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/*
* Copyright 2023 WebAssembly Community Group participants
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#ifndef wasm_analysis_lattice_h
#define wasm_analysis_lattice_h
#if __cplusplus >= 202002L
#include <concepts>
#endif // __cplusplus >= 202002L
namespace wasm::analysis {
enum LatticeComparison { NO_RELATION, EQUAL, LESS, GREATER };
// If parameter "comparison" compares x and y, the function returns the opposite
// direction comparison between y and x.
inline LatticeComparison reverseComparison(LatticeComparison comparison) {
if (comparison == LatticeComparison::LESS) {
return LatticeComparison::GREATER;
} else if (comparison == LatticeComparison::GREATER) {
return LatticeComparison::LESS;
} else {
return comparison;
}
}
#if __cplusplus >= 202002L
template<typename L>
concept Lattice = requires(const L& lattice,
const typename L::Element& constElem,
typename L::Element& elem) {
// Lattices must have elements.
typename L::Element;
requires std::copyable<typename L::Element>;
// Get the bottom element of this lattice.
{ lattice.getBottom() } noexcept -> std::same_as<typename L::Element>;
// Compare two elements of this lattice. TODO: use <=> and
// std::three_way_comparable once we support C++20 everywhere.
{
lattice.compare(constElem, constElem)
} noexcept -> std::same_as<LatticeComparison>;
// Modify `elem` in-place to be the join (aka least upper bound) of `elem` and
// `constElem`, returning true iff `elem` was modified, i.e. if it was not
// already an upper bound of `constElem`.
{ lattice.join(elem, constElem) } noexcept -> std::same_as<bool>;
};
// The analysis framework only uses bottom elements and least upper bounds (i.e.
// joins) directly, so lattices do not necessarily need to implement top
// elements and greatest lower bounds (i.e. meets) to be useable, even though
// they are required for mathematical lattices. Implementing top elements and
// meets does have the benefit of making a lattice generically invertable,
// though. See lattices/inverted.h.
template<typename L>
concept FullLattice =
Lattice<L> && requires(const L& lattice,
const typename L::Element& constElem,
typename L::Element& elem) {
// Get the top element of this lattice.
{ lattice.getTop() } noexcept -> std::same_as<typename L::Element>;
// Modify `elem` in-place to be the meet (aka greatest lower bound) of
// `elem` and `constEleme`, returning true iff `elem` was modified, i.e. if
// it was not already a lower bound of `constElem`.
{ lattice.meet(elem, constElem) } noexcept -> std::same_as<bool>;
};
#else // __cplusplus >= 202002L
#define Lattice typename
#define FullLattice typename
#endif // __cplusplus >= 202002L
} // namespace wasm::analysis
#endif // wasm_analysis_lattice_h
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