element sort of the given set Term)

    • n: Term of set Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

SET_INTER

Set intersection.

SET_IS_SINGLETON

Set is singleton tester.

Warning

This kind is experimental and may be changed or removed in future versions.

SET_MAP

Set map.

This operator applies the first argument, a function of Sort \((\rightarrow S_1 \; S_2)\) , to every element of the second argument, a set of Sort (Set \(S_1\) ), and returns a set of Sort (Set \(S_2\) ).

  • Arity: 2

    • 1: Term of function Sort \((\rightarrow S_1 \; S_2)\)

    • 2: Term of set Sort (Set \(S_1\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

SET_MEMBER

Set membership predicate.

Determines if the given set element is a member of the second set.

  • Arity: 2

    • 1: Term of any Sort (must match the element Sort of the given set Term)

    • 2: Term of set Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

SET_MINUS

Set subtraction.

SET_SINGLETON

Singleton set.

Construct a singleton set from an element given as a parameter. The returned set has the same Sort as the element.

SET_SUBSET

Subset predicate.

Determines if the first set is a subset of the second set.

SET_UNION

Set union.

SET_UNIVERSE

Finite universe set.

All set variables must be interpreted as subsets of it.

Note

SET_UNIVERSE is considered a special symbol of the theory of sets and is not considered as a set value, i.e., Term.isSetValue() will return false .

SEXPR

Symbolic expression.

Warning

This kind is experimental and may be changed or removed in future versions.

SINE

Sine function.

SKOLEM_ADD_TO_POOL

A skolemization-add-to-pool annotation.

An skolemization-add-to-pool annotation indicates that when a quantified formula is skolemized, the skolemized version of a term should be added to the given pool.

For example, consider a quantified formula: 

(FORALL (VARIABLE_LIST x) F
        (INST_PATTERN_LIST (SKOLEM_ADD_TO_POOL (ADD x 1) p)))

where assume that \(x\) has type Int. When this quantified formula is skolemized, e.g., with \(k\) of type Int, then the term (ADD k 1) is added to the pool \(p\) .

  • Arity: 2

    • 1: The Term whose free variables are bound by the quantified formula.

    • 2: The pool to add to, whose Sort should be a set of elements that match the Sort of the first argument.

  • Create Term of this Kind with:

  • Create Op of this kind with:

Warning

This kind is experimental and may be changed or removed in future versions.

Note

Should only be used as a child of INST_PATTERN_LIST .

SQRT

Square root.

STORE

Array store.

  • Arity: 3

    • 1: Term of array Sort

    • 2: Term of array index Sort

    • 3: Term of array element Sort

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_CHARAT

String character at.

Returns the character at index \(i\) from a string \(s\) . If the index is negative or the index is greater than the length of the string, the result is the empty string. Otherwise the result is a string of length 1.

  • Arity: 2

    • 1: Term of Sort String (string \(s\) )

    • 2: Term of Sort Int (index \(i\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_CONCAT

String concat.

STRING_CONTAINS

String contains.

Determines whether a string \(s_1\) contains another string \(s_2\) . If \(s_2\) is empty, the result is always true .

  • Arity: 2

    • 1: Term of Sort String (the string \(s_1\) )

    • 2: Term of Sort String (the string \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_FROM_CODE

String from code.

Returns a string containing a single character whose code point matches the argument to this function, or the empty string if the argument is out-of-bounds.

STRING_FROM_INT

Conversion from Int to String.

If the integer is negative this operator returns the empty string.

STRING_INDEXOF

String index-of.

Returns the index of a substring \(s_2\) in a string \(s_1\) starting at index \(i\) . If the index is negative or greater than the length of string \(s_1\) or the substring \(s_2\) does not appear in string \(s_1\) after index \(i\) , the result is -1.

  • Arity: 2

    • 1: Term of Sort String (substring \(s_1\) )

    • 2: Term of Sort String (substring \(s_2\) )

    • 3: Term of Sort Int (index \(i\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_INDEXOF_RE

String index-of regular expression match.

Returns the first match of a regular expression \(r\) in a string \(s\) . If the index is negative or greater than the length of string \(s_1\) , or \(r\) does not match a substring in \(s\) after index \(i\) , the result is -1.

  • Arity: 3

    • 1: Term of Sort String (string \(s\) )

    • 2: Term of Sort RegLan (regular expression \(r\) )

    • 3: Term of Sort Int (index \(i\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_IN_REGEXP

String membership.

STRING_IS_DIGIT

String is-digit.

Returns true if given string is a digit (it is one of "0" , …, "9" ).

STRING_LENGTH

String length.

STRING_LEQ

String less than or equal.

Returns true if string \(s_1\) is less than or equal to \(s_2\) based on a lexiographic ordering over code points.

  • Arity: 2

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_LT

String less than.

Returns true if string \(s_1\) is (strictly) less than \(s_2\) based on a lexiographic ordering over code points.

  • Arity: 2

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_PREFIX

String prefix-of.

Determines whether a string \(s_1\) is a prefix of string \(s_2\) . If string s1 is empty, this operator returns true .

  • Arity: 2

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_REPLACE

String replace.

Replaces a string \(s_2\) in a string \(s_1\) with string \(s_3\) . If \(s_2\) does not appear in \(s_1\) , \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of Sort String (string \(s_1\) )

    • 2: Term of Sort String (string \(s_2\) )

    • 3: Term of Sort String (string \(s_3\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_REPLACE_ALL

String replace all.

Replaces all occurrences of a string \(s_2\) in a string \(s_1\) with string \(s_3\) . If \(s_2\) does not appear in \(s_1\) , \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort String ( \(s_2\) )

    • 3: Term of Sort String ( \(s_3\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_REPLACE_RE

String replace regular expression match.

Replaces the first match of a regular expression \(r\) in string \(s_1\) with string \(s_2\) . If \(r\) does not match a substring of \(s_1\) , \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort RegLan

    • 3: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_REPLACE_RE_ALL

String replace all regular expression matches.

Replaces all matches of a regular expression \(r\) in string \(s_1\) with string \(s_2\) . If \(r\) does not match a substring of \(s_1\) , string \(s_1\) is returned unmodified.

  • Arity: 3

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort RegLan

    • 3: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_REV

String reverse.

STRING_SUBSTR

String substring.

Extracts a substring, starting at index \(i\) and of length \(l\) , from a string \(s\) . If the start index is negative, the start index is greater than the length of the string, or the length is negative, the result is the empty string.

  • Arity: 3

    • 1: Term of Sort String

    • 2: Term of Sort Int (index \(i\) )

    • 3: Term of Sort Int (length \(l\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_SUFFIX

String suffix-of.

Determines whether a string \(s_1\) is a suffix of the second string. If string \(s_1\) is empty, this operator returns true .

  • Arity: 2

    • 1: Term of Sort String ( \(s_1\) )

    • 2: Term of Sort String ( \(s_2\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

STRING_TO_CODE

String to code.

Returns the code point of a string if it has length one, or returns -1 otherwise.

STRING_TO_INT

String to integer (total function).

If the string does not contain an integer or the integer is negative, the operator returns -1 .

STRING_TO_LOWER

String to lower case.

STRING_TO_REGEXP

Conversion from string to regexp.

STRING_TO_UPPER

String to upper case.

STRING_UPDATE

String update.

Updates a string \(s\) by replacing its context starting at an index with string \(t\) . If the start index is negative, the start index is greater than the length of the string, the result is \(s\) . Otherwise, the length of the original string is preserved.

  • Arity: 3

    • 1: Term of Sort String

    • 2: Term of Sort Int (index \(i\) )

    • 3: Term of Sort Strong (replacement string \(t\) )

  • Create Term of this Kind with:

  • Create Op of this kind with:

SUB

Arithmetic subtraction, left associative.

TABLE_PRODUCT

Table cross product.

Warning

This kind is experimental and may be changed or removed in future versions.

TANGENT

Tangent function.

TO_INTEGER

Convert Term of sort Int or Real to Int via the floor function.

TO_REAL

Convert Term of Sort Int or Real to Real.

TUPLE_PROJECT

Tuple projection.

This operator takes a tuple as an argument and returns a tuple obtained by concatenating components of its argument at the provided indices.

For example, 

((_ tuple.project 1 2 2 3 1) (tuple 10 20 30 40))

yields 

(tuple 20 30 30 40 20)

  • Arity: 1

    • 1: Term of tuple Sort

  • Indices: n

    • 1..n: The tuple indices to project

  • Create Term of this Kind with:

  • Create Op of this kind with:

UNDEFINED_KIND

Undefined kind.

Note

Should never be exposed or created via the API.

UNINTERPRETED_SORT_VALUE

The value of an uninterpreted constant.

Note

May be returned as the result of an API call, but terms of this kind may not be created explicitly via the API and may not appear in assertions.

VARIABLE

(Bound) variable.

Note

Only permitted in bindings and in lambda and quantifier bodies.

VARIABLE_LIST

Variable list.

A list of variables (used to bind variables under a quantifier)

WITNESS

Witness.

The syntax of a witness term is similar to a quantified formula except that only one variable is allowed. For example, the term 

(witness ((x S)) F)

returns an element \(x\) of Sort \(S\) and asserts formula \(F\) .

The witness operator behaves like the description operator (see https: no \(x\) that satisfies \(F\) . But if such \(x\) exists, the witness operator does not enforce the following axiom which ensures uniqueness up to logical equivalence:

\[\forall x. F \equiv G \Rightarrow witness~x. F = witness~x. G\]

For example, if there are two elements of Sort \(S\) that satisfy formula \(F\) , then the following formula is satisfiable: 

(distinct
   (witness ((x Int)) F)
   (witness ((x Int)) F))

Note

This kind is primarily used internally, but may be returned in models (e.g., for arithmetic terms in non-linear queries). However, it is not supported by the parser. Moreover, the user of the API should be cautious when using this operator. In general, all witness terms (witness ((x Int)) F) should be such that (exists ((x Int)) F) is a valid formula. If this is not the case, then the semantics in formulas that use witness terms may be unintuitive. For example, the following formula is unsatisfiable: (or (= (witness ((x Int)) false) 0) (not (= (witness ((x Int)) false) 0)) , whereas notice that (or (= z 0) (not (= z 0))) is true for any \(z\) .

XOR

Logical exclusive disjunction, left associative.