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/*
* This file is part of the source code of the software program
* Vampire. It is protected by applicable
* copyright laws.
*
* This source code is distributed under the licence found here
* https://vprover.github.io/license.html
* and in the source directory
*/
#ifndef __NUM_TRAITS_H__
#define __NUM_TRAITS_H__
#include "Forwards.hpp"
#include "Term.hpp"
#include "Theory.hpp"
#include "Signature.hpp"
#include "Lib/Environment.hpp"
namespace Kernel {
/** This struct provides a unified interface to the "number" theories. i.e. these
* are the theories of integers, rationals, and reals.
*
* For each ConstantType in {IntegerConstantType, RationalConstantType, RealConstantType},
* there is a specialisation NumTraits<ConstantType> which provides functions for building
* terms and literals, accessing the functor/interpretation of some predicate or function.
*
* There are associated constants for the related Sorts::DefaultSorts values, constexpr s
* to pattern match on interpretations and special constants (like zero and one), etc.
*
* =====
*
* To access the functor of some symbol "sym", there is a function
* static unsigned symF();
*
* e.g.: NumTraits<IntegerConstantType>::lessF()
* NumTraits<IntegerConstantType>::addF()
*
* =====
*
* To access the interpretation of some symbol "sym", there is a constant
* static Theory::Interpretation symI;
*
* e.g.: NumTraits<IntegerConstantType>::lessI // == Theory::Interpretation INT_LESS;
* NumTraits<IntegerConstantType>::addI // == Theory::Interpretation INT_PLUS;
*
* =====
*
* To build a term from some function symbol "sym", there is a function
* static TermList static sym(TermList...);
*
* e.g.: NumTraits<IntegerConstantType>::add(lhs, rhs)
*
* =====
*
* To build a literal from some predicate symbol "sym", there is a function
* static Literal* static sym(bool polarity, TermList...);
*
* e.g.: NumTraits<IntegerConstantType>::less(true, lhs, rhs)
*
* =====
*
* For a complete picture build the doxygen documentation.
*
*/
template<class ConstantType>
struct NumTraits;
#define FOR_ARITY_RANGE_0(f)
#define FOR_ARITY_RANGE_1(f) f(0)
#define FOR_ARITY_RANGE_2(f) FOR_ARITY_RANGE_1(f), f(1)
#define FOR_ARITY_RANGE_3(f) FOR_ARITY_RANGE_2(f), f(2)
#define FOR_ARITY_RANGE_4(f) FOR_ARITY_RANGE_3(f), f(3)
#define FOR_ARITY_RANGE_5(f) FOR_ARITY_RANGE_4(f), f(4)
#define FOR_ARITY_RANGE_6(f) FOR_ARITY_RANGE_5(f), f(5)
#define FOR_ARITY_RANGE_7(f) FOR_ARITY_RANGE_6(f), f(6)
#define FOR_ARITY_RANGE_8(f) FOR_ARITY_RANGE_7(f), f(7)
#define FOR_ARITY_RANGE_9(f) FOR_ARITY_RANGE_8(f), f(8)
#define FOR_ARITY_RANGE_10(f) FOR_ARITY_RANGE_9(f), f(9)
#define FOR_ARITY_RANGE_11(f) FOR_ARITY_RANGE_10(f), f(10)
#define FOR_ARITY_RANGE(arity) FOR_ARITY_RANGE_ ## arity
#define IMPL_NUM_TRAITS__ARG_DECL_1(Type) Type a1
#define IMPL_NUM_TRAITS__ARG_DECL_2(Type) IMPL_NUM_TRAITS__ARG_DECL_1(Type), Type a2
#define IMPL_NUM_TRAITS__ARG_DECL_3(Type) IMPL_NUM_TRAITS__ARG_DECL_2(Type), Type a3
#define IMPL_NUM_TRAITS__ARG_DECL_4(Type) IMPL_NUM_TRAITS__ARG_DECL_3(Type), Type a4
#define IMPL_NUM_TRAITS__ARG_DECL_5(Type) IMPL_NUM_TRAITS__ARG_DECL_4(Type), Type a5
#define IMPL_NUM_TRAITS__ARG_DECL_6(Type) IMPL_NUM_TRAITS__ARG_DECL_5(Type), Type a6
#define IMPL_NUM_TRAITS__ARG_DECL_7(Type) IMPL_NUM_TRAITS__ARG_DECL_6(Type), Type a7
#define IMPL_NUM_TRAITS__ARG_DECL_8(Type) IMPL_NUM_TRAITS__ARG_DECL_7(Type), Type a8
#define IMPL_NUM_TRAITS__ARG_DECL_9(Type) IMPL_NUM_TRAITS__ARG_DECL_8(Type), Type a9
#define IMPL_NUM_TRAITS__ARG_DECL_10(Type) IMPL_NUM_TRAITS__ARG_DECL_9(Type), Type a10
#define IMPL_NUM_TRAITS__ARG_DECL(Type, arity) IMPL_NUM_TRAITS__ARG_DECL_ ## arity (Type)
#define IMPL_NUM_TRAITS__ARG_EXPR(arity) IMPL_NUM_TRAITS__ARG_DECL_ ## arity ()
#define IMPL_NUM_TRAITS__INTERPRETED_SYMBOL(name, Name, SORT_SHORT, _INTERPRETATION) \
static constexpr Theory::Interpretation name ## I = Theory::SORT_SHORT ## _INTERPRETATION; \
\
static unsigned name ## F() { \
static const unsigned functor = env.signature->getInterpretingSymbol(name ## I); \
return functor; \
} \
#define IMPL_NUM_TRAITS__INTERPRETED_PRED(name, Name, SORT_SHORT, _INTERPRETATION, arity) \
IMPL_NUM_TRAITS__INTERPRETED_SYMBOL(name, Name, SORT_SHORT, _INTERPRETATION) \
\
template<class LitOrFunctor> \
static bool is ## Name(LitOrFunctor f) \
{ return theory->isInterpretedPredicate(f, name ## I); } \
\
template<class F> \
static auto if ## Name(Literal* t, F fun) { \
return someIf(is ## Name(t->functor()), \
[&]() { return fun(t->isPositive(), FOR_ARITY_RANGE(arity)(t->termArg)); }); \
} \
\
static Literal* name(bool polarity, IMPL_NUM_TRAITS__ARG_DECL(TermList, arity)) { \
return Literal::create( \
name##F(), \
polarity, \
{ IMPL_NUM_TRAITS__ARG_EXPR( arity ) }); \
} \
#define IMPL_NUM_TRAITS__INTERPRETED_FUN(name, Name, SORT_SHORT, _INTERPRETATION, arity) \
IMPL_NUM_TRAITS__INTERPRETED_SYMBOL(name, Name, SORT_SHORT, _INTERPRETATION) \
\
static bool is ## Name(unsigned f) \
{ return theory->isInterpretedFunction(f, name ## I); } \
\
static bool is ## Name(Term* t) \
{ return is ## Name(t->functor()); } \
\
static bool is ## Name(TermList t) \
{ return t.isTerm() && is ## Name(t.term()); } \
\
template<class F> \
static auto if ## Name(Term* t, F fun) { \
return someIf(is ## Name(t->functor()), \
[&]() { return fun(FOR_ARITY_RANGE(arity)(t->termArg)); }); \
} \
template<class F> \
static auto if ## Name(TermList t, F fun) { \
return someIf(t.isTerm(), [&]() { return if ## Name(t.term(), fun); }).flatten(); \
} \
\
static TermList name(IMPL_NUM_TRAITS__ARG_DECL(TermList, arity)) { \
return TermList( \
Term::create( \
name##F(), \
{ IMPL_NUM_TRAITS__ARG_EXPR(arity) })); \
} \
#define IMPL_NUM_TRAITS__SPECIAL_CONSTANT(name, Name, value) \
static ConstantType name ## C() { \
return ConstantType(value); \
} \
static Term* name ## T() { \
static Term* trm = theory->representConstant(name ## C()); \
return trm; \
} \
static unsigned name ## F() { \
static unsigned f = name ## T()->functor(); \
return f; \
} \
static TermList name() \
{ return TermList(name ## T()); } \
\
static bool is ## Name(const TermList& l) \
{ return l == name(); } \
#define IMPL_NUM_TRAITS__QUOTIENT_REMAINDER(SHORT, X) \
IMPL_NUM_TRAITS__INTERPRETED_FUN( quotient ## X, Quotient ## X, SHORT, _QUOTIENT_ ## X, 2) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(remainder ## X, Remainder ## X, SHORT, _REMAINDER_ ## X, 2) \
#define IMPL_NUM_TRAITS(CamelCase, lowerCase, LONG, SHORT) \
template<> struct NumTraits<CamelCase ## ConstantType> { \
/* dummy operator== to be able to compare Coproduct<IntTraits, RatTraits, ...> */ \
friend bool operator==(NumTraits const& l, NumTraits const& r) \
{ return true; } \
\
friend bool operator!=(NumTraits const& l, NumTraits const& r) \
{ return !(l == r); } \
\
using ConstantType = CamelCase ## ConstantType; \
static TermList sort() { return AtomicSort::lowerCase ## Sort(); }; \
\
template<class I1, class I2, class... Is> \
static TermList sum(I1 i1, I2 i2, Is... is) \
{ return sum(concatIters(i1, i2, is...)); }; \
\
static TermList mulSimpl(ConstantType c, TermList t) \
{ return c == ConstantType(1) ? t \
: c == ConstantType(-1) ? (t == zero() ? t : minus(t)) \
: t == zero() ? zero() \
: t == one() ? constantTl(c) \
: NumTraits::mul(constantTl(c), t); } \
\
template<class Iter> \
static TermList sum(Iter iter) { \
if (iter.hasNext()) { \
auto out = iter.next(); \
while (iter.hasNext()) { \
out = NumTraits::add(iter.next(), out); \
} \
return out; \
} else { \
return NumTraits::zero(); \
} \
}; \
\
template<class Iter> \
static TermList product(Iter iter) { \
if (iter.hasNext()) { \
auto out = iter.next(); \
while (iter.hasNext()) { \
out = NumTraits::mul(iter.next(), out); \
} \
return out; \
} else { \
return NumTraits::one(); \
} \
}; \
\
static bool isEq(bool positive, Literal* lit) \
{ return (lit->isPositive() == positive) \
&& lit->isEquality() \
&& (lit->eqArgSort() == sort()); } \
\
static bool isPosEq(Literal* lit) { return isEq(true , lit); } \
static bool isNegEq(Literal* lit) { return isEq(false, lit); } \
\
IMPL_NUM_TRAITS__INTERPRETED_PRED(less, Less, SHORT, _LESS, 2) \
IMPL_NUM_TRAITS__INTERPRETED_PRED(leq, Leq, SHORT, _LESS_EQUAL, 2) \
IMPL_NUM_TRAITS__INTERPRETED_PRED(greater, Greater, SHORT, _GREATER, 2) \
IMPL_NUM_TRAITS__INTERPRETED_PRED(geq, Geq, SHORT, _GREATER_EQUAL, 2) \
\
static Literal* eq(bool polarity, TermList lhs, TermList rhs) \
{ return Literal::createEquality(polarity, lhs, rhs, sort()); } \
\
IMPL_NUM_TRAITS__INTERPRETED_FUN(toInt, ToInt, SHORT, _TO_INT , 1) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(toRat, ToRat, SHORT, _TO_RAT , 1) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(toReal, ToReal, SHORT, _TO_REAL , 1) \
\
IMPL_NUM_TRAITS__INTERPRETED_PRED(isInt, IsInt, SHORT, _IS_INT , 1) \
IMPL_NUM_TRAITS__INTERPRETED_PRED(isRat, IsRat, SHORT, _IS_RAT , 1) \
IMPL_NUM_TRAITS__INTERPRETED_PRED(isReal, IsReal, SHORT, _IS_REAL , 1) \
\
IMPL_NUM_TRAITS__QUOTIENT_REMAINDER(SHORT, E) \
IMPL_NUM_TRAITS__QUOTIENT_REMAINDER(SHORT, T) \
IMPL_NUM_TRAITS__QUOTIENT_REMAINDER(SHORT, F) \
\
IMPL_NUM_TRAITS__INTERPRETED_FUN(minus, Minus, SHORT, _UNARY_MINUS, 1) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(binMinus, BinMinus, SHORT, _MINUS, 2) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(add , Add , SHORT, _PLUS , 2) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(mul , Mul , SHORT, _MULTIPLY , 2) \
IMPL_NUM_TRAITS__INTERPRETED_FUN(floor, Floor, SHORT, _FLOOR, 1) \
__NUM_TRAITS_IF_FRAC(SHORT, \
IMPL_NUM_TRAITS__INTERPRETED_FUN(div, Div, SHORT, _QUOTIENT, 2) \
static ConstantType constant(int num, int den) { return ConstantType(num, den); } \
static auto constantT (int num, int den) { return constantT (constant(num, den)); } \
static auto constantF (int num, int den) { return constantF (constant(num, den)); } \
static auto constantTl(int num, int den) { return constantTl(constant(num, den)); } \
static bool isFractional() { return true; } \
) \
\
__NUM_TRAITS_IF_NOT_FRAC(SHORT, \
static bool isFractional() { return false; } \
IMPL_NUM_TRAITS__INTERPRETED_PRED(divides, Divides, SHORT, _DIVIDES, 2) \
) \
\
IMPL_NUM_TRAITS__SPECIAL_CONSTANT(one , One , 1) \
IMPL_NUM_TRAITS__SPECIAL_CONSTANT(zero, Zero, 0) \
\
template<class T> \
static Option<ConstantType const&> tryLinMul(T t) \
{ return ifLinMul(t, [](auto& c, auto t) -> auto& { return c; }); } \
\
static Option<ConstantType const&> tryLinMul(unsigned f) \
{ return env.signature->tryLinMul<ConstantType>(f); } \
\
static unsigned linMulF(ConstantType const& c) \
{ return env.signature->addLinMul(c); } \
\
static bool isLinMul(unsigned t) \
{ return tryLinMul(t).isSome(); } \
\
template<class T> \
static bool isLinMul(T t) \
{ return ifLinMul(t, [](auto...) { return true; }); } \
\
template<class F> \
static auto ifLinMul(TermList t, F func) \
{ return someIf(t.isTerm(), [&]() { return ifLinMul(t.term(), std::move(func)); }) \
.flatten(); } \
\
template<class F> \
static auto ifLinMul(Term const* t, F func) \
{ \
auto c = tryLinMul(t->functor()); \
return someIf(c.isSome(), [&]() { return func(*c, t->termArg(0)); }); \
} \
\
static TermList linMul(ConstantType const& c, TermList t) \
{ return TermList(Term::create(linMulF(c), {t})); } \
\
static ConstantType constant(int i) { return ConstantType(i); } \
static auto constantF (int i) { return constantF (constant(i)); } \
static auto constantT (int i) { return constantT (constant(i)); } \
static auto constantTl(int i) { return constantTl(constant(i)); } \
\
static unsigned constantF(ConstantType const& i) \
{ return env.signature->addNumeralConstant(i); } \
\
static Term* constantT(ConstantType const& i) { return Term::create(constantF(i), {}); } \
static TermList constantTl(ConstantType const& i) { return TermList(constantT(i)); } \
static Option<ConstantType const&> tryNumeral(unsigned functor) \
{ \
Signature::Symbol* sym = env.signature->getFunction(functor); \
if (!sym->numeralConstant<ConstantType>()) { \
return {}; \
} \
return Option<ConstantType const&>(sym->numeralValue<ConstantType>()); \
} \
\
static Option<ConstantType const&> tryNumeral(Term* t) \
{ return tryNumeral(t->functor()); } \
\
static Option<ConstantType const&> tryNumeral(TermList t) { \
if (t.isTerm()) return tryNumeral(t.term()); \
else return {}; \
} \
\
template<class TermOrFunctor> \
static bool isNumeral(TermOrFunctor t) { return tryNumeral(t).isSome(); } \
template<class TermOrFunctor> \
static bool isNumeral(TermOrFunctor t, ConstantType n) { return tryNumeral(t) == some(n); } \
template<class Term, class F> \
static auto ifNumeral(Term t, F fun) -> Option<std::invoke_result_t<F, ConstantType const&>> \
{ return tryNumeral(t).map([&](ConstantType const& n) { return fun(n); }); } \
static unsigned numeralF(ConstantType c) { return constantT(c)->functor(); } \
\
static const char* name() {return #CamelCase;} \
}; \
#define __NUM_TRAITS_IF_FRAC(sort, ...) __NUM_TRAITS_IF_FRAC_ ## sort (__VA_ARGS__)
#define __NUM_TRAITS_IF_FRAC_INT(...)
#define __NUM_TRAITS_IF_FRAC_REAL(...) __VA_ARGS__
#define __NUM_TRAITS_IF_FRAC_RAT(...) __VA_ARGS__
#define __NUM_TRAITS_IF_NOT_FRAC(sort, ...) __NUM_TRAITS_IF_NOT_FRAC_ ## sort (__VA_ARGS__)
#define __NUM_TRAITS_IF_NOT_FRAC_INT(...) __VA_ARGS__
#define __NUM_TRAITS_IF_NOT_FRAC_REAL(...)
#define __NUM_TRAITS_IF_NOT_FRAC_RAT(...)
IMPL_NUM_TRAITS(Rational, rational, RATIONAL, RAT )
IMPL_NUM_TRAITS(Real , real , REAL , REAL)
IMPL_NUM_TRAITS(Integer , int , INTEGER , INT )
#define FOR_NUM_TRAITS(macro) \
macro(Kernel::NumTraits<Kernel:: IntegerConstantType>) \
macro(Kernel::NumTraits<Kernel:: RealConstantType>) \
macro(Kernel::NumTraits<Kernel::RationalConstantType>) \
using IntTraits = NumTraits< IntegerConstantType>;
using RatTraits = NumTraits<RationalConstantType>;
using RealTraits = NumTraits< RealConstantType>;
template<class Clsr>
auto forAnyNumTraits(Clsr clsr) {
return clsr( IntTraits{})
|| clsr( RatTraits{})
|| clsr(RealTraits{});
}
template<class Clsr>
auto forAllNumTraits(Clsr clsr) {
return clsr( IntTraits{})
&& clsr( RatTraits{})
&& clsr(RealTraits{});
}
template<class Clsr>
auto numTraitsIter(Clsr clsr) {
return getConcatenatedIterator( clsr( IntTraits{}),
getConcatenatedIterator( clsr( RatTraits{}),
clsr(RealTraits{})));
}
template<class Clsr>
auto forEachNumTraits(Clsr clsr) {
clsr( IntTraits{});
clsr( RatTraits{});
clsr(RealTraits{});
}
template<class Clsr>
auto tryNumTraits(Clsr clsr) {
return clsr( IntTraits{})
|| [&] { return clsr( RatTraits{}); }
|| [&] { return clsr(RealTraits{}); };
}
template<class Clsr>
auto tryFracNumTraits(Clsr clsr) {
clsr( RatTraits{})
|| [&] { return clsr(RealTraits{}); };
}
template<class IfInt, class Else>
auto ifIntTraits(IntTraits n, IfInt ifIntF, Else)
{ return ifIntF(std::move(n)); }
template<class IfInt, class Else, class NumTraits>
auto ifIntTraits(NumTraits n, IfInt, Else elseF)
{ return elseF(std::move(n)); }
template<class T, class Val, class IfT, class IfNotT>
struct IfOfType
{
auto operator()(Val val, IfT ifT, IfNotT ifNotT)
{ return ifNotT(std::move(val)); }
};
template<class T, class IfT, class IfNotT>
struct IfOfType<T, T, IfT, IfNotT>
{
auto operator()(T val, IfT ifT, IfNotT ifNotT)
{ return ifT(std::move(val)); }
};
template<class T, class Val, class IfT, class IfNotT>
auto ifOfType(Val val, IfT ifT, IfNotT ifNotT)
{ return IfOfType<T, Val, IfT, IfNotT>{}(std::move(val), ifT, ifNotT); }
}
#endif // __NUM_TRAITS_H__