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

theory THEORY_ARITH ::CVC4::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 ::CVC4::theory::arith::ArithRewriter "theory/arith/arith_rewriter.h"

operator PLUS 2: "arithmetic addition (N-ary)"
operator MULT 2: "arithmetic multiplication (N-ary)"
operator NONLINEAR_MULT 2: "synonym for MULT"
operator MINUS 2 "arithmetic binary subtraction operator"
operator UMINUS 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 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 \
        ::CVC4::Divisible \
        ::CVC4::DivisibleHashFunction \
        "util/divisible.h" \
        "operator for the divisibility-by-k predicate; payload is an instance of the CVC4::Divisible class"

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

constant CONST_RATIONAL \
    ::CVC4::Rational \
    ::CVC4::RationalHashFunction \
    "util/rational.h" \
    "a multiple-precision rational constant; payload is an instance of the CVC4::Rational class"

enumerator REAL_TYPE \
    "::CVC4::theory::arith::RationalEnumerator" \
    "theory/arith/type_enumerator.h"
enumerator INTEGER_TYPE \
    "::CVC4::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"

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; this is a no-op in CVC4, as integer is a subtype of real)"

typerule PLUS ::CVC4::theory::arith::ArithOperatorTypeRule
typerule MULT ::CVC4::theory::arith::ArithOperatorTypeRule
typerule NONLINEAR_MULT ::CVC4::theory::arith::ArithOperatorTypeRule
typerule MINUS ::CVC4::theory::arith::ArithOperatorTypeRule
typerule UMINUS ::CVC4::theory::arith::ArithOperatorTypeRule
typerule DIVISION ::CVC4::theory::arith::ArithOperatorTypeRule
typerule POW ::CVC4::theory::arith::ArithOperatorTypeRule

typerule CONST_RATIONAL ::CVC4::theory::arith::ArithConstantTypeRule

typerule LT ::CVC4::theory::arith::ArithPredicateTypeRule
typerule LEQ ::CVC4::theory::arith::ArithPredicateTypeRule
typerule GT ::CVC4::theory::arith::ArithPredicateTypeRule
typerule GEQ ::CVC4::theory::arith::ArithPredicateTypeRule

typerule TO_REAL ::CVC4::theory::arith::ArithOperatorTypeRule
typerule TO_INTEGER ::CVC4::theory::arith::ArithOperatorTypeRule
typerule IS_INTEGER ::CVC4::theory::arith::ArithUnaryPredicateTypeRule

typerule ABS ::CVC4::theory::arith::IntOperatorTypeRule
typerule INTS_DIVISION ::CVC4::theory::arith::IntOperatorTypeRule
typerule INTS_MODULUS ::CVC4::theory::arith::IntOperatorTypeRule
typerule DIVISIBLE ::CVC4::theory::arith::IntUnaryPredicateTypeRule

typerule DIVISION_TOTAL ::CVC4::theory::arith::ArithOperatorTypeRule
typerule INTS_DIVISION_TOTAL ::CVC4::theory::arith::IntOperatorTypeRule
typerule INTS_MODULUS_TOTAL ::CVC4::theory::arith::IntOperatorTypeRule

typerule EXPONENTIAL ::CVC4::theory::arith::RealOperatorTypeRule
typerule SINE ::CVC4::theory::arith::RealOperatorTypeRule
typerule COSINE ::CVC4::theory::arith::RealOperatorTypeRule
typerule TANGENT ::CVC4::theory::arith::RealOperatorTypeRule
typerule COSECANT ::CVC4::theory::arith::RealOperatorTypeRule
typerule SECANT ::CVC4::theory::arith::RealOperatorTypeRule
typerule COTANGENT ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCSINE ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCCOSINE ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCTANGENT ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCCOSECANT ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCSECANT ::CVC4::theory::arith::RealOperatorTypeRule
typerule ARCCOTANGENT ::CVC4::theory::arith::RealOperatorTypeRule

typerule SQRT ::CVC4::theory::arith::RealOperatorTypeRule

nullaryoperator PI "pi"

typerule PI ::CVC4::theory::arith::RealNullaryOperatorTypeRule

endtheory