Implemented advanced simplification (some formulas not covered yet).
This commit is contained in:
parent
fc538eb7fc
commit
bf8cf75369
GPG Key ID:
05F3611E97A70ABF
@ -1,5 +1,7 @@
|
||||
#include <anthem/Simplification.h>
|
||||
|
||||
#include <iostream>
|
||||
|
||||
namespace anthem
|
||||
{
|
||||
|
||||
@ -11,75 +13,196 @@ namespace anthem
|
||||
|
||||
bool isPrimitiveTerm(const ast::Term &term)
|
||||
{
|
||||
const auto binaryOperationIsNotPrimitiveTerm =
|
||||
const auto handleBinaryOperation =
|
||||
[](const ast::BinaryOperationPointer &)
|
||||
{
|
||||
return false;
|
||||
};
|
||||
|
||||
const auto intervalIsNotPrimitiveTerm =
|
||||
const auto handleInterval =
|
||||
[](const ast::IntervalPointer &)
|
||||
{
|
||||
return false;
|
||||
};
|
||||
|
||||
const auto defaultIsPrimitiveTerm =
|
||||
const auto handleDefault =
|
||||
[](const auto &)
|
||||
{
|
||||
return true;
|
||||
};
|
||||
|
||||
return term.match(binaryOperationIsNotPrimitiveTerm, intervalIsNotPrimitiveTerm, defaultIsPrimitiveTerm);
|
||||
return term.match(handleBinaryOperation, handleInterval, handleDefault);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
ast::Formula simplifyFormula(ast::Formula &&formula)
|
||||
bool matchesVariable(const ast::Term &term, const ast::VariablePointer &variable)
|
||||
{
|
||||
const auto simplifyAnd =
|
||||
const auto handleVariable =
|
||||
[&](const ast::VariablePointer &other)
|
||||
{
|
||||
return variable->name == other->name;
|
||||
};
|
||||
|
||||
const auto handleDefault =
|
||||
[](const auto &)
|
||||
{
|
||||
return false;
|
||||
};
|
||||
|
||||
return term.match(handleVariable, handleDefault);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
std::experimental::optional<ast::Term> extractAssignedTerm(ast::Formula &formula, const ast::VariablePointer &variable)
|
||||
{
|
||||
const auto handleComparison =
|
||||
[&](ast::ComparisonPointer &comparison) -> std::experimental::optional<ast::Term>
|
||||
{
|
||||
if (comparison->operator_ != ast::Comparison::Operator::Equal)
|
||||
return std::experimental::nullopt;
|
||||
|
||||
if (matchesVariable(comparison->left, variable))
|
||||
return std::move(comparison->right);
|
||||
|
||||
if (matchesVariable(comparison->right, variable))
|
||||
return std::move(comparison->left);
|
||||
|
||||
return std::experimental::nullopt;
|
||||
};
|
||||
|
||||
const auto handleDefault =
|
||||
[](auto &) -> std::experimental::optional<ast::Term>
|
||||
{
|
||||
return std::experimental::nullopt;
|
||||
};
|
||||
|
||||
return formula.match(handleComparison, handleDefault);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
ast::Formula simplify(ast::ExistsPointer &exists)
|
||||
{
|
||||
if (!exists->argument.is<ast::AndPointer>())
|
||||
return std::move(exists);
|
||||
|
||||
auto &conjunction = exists->argument.get_unchecked<ast::AndPointer>();
|
||||
auto &arguments = conjunction->arguments;
|
||||
|
||||
// Check that formula is in normal form
|
||||
if (!arguments.back().is<ast::PredicatePointer>())
|
||||
return std::move(exists);
|
||||
|
||||
const auto replaceVariableInPredicateWithTerm =
|
||||
[](ast::PredicatePointer &predicate, const ast::VariablePointer &variable, ast::Term &&term)
|
||||
{
|
||||
for (auto &argument : predicate->arguments)
|
||||
{
|
||||
if (!matchesVariable(argument, variable))
|
||||
continue;
|
||||
|
||||
argument = std::move(term);
|
||||
break;
|
||||
}
|
||||
};
|
||||
|
||||
// Simplify formulas of type “exists X (X = t and F(Y))” to “F(t)”
|
||||
for (auto i = exists->variables.begin(); i != exists->variables.end();)
|
||||
{
|
||||
auto &variable = *i;
|
||||
|
||||
bool wasVariableReplaced = false;
|
||||
|
||||
for (auto j = arguments.begin(); j != arguments.end(); j++)
|
||||
{
|
||||
auto &argument = *j;
|
||||
auto assignedTerm = extractAssignedTerm(argument, variable);
|
||||
|
||||
if (!assignedTerm)
|
||||
continue;
|
||||
|
||||
auto &lastArgument = arguments.back().get_unchecked<ast::PredicatePointer>();
|
||||
|
||||
// If this argument is an assignment of the variable to some other term, remove the assignment and replace the variable with the other term
|
||||
replaceVariableInPredicateWithTerm(lastArgument, variable, std::move(assignedTerm.value()));
|
||||
|
||||
arguments.erase(j);
|
||||
wasVariableReplaced = true;
|
||||
break;
|
||||
}
|
||||
|
||||
if (wasVariableReplaced)
|
||||
{
|
||||
i = exists->variables.erase(i);
|
||||
continue;
|
||||
}
|
||||
|
||||
i++;
|
||||
}
|
||||
|
||||
if (exists->variables.empty())
|
||||
{
|
||||
assert(!conjunction->arguments.empty());
|
||||
|
||||
if (conjunction->arguments.size() == 1)
|
||||
return std::move(conjunction->arguments.front());
|
||||
|
||||
return std::move(exists->argument);
|
||||
}
|
||||
|
||||
return std::move(exists);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
ast::Formula simplify(ast::Formula &&formula)
|
||||
{
|
||||
const auto handleAnd =
|
||||
[&](ast::AndPointer &and_) -> ast::Formula
|
||||
{
|
||||
for (auto &argument : and_->arguments)
|
||||
argument = simplifyFormula(std::move(argument));
|
||||
argument = simplify(std::move(argument));
|
||||
|
||||
return std::move(and_);
|
||||
};
|
||||
|
||||
const auto simplifyBiconditional =
|
||||
const auto handleBiconditional =
|
||||
[&](ast::BiconditionalPointer &biconditional) -> ast::Formula
|
||||
{
|
||||
biconditional->left = simplifyFormula(std::move(biconditional->left));
|
||||
biconditional->right = simplifyFormula(std::move(biconditional->right));
|
||||
biconditional->left = simplify(std::move(biconditional->left));
|
||||
biconditional->right = simplify(std::move(biconditional->right));
|
||||
|
||||
return std::move(biconditional);
|
||||
};
|
||||
|
||||
const auto simplifyExists =
|
||||
const auto handleExists =
|
||||
[&](ast::ExistsPointer &exists) -> ast::Formula
|
||||
{
|
||||
exists->argument = simplifyFormula(std::move(exists->argument));
|
||||
exists->argument = simplify(std::move(exists->argument));
|
||||
|
||||
return std::move(exists);
|
||||
return simplify(exists);
|
||||
};
|
||||
|
||||
const auto simplifyForAll =
|
||||
const auto handleForAll =
|
||||
[&](ast::ForAllPointer &forAll) -> ast::Formula
|
||||
{
|
||||
forAll->argument = simplifyFormula(std::move(forAll->argument));
|
||||
forAll->argument = simplify(std::move(forAll->argument));
|
||||
|
||||
return std::move(forAll);
|
||||
};
|
||||
|
||||
const auto simplifyImplies =
|
||||
const auto handleImplies =
|
||||
[&](ast::ImpliesPointer &implies) -> ast::Formula
|
||||
{
|
||||
implies->antecedent = simplifyFormula(std::move(implies->antecedent));
|
||||
implies->consequent = simplifyFormula(std::move(implies->consequent));
|
||||
implies->antecedent = simplify(std::move(implies->antecedent));
|
||||
implies->consequent = simplify(std::move(implies->consequent));
|
||||
|
||||
return std::move(implies);
|
||||
};
|
||||
|
||||
const auto simplifyIn =
|
||||
const auto handleIn =
|
||||
[](ast::InPointer &in) -> ast::Formula
|
||||
{
|
||||
if (!isPrimitiveTerm(in->element) || !isPrimitiveTerm(in->set))
|
||||
@ -89,37 +212,30 @@ ast::Formula simplifyFormula(ast::Formula &&formula)
|
||||
return std::make_unique<ast::Comparison>(ast::Comparison::Operator::Equal, std::move(in->element), std::move(in->set));
|
||||
};
|
||||
|
||||
const auto simplifyNot =
|
||||
const auto handleNot =
|
||||
[&](ast::NotPointer ¬_) -> ast::Formula
|
||||
{
|
||||
not_->argument = simplifyFormula(std::move(not_->argument));
|
||||
not_->argument = simplify(std::move(not_->argument));
|
||||
|
||||
return std::move(not_);
|
||||
};
|
||||
|
||||
const auto simplifyOr =
|
||||
const auto handleOr =
|
||||
[&](ast::OrPointer &or_) -> ast::Formula
|
||||
{
|
||||
for (auto &argument : or_->arguments)
|
||||
argument = simplifyFormula(std::move(argument));
|
||||
argument = simplify(std::move(argument));
|
||||
|
||||
return std::move(or_);
|
||||
};
|
||||
|
||||
const auto defaultDoNothing =
|
||||
const auto handleDefault =
|
||||
[&](auto &x) -> ast::Formula
|
||||
{
|
||||
return std::move(x);
|
||||
};
|
||||
|
||||
return formula.match(simplifyAnd, simplifyBiconditional, simplifyExists, simplifyForAll, simplifyImplies, simplifyIn, simplifyNot, simplifyOr, defaultDoNothing);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
ast::Formula simplify(ast::Formula &&formula)
|
||||
{
|
||||
return simplifyFormula(std::move(formula));
|
||||
return formula.match(handleAnd, handleBiconditional, handleExists, handleForAll, handleImplies, handleIn, handleNot, handleOr, handleDefault);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
Loading…
Reference in New Issue
Block a user