anthem/src/anthem/IntegerVariableDetection.cpp

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#include <anthem/IntegerVariableDetection.h>
#include <anthem/ASTCopy.h>
#include <anthem/ASTUtils.h>
#include <anthem/ASTVisitors.h>
#include <anthem/Exception.h>
#include <anthem/Simplification.h>
#include <anthem/output/AST.h>
namespace anthem
{
////////////////////////////////////////////////////////////////////////////////////////////////////
//
// IntegerVariableDetection
//
////////////////////////////////////////////////////////////////////////////////////////////////////
using VariableDomainMap = std::map<const ast::VariableDeclaration *, ast::Domain>;
////////////////////////////////////////////////////////////////////////////////////////////////////
ast::Domain domain(const ast::Variable &variable, VariableDomainMap &variableDomainMap)
{
if (variable.declaration->domain != ast::Domain::Unknown)
return variable.declaration->domain;
const auto match = variableDomainMap.find(variable.declaration);
if (match == variableDomainMap.end())
return ast::Domain::Unknown;
return match->second;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
void clearVariableDomainMap(VariableDomainMap &variableDomainMap)
{
for (auto &variableDeclaration : variableDomainMap)
variableDeclaration.second = ast::Domain::Unknown;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
enum class OperationResult
{
Unchanged,
Changed,
};
////////////////////////////////////////////////////////////////////////////////////////////////////
enum class EvaluationResult
{
True,
False,
Unknown,
Error,
};
////////////////////////////////////////////////////////////////////////////////////////////////////
EvaluationResult isArithmetic(const ast::Term &term, VariableDomainMap &variableDomainMap);
////////////////////////////////////////////////////////////////////////////////////////////////////
struct IsTermArithmeticVisitor
{
static EvaluationResult visit(const ast::BinaryOperation &binaryOperation, VariableDomainMap &variableDomainMap)
{
const auto isLeftArithemtic = isArithmetic(binaryOperation.left, variableDomainMap);
const auto isRightArithmetic = isArithmetic(binaryOperation.right, variableDomainMap);
if (isLeftArithemtic == EvaluationResult::Error || isRightArithmetic == EvaluationResult::Error)
return EvaluationResult::Error;
if (isLeftArithemtic == EvaluationResult::False || isRightArithmetic == EvaluationResult::False)
return EvaluationResult::Error;
if (isLeftArithemtic == EvaluationResult::Unknown || isRightArithmetic == EvaluationResult::Unknown)
return EvaluationResult::Unknown;
return EvaluationResult::True;
}
static EvaluationResult visit(const ast::Boolean &, VariableDomainMap &)
{
return EvaluationResult::False;
}
static EvaluationResult visit(const ast::Function &function, VariableDomainMap &)
{
switch (function.declaration->domain)
{
case ast::Domain::General:
return EvaluationResult::False;
case ast::Domain::Integer:
return EvaluationResult::True;
case ast::Domain::Unknown:
return EvaluationResult::Unknown;
}
return EvaluationResult::Unknown;
}
static EvaluationResult visit(const ast::Integer &, VariableDomainMap &)
{
return EvaluationResult::True;
}
static EvaluationResult visit(const ast::Interval &interval, VariableDomainMap &variableDomainMap)
{
const auto isFromArithmetic = isArithmetic(interval.from, variableDomainMap);
const auto isToArithmetic = isArithmetic(interval.to, variableDomainMap);
if (isFromArithmetic == EvaluationResult::Error || isToArithmetic == EvaluationResult::Error)
return EvaluationResult::Error;
if (isFromArithmetic == EvaluationResult::False || isToArithmetic == EvaluationResult::False)
return EvaluationResult::Error;
if (isFromArithmetic == EvaluationResult::Unknown || isToArithmetic == EvaluationResult::Unknown)
return EvaluationResult::Unknown;
return EvaluationResult::True;
}
static EvaluationResult visit(const ast::SpecialInteger &, VariableDomainMap &)
{
return EvaluationResult::False;
}
static EvaluationResult visit(const ast::String &, VariableDomainMap &)
{
return EvaluationResult::False;
}
static EvaluationResult visit(const ast::UnaryOperation &unaryOperation, VariableDomainMap &variableDomainMap)
{
const auto isArgumentArithmetic = isArithmetic(unaryOperation.argument, variableDomainMap);
switch (unaryOperation.operator_)
{
case ast::UnaryOperation::Operator::Absolute:
return (isArgumentArithmetic == EvaluationResult::False ? EvaluationResult::Error : isArgumentArithmetic);
}
return EvaluationResult::Unknown;
}
static EvaluationResult visit(const ast::Variable &variable, VariableDomainMap &variableDomainMap)
{
switch (domain(variable, variableDomainMap))
{
case ast::Domain::General:
return EvaluationResult::False;
case ast::Domain::Integer:
return EvaluationResult::True;
case ast::Domain::Unknown:
return EvaluationResult::Unknown;
}
return EvaluationResult::Unknown;
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
EvaluationResult isArithmetic(const ast::Term &term, VariableDomainMap &variableDomainMap)
{
return term.accept(IsTermArithmeticVisitor(), variableDomainMap);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
EvaluationResult evaluate(const ast::Formula &formula, VariableDomainMap &variableDomainMap);
////////////////////////////////////////////////////////////////////////////////////////////////////
struct EvaluateFormulaVisitor
{
static EvaluationResult visit(const ast::And &and_, VariableDomainMap &variableDomainMap)
{
bool someFalse = false;
bool someUnknown = false;
for (const auto &argument : and_.arguments)
{
const auto result = evaluate(argument, variableDomainMap);
switch (result)
{
case EvaluationResult::Error:
return EvaluationResult::Error;
case EvaluationResult::True:
break;
case EvaluationResult::False:
someFalse = true;
break;
case EvaluationResult::Unknown:
someUnknown = true;
break;
}
}
if (someFalse)
return EvaluationResult::False;
if (someUnknown)
return EvaluationResult::Unknown;
return EvaluationResult::True;
}
static EvaluationResult visit(const ast::Biconditional &biconditional, VariableDomainMap &variableDomainMap)
{
const auto leftResult = evaluate(biconditional.left, variableDomainMap);
const auto rightResult = evaluate(biconditional.right, variableDomainMap);
if (leftResult == EvaluationResult::Error || rightResult == EvaluationResult::Error)
return EvaluationResult::Error;
if (leftResult == EvaluationResult::Unknown || rightResult == EvaluationResult::Unknown)
return EvaluationResult::Unknown;
return (leftResult == rightResult ? EvaluationResult::True : EvaluationResult::False);
}
static EvaluationResult visit(const ast::Boolean &boolean, VariableDomainMap &)
{
return (boolean.value == true ? EvaluationResult::True : EvaluationResult::False);
}
static EvaluationResult visit(const ast::Comparison &comparison, VariableDomainMap &variableDomainMap)
{
const auto isLeftArithmetic = isArithmetic(comparison.left, variableDomainMap);
const auto isRightArithmetic = isArithmetic(comparison.right, variableDomainMap);
if (isLeftArithmetic == EvaluationResult::Error || isRightArithmetic == EvaluationResult::Error)
return EvaluationResult::Error;
if (isLeftArithmetic == EvaluationResult::Unknown || isRightArithmetic == EvaluationResult::Unknown)
return EvaluationResult::Unknown;
if (isLeftArithmetic == isRightArithmetic)
return EvaluationResult::Unknown;
// Handle the case where one side is arithmetic but the other one isnt
switch (comparison.operator_)
{
case ast::Comparison::Operator::Equal:
return EvaluationResult::False;
case ast::Comparison::Operator::NotEqual:
return EvaluationResult::True;
default:
// TODO: implement more cases
return EvaluationResult::Unknown;
}
}
static EvaluationResult visit(const ast::Exists &exists, VariableDomainMap &variableDomainMap)
{
return evaluate(exists.argument, variableDomainMap);
}
static EvaluationResult visit(const ast::ForAll &forAll, VariableDomainMap &variableDomainMap)
{
return evaluate(forAll.argument, variableDomainMap);
}
static EvaluationResult visit(const ast::Implies &implies, VariableDomainMap &variableDomainMap)
{
const auto antecedentResult = evaluate(implies.antecedent, variableDomainMap);
const auto consequentResult = evaluate(implies.consequent, variableDomainMap);
if (antecedentResult == EvaluationResult::Error || consequentResult == EvaluationResult::Error)
return EvaluationResult::Error;
if (antecedentResult == EvaluationResult::False)
return EvaluationResult::True;
if (consequentResult == EvaluationResult::True)
return EvaluationResult::True;
if (antecedentResult == EvaluationResult::True && consequentResult == EvaluationResult::False)
return EvaluationResult::False;
return EvaluationResult::Unknown;
}
static EvaluationResult visit(const ast::In &in, VariableDomainMap &variableDomainMap)
{
const auto isElementArithmetic = isArithmetic(in.element, variableDomainMap);
const auto isSetArithmetic = isArithmetic(in.set, variableDomainMap);
if (isElementArithmetic == EvaluationResult::Error || isSetArithmetic == EvaluationResult::Error)
return EvaluationResult::Error;
if (isElementArithmetic == EvaluationResult::Unknown || isSetArithmetic == EvaluationResult::Unknown)
return EvaluationResult::Unknown;
if (isElementArithmetic == isSetArithmetic)
return EvaluationResult::Unknown;
// If one side is arithmetic, but the other one isnt, set inclusion is never satisfied
return EvaluationResult::False;
}
static EvaluationResult visit(const ast::Not &not_, VariableDomainMap &variableDomainMap)
{
const auto result = evaluate(not_.argument, variableDomainMap);
if (result == EvaluationResult::Error || result == EvaluationResult::Unknown)
return result;
return (result == EvaluationResult::True ? EvaluationResult::False : EvaluationResult::True);
}
static EvaluationResult visit(const ast::Or &or_, VariableDomainMap &variableDomainMap)
{
bool someTrue = false;
bool someUnknown = false;
for (const auto &argument : or_.arguments)
{
const auto result = evaluate(argument, variableDomainMap);
switch (result)
{
case EvaluationResult::Error:
return EvaluationResult::Error;
case EvaluationResult::True:
someTrue = true;
break;
case EvaluationResult::False:
break;
case EvaluationResult::Unknown:
someUnknown = true;
break;
}
}
if (someTrue)
return EvaluationResult::True;
if (someUnknown)
return EvaluationResult::Unknown;
return EvaluationResult::False;
}
static EvaluationResult visit(const ast::Predicate &predicate, VariableDomainMap &variableDomainMap)
{
assert(predicate.arguments.size() == predicate.declaration->arity());
for (size_t i = 0; i < predicate.arguments.size(); i++)
{
const auto &argument = predicate.arguments[i];
const auto &parameter = predicate.declaration->parameters[i];
if (parameter.domain != ast::Domain::Integer)
continue;
const auto isArgumentArithmetic = isArithmetic(argument, variableDomainMap);
if (isArgumentArithmetic == EvaluationResult::Error || isArgumentArithmetic == EvaluationResult::False)
return isArgumentArithmetic;
}
return EvaluationResult::Unknown;
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
EvaluationResult evaluate(const ast::Formula &formula, VariableDomainMap &variableDomainMap)
{
return formula.accept(EvaluateFormulaVisitor(), variableDomainMap);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
OperationResult detectIntegerVariables(ast::Formula &formula, ast::Formula &definition, VariableDomainMap &variableDomainMap);
////////////////////////////////////////////////////////////////////////////////////////////////////
struct DetectIntegerVariablesVisitor
{
static OperationResult visit(ast::And &and_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
for (auto &argument : and_.arguments)
if (detectIntegerVariables(argument, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
return operationResult;
}
static OperationResult visit(ast::Biconditional &biconditional, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
if (detectIntegerVariables(biconditional.left, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
if (detectIntegerVariables(biconditional.right, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
return operationResult;
}
static OperationResult visit(ast::Boolean &, ast::Formula &, VariableDomainMap &)
{
return OperationResult::Unchanged;
}
static OperationResult visit(ast::Comparison &, ast::Formula &, VariableDomainMap &)
{
return OperationResult::Unchanged;
}
static OperationResult visit(ast::Exists &exists, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
if (detectIntegerVariables(exists.argument, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
for (auto &variableDeclaration : exists.variables)
{
if (variableDeclaration->domain != ast::Domain::Unknown)
continue;
clearVariableDomainMap(variableDomainMap);
auto argumentResult = evaluate(exists.argument, variableDomainMap);
auto definitionResult = evaluate(definition, variableDomainMap);
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
{
continue;
}
// As a hypothesis, make the parameters domain noninteger
variableDomainMap[variableDeclaration.get()] = ast::Domain::General;
argumentResult = evaluate(exists.argument, variableDomainMap);
definitionResult = evaluate(definition, variableDomainMap);
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
{
// If making the variable noninteger leads to a false or erroneous result, its proven to be integer
operationResult = OperationResult::Changed;
variableDeclaration->domain = ast::Domain::Integer;
}
}
return operationResult;
}
static OperationResult visit(ast::ForAll &forAll, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
if (detectIntegerVariables(forAll.argument, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
for (auto &variableDeclaration : forAll.variables)
{
if (variableDeclaration->domain != ast::Domain::Unknown)
continue;
clearVariableDomainMap(variableDomainMap);
auto argumentResult = evaluate(forAll.argument, variableDomainMap);
auto definitionResult = evaluate(definition, variableDomainMap);
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
{
continue;
}
// As a hypothesis, make the parameters domain noninteger
variableDomainMap[variableDeclaration.get()] = ast::Domain::General;
argumentResult = evaluate(forAll.argument, variableDomainMap);
definitionResult = evaluate(definition, variableDomainMap);
if (argumentResult == EvaluationResult::Error || argumentResult == EvaluationResult::False
|| definitionResult == EvaluationResult::Error || definitionResult == EvaluationResult::False)
{
// If making the variable noninteger leads to a false or erroneous result, its proven to be integer
operationResult = OperationResult::Changed;
variableDeclaration->domain = ast::Domain::Integer;
}
}
return operationResult;
}
static OperationResult visit(ast::Implies &implies, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
if (detectIntegerVariables(implies.antecedent, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
if (detectIntegerVariables(implies.consequent, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
return operationResult;
}
static OperationResult visit(ast::In &, ast::Formula &, VariableDomainMap &)
{
return OperationResult::Unchanged;
}
static OperationResult visit(ast::Not &not_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
return detectIntegerVariables(not_.argument, definition, variableDomainMap);
}
static OperationResult visit(ast::Or &or_, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
auto operationResult = OperationResult::Unchanged;
for (auto &argument : or_.arguments)
if (detectIntegerVariables(argument, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
return operationResult;
}
static OperationResult visit(ast::Predicate &predicate, ast::Formula &, VariableDomainMap &)
{
auto operationResult = OperationResult::Unchanged;
assert(predicate.arguments.size() == predicate.declaration->arity());
// Propagate integer domains from predicates to variables
for (size_t i = 0; i < predicate.arguments.size(); i++)
{
auto &variableArgument = predicate.arguments[i];
auto &parameter = predicate.declaration->parameters[i];
if (parameter.domain != ast::Domain::Integer)
continue;
if (!variableArgument.is<ast::Variable>())
continue;
auto &variable = variableArgument.get<ast::Variable>();
if (variable.declaration->domain == ast::Domain::Integer)
continue;
operationResult = OperationResult::Changed;
variable.declaration->domain = ast::Domain::Integer;
}
return operationResult;
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
OperationResult detectIntegerVariables(ast::Formula &formula, ast::Formula &definition, VariableDomainMap &variableDomainMap)
{
return formula.accept(DetectIntegerVariablesVisitor(), definition, variableDomainMap);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
// Assumes the completed formulas to be in translated but not simplified form.
// That is, completed formulas are either variable-free or universally quantified
void detectIntegerVariables(std::vector<ast::Formula> &completedFormulas)
{
VariableDomainMap variableDomainMap;
auto operationResult = OperationResult::Changed;
while (operationResult == OperationResult::Changed)
{
operationResult = OperationResult::Unchanged;
for (auto &completedFormula : completedFormulas)
{
if (detectIntegerVariables(completedFormula, completedFormula, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
if (!completedFormula.is<ast::ForAll>())
continue;
auto &forAll = completedFormula.get<ast::ForAll>();
if (!forAll.argument.is<ast::Biconditional>())
continue;
auto &biconditional = forAll.argument.get<ast::Biconditional>();
if (!biconditional.left.is<ast::Predicate>())
continue;
auto &predicate = biconditional.left.get<ast::Predicate>();
auto &definition = biconditional.right;
assert(predicate.arguments.size() == predicate.declaration->arity());
if (detectIntegerVariables(definition, definition, variableDomainMap) == OperationResult::Changed)
operationResult = OperationResult::Changed;
for (size_t i = 0; i < predicate.arguments.size(); i++)
{
auto &variableArgument = predicate.arguments[i];
auto &parameter = predicate.declaration->parameters[i];
assert(variableArgument.is<ast::Variable>());
auto &variable = variableArgument.get<ast::Variable>();
if (parameter.domain != ast::Domain::Unknown)
continue;
clearVariableDomainMap(variableDomainMap);
auto result = evaluate(definition, variableDomainMap);
if (result == EvaluationResult::Error || result == EvaluationResult::False)
continue;
// As a hypothesis, make the parameters domain noninteger
variableDomainMap[variable.declaration] = ast::Domain::General;
result = evaluate(definition, variableDomainMap);
if (result == EvaluationResult::Error || result == EvaluationResult::False)
{
// If making the variable noninteger leads to a false or erroneous result, its proven to be integer
operationResult = OperationResult::Changed;
variable.declaration->domain = ast::Domain::Integer;
parameter.domain = ast::Domain::Integer;
}
}
}
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////
}