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# kinds                                                               -*- sh -*-
#
# For documentation on this file format, please refer to
# src/theory/builtin/kinds.
#

theory THEORY_ARITH ::cvc5::internal::theory::arith::TheoryArith "theory/arith/theory_arith.h"
typechecker "theory/arith/theory_arith_type_rules.h"

properties stable-infinite
properties check propagate ppStaticLearn presolve notifyRestart

rewriter ::cvc5::internal::theory::arith::ArithRewriter "theory/arith/arith_rewriter.h"

operator ADD 2: "arithmetic addition (N-ary)"
operator MULT 2: "arithmetic multiplication (N-ary)"
operator NONLINEAR_MULT 2: "synonym for MULT"
operator SUB 2 "arithmetic binary subtraction operator"
operator NEG 1 "arithmetic unary negation"
operator DIVISION 2 "real division, division by 0 undefined (user symbol)"
operator DIVISION_TOTAL 2 "real division with interpreted division by 0 (internal symbol)"
operator INTS_DIVISION 2 "integer division, division by 0 undefined (user symbol)"
operator INTS_DIVISION_TOTAL 2 "integer division with interpreted division by 0 (internal symbol)"
operator INTS_MODULUS 2 "integer modulus, division by 0 undefined (user symbol)"
operator INTS_MODULUS_TOTAL 2 "integer modulus with interpreted division by 0 (internal symbol)"
operator ABS 1 "absolute value"
parameterized DIVISIBLE DIVISIBLE_OP 1 "divisibility-by-k predicate; first parameter is a DIVISIBLE_OP, second is integer term"
operator POW 2 "arithmetic power"
operator POW2 1 "arithmetic power of 2"
operator INTS_ISPOW2 1 "test if an integer is a power of 2"
operator INTS_LOG2 1 "integer logarithm base 2 (round down to power of 2)"

operator EXPONENTIAL 1 "exponential"
operator SINE 1 "sine"
operator COSINE 1 "consine"
operator TANGENT 1 "tangent"
operator COSECANT 1 "cosecant"
operator SECANT 1 "secant"
operator COTANGENT 1 "cotangent"
operator ARCSINE 1 "arc sine"
operator ARCCOSINE 1 "arc consine"
operator ARCTANGENT 1 "arc tangent"
operator ARCCOSECANT 1 "arc cosecant"
operator ARCSECANT 1 "arc secant"
operator ARCCOTANGENT 1 "arc cotangent"

operator SQRT 1 "square root"

constant DIVISIBLE_OP \
  struct \
  Divisible \
  ::cvc5::internal::DivisibleHashFunction \
  "util/divisible.h" \
  "operator for the divisibility-by-k predicate; payload is an instance of the cvc5::internal::Divisible class"

sort REAL_TYPE \
    Cardinality::REALS \
    well-founded \
        "NodeManager::currentNM()->mkConstReal(Rational(0))" \
        "expr/node_manager.h" \
    "real type"
sort INTEGER_TYPE \
    Cardinality::INTEGERS \
    well-founded \
        "NodeManager::currentNM()->mkConstInt(Rational(0))" \
        "expr/node_manager.h" \
    "integer type"

constant CONST_RATIONAL \
    class \
    Rational+ \
    ::cvc5::internal::RationalHashFunction \
    "util/rational.h" \
    "a multiple-precision rational constant; payload is an instance of the cvc5::internal::Rational class"

constant CONST_INTEGER \
    class \
    Rational+ \
    ::cvc5::internal::RationalHashFunction \
    "util/rational.h" \
    "a multiple-precision integer constant; payload is an instance of the cvc5::internal::Rational class"

constant REAL_ALGEBRAIC_NUMBER_OP \
    class \
    RealAlgebraicNumber+ \
    ::cvc5::internal::RealAlgebraicNumberHashFunction \
    "util/real_algebraic_number.h" \
    "a real algebraic number constant; payload is an instance of the cvc5::internal::RealAlgebraicNumber class"
parameterized REAL_ALGEBRAIC_NUMBER REAL_ALGEBRAIC_NUMBER_OP 0 "a real algebraic number constant; payload is an instance of the cvc5::internal::RealAlgebraicNumber class"

enumerator REAL_TYPE \
    "::cvc5::internal::theory::arith::RationalEnumerator" \
    "theory/arith/type_enumerator.h"
enumerator INTEGER_TYPE \
    "::cvc5::internal::theory::arith::IntegerEnumerator" \
    "theory/arith/type_enumerator.h"

operator LT 2 "less than, x < y"
operator LEQ 2 "less than or equal, x <= y"
operator GT 2 "greater than, x > y"
operator GEQ 2 "greater than or equal, x >= y"

# represents an indexed root predicate. See util/indexed_root_predicate.h for more documentation.
constant INDEXED_ROOT_PREDICATE_OP \
  struct \
  IndexedRootPredicate \
  ::cvc5::internal::IndexedRootPredicateHashFunction \
  "util/indexed_root_predicate.h" \
  "operator for the indexed root predicate; payload is an instance of the cvc5::internal::IndexedRootPredicate class"
parameterized INDEXED_ROOT_PREDICATE INDEXED_ROOT_PREDICATE_OP 2 "indexed root predicate; first parameter is a INDEXED_ROOT_PREDICATE_OP, second is a real variable compared to zero, third is a polynomial"

operator IS_INTEGER 1 "term-is-integer predicate (parameter is a real-sorted term)"
operator TO_INTEGER 1 "convert term to integer by the floor function (parameter is a real-sorted term)"
operator TO_REAL 1 "cast term to real (parameter is an integer-sorted term)"

typerule ADD ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule MULT ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule NONLINEAR_MULT ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule SUB ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule NEG ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule DIVISION ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule POW ::cvc5::internal::theory::arith::ArithOperatorTypeRule

typerule CONST_RATIONAL ::cvc5::internal::theory::arith::ArithConstantTypeRule
typerule CONST_INTEGER ::cvc5::internal::theory::arith::ArithConstantTypeRule

typerule REAL_ALGEBRAIC_NUMBER_OP ::cvc5::internal::theory::arith::ArithRealAlgebraicNumberOpTypeRule
typerule REAL_ALGEBRAIC_NUMBER ::cvc5::internal::theory::arith::ArithRealAlgebraicNumberTypeRule

typerule LT ::cvc5::internal::theory::arith::ArithRelationTypeRule
typerule LEQ ::cvc5::internal::theory::arith::ArithRelationTypeRule
typerule GT ::cvc5::internal::theory::arith::ArithRelationTypeRule
typerule GEQ ::cvc5::internal::theory::arith::ArithRelationTypeRule

typerule INDEXED_ROOT_PREDICATE_OP "SimpleTypeRule"
typerule INDEXED_ROOT_PREDICATE ::cvc5::internal::theory::arith::IndexedRootPredicateTypeRule

typerule TO_REAL "SimpleTypeRule"
typerule TO_INTEGER "SimpleTypeRule"
typerule IS_INTEGER "SimpleTypeRule"

typerule ABS ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule INTS_DIVISION "SimpleTypeRule"
typerule INTS_MODULUS "SimpleTypeRule"
typerule DIVISIBLE "SimpleTypeRule"
typerule DIVISIBLE_OP "SimpleTypeRule"

typerule DIVISION_TOTAL ::cvc5::internal::theory::arith::ArithOperatorTypeRule
typerule INTS_DIVISION_TOTAL "SimpleTypeRule"
typerule INTS_MODULUS_TOTAL "SimpleTypeRule"

typerule EXPONENTIAL "SimpleTypeRule"
typerule SINE "SimpleTypeRule"
typerule COSINE "SimpleTypeRule"
typerule TANGENT "SimpleTypeRule"
typerule COSECANT "SimpleTypeRule"
typerule SECANT "SimpleTypeRule"
typerule COTANGENT "SimpleTypeRule"
typerule ARCSINE "SimpleTypeRule"
typerule ARCCOSINE "SimpleTypeRule"
typerule ARCTANGENT "SimpleTypeRule"
typerule ARCCOSECANT "SimpleTypeRule"
typerule ARCSECANT "SimpleTypeRule"
typerule ARCCOTANGENT "SimpleTypeRule"
typerule POW2 "SimpleTypeRule"
typerule INTS_ISPOW2 "SimpleTypeRule"
typerule INTS_LOG2 "SimpleTypeRule"

typerule SQRT "SimpleTypeRule"

nullaryoperator PI "pi"

typerule PI ::cvc5::internal::theory::arith::RealNullaryOperatorTypeRule

# Integer AND, which is parameterized by a (positive) bitwidth k.
# ((_ iand k) i1 i2) is equivalent to:
# (bv2int (bvand ((_ int2bv k) i1) ((_ int2bv k) i2)))
# for all integers i1, i2.
constant IAND_OP \
  struct \
  IntAnd \
  "::cvc5::internal::UnsignedHashFunction< ::cvc5::internal::IntAnd >" \
  "util/iand.h" \
  "operator for integer AND; payload is an instance of the cvc5::internal::IntAnd class"
parameterized IAND IAND_OP 2 "integer version of AND operator; first parameter is an IAND_OP, second and third are integer terms"

typerule IAND_OP "SimpleTypeRule"
typerule IAND ::cvc5::internal::theory::arith::IAndTypeRule

endtheory