/// <summary>
/// Combines a list of unifiers for the term product
/// </summary>
private UnificationResult ComposeUnifiers(IEnumerable <UnificationResult> unifierList)
{
if (unifierList.Count() == 1)
{
return(unifierList.First());
}
UnificationResult retVal = new UnificationResult();
var composedUnifier = new Dictionary <TrsVariable, TrsTermBase>();
foreach (var unifier in unifierList)
{
foreach (var substitution in unifier.Unifier)
{
TrsTermBase subValue = null;
if (!composedUnifier.TryGetValue(substitution.Variable, out subValue))
{
composedUnifier.Add(substitution.Variable, substitution.SubstitutionTerm);
}
else if (!subValue.Equals(substitution.SubstitutionTerm))
{
// Conflicting mapping found.
retVal.Succeed = false;
return(retVal);
}
}
}
retVal.Succeed = true;
retVal.Unifier = new List <Substitution>();
retVal.Unifier.AddRange(composedUnifier.Select(pair => new Substitution
{
Variable = pair.Key,
SubstitutionTerm = pair.Value
}));
return(retVal);
}
public InterpreterEvaluationTerm(TrsTermBase root, TrsTermBase subterm, InterpreterTerm cacheSourceTerm,
UnificationResult currentUnifier)
: base(root)
{
if (subterm == null) throw new ArgumentException("subterm");
if (cacheSourceTerm == null) throw new ArgumentException("cacheSourceTerm");
if (currentUnifier == null) throw new ArgumentException("currentUnifier");
CurrentSubTerm = subterm;
CacheSourceTerm = cacheSourceTerm;
Unifier = currentUnifier;
}
public override bool Equals(object obj)
{
UnificationResult otherUnifier = obj as UnificationResult;
if (otherUnifier == null)
{
return(false);
}
var substitutionSetOther = new HashSet <Substitution>(otherUnifier.Unifier);
var subtitutionSetThis = new HashSet <Substitution>(Unifier);
substitutionSetOther.IntersectWith(subtitutionSetThis);
return(Succeed == otherUnifier.Succeed &&
substitutionSetOther.Count == subtitutionSetThis.Count);
}
public InterpreterEvaluationTerm(TrsTermBase root, TrsTermBase subterm, InterpreterTerm cacheSourceTerm,
UnificationResult currentUnifier)
: base(root)
{
if (subterm == null)
{
throw new ArgumentException("subterm");
}
if (cacheSourceTerm == null)
{
throw new ArgumentException("cacheSourceTerm");
}
if (currentUnifier == null)
{
throw new ArgumentException("currentUnifier");
}
CurrentSubTerm = subterm;
CacheSourceTerm = cacheSourceTerm;
Unifier = currentUnifier;
}
/// <summary>
/// Checks that the given unifier is valid in terms of the type definitions.
/// </summary>
private bool IsUnifierValid(UnificationResult unifier, TrsTermBase matchedRuleHead)
{
// Variables at this level must be validated in a way that is sensitive to AC term type definitions
// to account for semantics. If it is not add[:x,:y] will not match add[1,2,3] with limit :x,:y to $TrsNumber
if (!unifier.Succeed)
{
return(false);
}
if (unifier.Unifier.Count == 0)
{
return(true); // equal terms, nothing to validate
}
// Keep track of variable parent cases
Stack <TrsTermBase> evalStack = new Stack <TrsTermBase>();
Dictionary <TrsVariable, bool> isAcParent = new Dictionary <TrsVariable, bool>();
Dictionary <TrsVariable, bool> isNonAcParent = new Dictionary <TrsVariable, bool>();
Dictionary <TrsVariable, HashSet <string> > variableTermNames = new Dictionary <TrsVariable, HashSet <string> >();
evalStack.Push(matchedRuleHead);
Action <TrsVariable, bool, Dictionary <TrsVariable, bool> > updateLookups =
delegate(TrsVariable v, bool b, Dictionary <TrsVariable, bool> target)
{
if (target.ContainsKey(v))
{
target[v] = b;
}
else
{
target.Add(v, b);
}
};
while (evalStack.Count > 0)
{
var current = evalStack.Pop();
// Variable only case ... this should not happen unless variable only reduction rule heads are allowed in the future
var currentVariable = current as TrsVariable;
if (currentVariable != null)
{
updateLookups(currentVariable, false, isAcParent);
updateLookups(currentVariable, false, isNonAcParent);
}
else
{
// Check arguments
var curTerm = current as TrsTerm;
var curAcTerm = current as TrsAcTerm;
foreach (var variable in Enumerable.Concat(curTerm == null ? new TrsVariable[0] : curTerm.Arguments.Where(arg => arg is TrsVariable).Cast <TrsVariable>(),
curAcTerm == null ? new TrsVariable[0] : curAcTerm.OnfArguments.Where(arg => arg.Term is TrsVariable).Select(arg => arg.Term).Cast <TrsVariable>()))
{
updateLookups(variable, curTerm != null, isNonAcParent);
updateLookups(variable, curAcTerm != null, isAcParent);
if (curAcTerm != null)
{
HashSet <string> termNames;
if (!variableTermNames.TryGetValue(variable, out termNames))
{
variableTermNames.Add(variable, termNames = new HashSet <string>());
}
termNames.Add(curAcTerm.Name);
}
}
}
}
bool isValid = true;
foreach (var substitution in unifier.Unifier)
{
// It is possible that the variable being tested does not occur in the term head ...
if (!isNonAcParent.ContainsKey(substitution.Variable) &&
!isAcParent.ContainsKey(substitution.Variable))
{
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
continue;
}
// AC term case
if (isNonAcParent.ContainsKey(substitution.Variable) &&
isNonAcParent[substitution.Variable])
{
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
}
// Non-AC term case
if (isAcParent.ContainsKey(substitution.Variable) &&
isAcParent[substitution.Variable])
{
var acSubstitutionTerm = substitution.SubstitutionTerm as TrsAcTerm;
if (acSubstitutionTerm == null ||
!variableTermNames[substitution.Variable].Contains(acSubstitutionTerm.Name))
{
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
}
else
{
// In this case, test each nested argument of the AC substitution term to match the term head variable.
// This is due to the ONF convertion for AC terms. It keeps type checking in line with AC semantics.
foreach (var argTerm in acSubstitutionTerm.OnfArguments.Select(arg => arg.Term))
{
var testSubstitution = new Substitution {
Variable = substitution.Variable, SubstitutionTerm = argTerm
};
isValid = isValid && typeChecker.IsSubstitutionValid(testSubstitution);
}
}
}
}
return(isValid);
}
private void ApplyReductionRuleToCache(TrsReductionRule rule)
{
// This data structure stores the Cartesian product used for term products
// The length of each sub-List is the size of an alphabet for calculating a "Godel string" of terms.
// This avoids the need for seperate sub-enumerators.
var rewriteCandidates = new List <List <InterpreterEvaluationTerm> >();
// Populate the rewriteCandidates
TrsTermProduct ruleHead = (TrsTermProduct)rule.Head;
int productLength = ruleHead.TermList.Count;
for (int termProductIndex = 0; termProductIndex < productLength; termProductIndex++)
{
rewriteCandidates.Add(new List <InterpreterEvaluationTerm>());
foreach (var termInCache in executionCache)
{
// Do not rewrite new terms, we are doing one rewrite step at a time
if (termInCache.IsNewTerm)
{
continue;
}
// Test all sub-terms
var expantionStack = new Stack <TrsTermBase>();
expantionStack.Push(termInCache.RootTerm);
while (expantionStack.Count > 0)
{
var current = expantionStack.Pop();
// Ignore the "variable only" case to avoid matching all rewrite rules to a sub-term.
if (current is TrsVariable)
{
continue;
}
// Type rules applied here ... cater for multiple unification results by duplicating candidates
foreach (var unifier in mguCalculation.GetUnifier(ruleHead.TermList[termProductIndex], current))
{
if (IsUnifierValid(unifier, ruleHead.TermList[termProductIndex]))
{
rewriteCandidates[termProductIndex].Add(new InterpreterEvaluationTerm(termInCache.RootTerm, current, termInCache, unifier));
}
}
// Apply rewrite rule to subterms
if (current is TrsTerm)
{
foreach (var subTerm in ((TrsTerm)current).Arguments)
{
expantionStack.Push(subTerm);
}
}
else if (current is TrsAcTerm)
{
foreach (var subTerm in ((TrsAcTerm)current).OnfArguments)
{
expantionStack.Push(subTerm.Term);
}
}
}
}
}
// Execute rewite step ... iterate over cartesian term product
// This iterationCount variable will prevent rewriting in the case where any of the lists are empty
int iterationCount = rewriteCandidates.First().Count;
foreach (var termList in rewriteCandidates.Skip(1))
{
iterationCount *= termList.Count;
}
var matchTupple = new List <InterpreterEvaluationTerm>(rewriteCandidates.Count);
for (int tuppleNumber = 0; tuppleNumber < iterationCount; tuppleNumber++)
{
var currDiv = tuppleNumber;
UnificationResult currentUnifier = null;
UnificationResult testUnifier = null;
matchTupple.Clear();
// In order to do a substitution, all variables must bind to the same values across the tupple members
for (int termColumn = 0; termColumn < rewriteCandidates.Count; termColumn++)
{
var currMod = currDiv % rewriteCandidates[termColumn].Count;
currDiv = currDiv / rewriteCandidates[termColumn].Count;
var targetTerm = rewriteCandidates[termColumn][currMod];
currentUnifier = targetTerm.Unifier;
if (testUnifier == null)
{
testUnifier = currentUnifier;
}
matchTupple.Add(targetTerm);
}
var termProductUnifier = ComposeUnifiers(matchTupple.Select(term => term.Unifier));
if (termProductUnifier.Succeed)
{
foreach (var term in matchTupple)
{
ExecuteRewriteForRule(term, rule, termProductUnifier);
}
}
}
}
private void ExecuteRewriteForRule(InterpreterEvaluationTerm termToRewrite, TrsReductionRule rule, UnificationResult composedUnifier)
{
bool rewritingTookPlaceLocal = false;
if (composedUnifier.Succeed)
{
if (rule.Tail.GetType() == typeof(TrsNativeKeyword))
{
// Replacing term value with a native function generated value
var nativeTermInHead = ((TrsTermBase)termToRewrite.CurrentSubTerm.CreateCopy()).ApplySubstitutions(composedUnifier.Unifier);
foreach (var native in nativeFunctions)
{
var processedTerm = native.Evaluate(nativeTermInHead);
if (processedTerm == null)
{
throw new Exception(string.Format("Native function in type {0} returned null", native.GetType().FullName));
}
// If the rewrite result is the same, no rewriting took place ...
if (!nativeTermInHead.Equals(processedTerm))
{
var newTerm = termToRewrite.RootTerm.CreateCopyAndReplaceSubTerm(termToRewrite.CurrentSubTerm, processedTerm);
rewritingTookPlaceLocal = true;
var newTermWrapper = new InterpreterTerm(newTerm);
newTermWrapper.IsNewTerm = true;
executionCache.Add(newTermWrapper);
}
}
}
else
{
// Normal rewriting without native eval functions
var replacementTerm = ((TrsTermBase)rule.Tail.CreateCopy()).ApplySubstitutions(composedUnifier.Unifier);
if (!termToRewrite.CurrentSubTerm.Equals(replacementTerm))
{
var newTerm = termToRewrite.RootTerm.CreateCopyAndReplaceSubTerm(termToRewrite.CurrentSubTerm, replacementTerm);
rewritingTookPlaceLocal = true;
var newTermWrapper = new InterpreterTerm(newTerm);
newTermWrapper.IsNewTerm = true;
executionCache.Add(newTermWrapper);
}
}
}
if (rewritingTookPlaceLocal)
{
rewritingTookPlace = true; // stops rewriting on next rewrite step
termToRewrite.CacheSourceTerm.MustDeletFromCache = true;
}
}
/// <summary>
/// Checks that the given unifier is valid in terms of the type definitions.
/// </summary>
private bool IsUnifierValid(UnificationResult unifier, TrsTermBase matchedRuleHead)
{
// Variables at this level must be validated in a way that is sensitive to AC term type definitions
// to account for semantics. If it is not add[:x,:y] will not match add[1,2,3] with limit :x,:y to $TrsNumber
if (!unifier.Succeed) return false;
if (unifier.Unifier.Count == 0) return true; // equal terms, nothing to validate
// Keep track of variable parent cases
Stack<TrsTermBase> evalStack = new Stack<TrsTermBase>();
Dictionary<TrsVariable, bool> isAcParent = new Dictionary<TrsVariable, bool>();
Dictionary<TrsVariable, bool> isNonAcParent = new Dictionary<TrsVariable, bool>();
Dictionary<TrsVariable, HashSet<string>> variableTermNames = new Dictionary<TrsVariable, HashSet<string>>();
evalStack.Push(matchedRuleHead);
Action<TrsVariable, bool, Dictionary<TrsVariable, bool>> updateLookups =
delegate(TrsVariable v, bool b, Dictionary<TrsVariable, bool> target)
{
if (target.ContainsKey(v)) target[v] = b;
else target.Add(v, b);
};
while (evalStack.Count > 0)
{
var current = evalStack.Pop();
// Variable only case ... this should not happen unless variable only reduction rule heads are allowed in the future
var currentVariable = current as TrsVariable;
if (currentVariable != null)
{
updateLookups(currentVariable, false, isAcParent);
updateLookups(currentVariable, false, isNonAcParent);
}
else
{
// Check arguments
var curTerm = current as TrsTerm;
var curAcTerm = current as TrsAcTerm;
foreach (var variable in Enumerable.Concat(curTerm == null ? new TrsVariable[0] : curTerm.Arguments.Where(arg => arg is TrsVariable).Cast<TrsVariable>(),
curAcTerm == null ? new TrsVariable[0] : curAcTerm.OnfArguments.Where(arg => arg.Term is TrsVariable).Select(arg => arg.Term).Cast<TrsVariable>()))
{
updateLookups(variable, curTerm != null, isNonAcParent);
updateLookups(variable, curAcTerm != null, isAcParent);
if (curAcTerm != null)
{
HashSet<string> termNames;
if (!variableTermNames.TryGetValue(variable, out termNames))
variableTermNames.Add(variable, termNames = new HashSet<string>());
termNames.Add(curAcTerm.Name);
}
}
}
}
bool isValid = true;
foreach (var substitution in unifier.Unifier)
{
// It is possible that the variable being tested does not occur in the term head ...
if (!isNonAcParent.ContainsKey(substitution.Variable)
&& !isAcParent.ContainsKey(substitution.Variable))
{
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
continue;
}
// AC term case
if (isNonAcParent.ContainsKey(substitution.Variable) &&
isNonAcParent[substitution.Variable])
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
// Non-AC term case
if (isAcParent.ContainsKey(substitution.Variable)
&& isAcParent[substitution.Variable])
{
var acSubstitutionTerm = substitution.SubstitutionTerm as TrsAcTerm;
if (acSubstitutionTerm == null
|| !variableTermNames[substitution.Variable].Contains(acSubstitutionTerm.Name))
{
isValid = isValid && typeChecker.IsSubstitutionValid(substitution);
}
else
{
// In this case, test each nested argument of the AC substitution term to match the term head variable.
// This is due to the ONF convertion for AC terms. It keeps type checking in line with AC semantics.
foreach (var argTerm in acSubstitutionTerm.OnfArguments.Select(arg => arg.Term))
{
var testSubstitution = new Substitution { Variable = substitution.Variable, SubstitutionTerm = argTerm };
isValid = isValid && typeChecker.IsSubstitutionValid(testSubstitution);
}
}
}
}
return isValid;
}
private void ExecuteRewriteForRule(InterpreterEvaluationTerm termToRewrite, TrsReductionRule rule, UnificationResult composedUnifier)
{
bool rewritingTookPlaceLocal = false;
if (composedUnifier.Succeed)
{
if (rule.Tail.GetType() == typeof(TrsNativeKeyword))
{
// Replacing term value with a native function generated value
var nativeTermInHead = ((TrsTermBase)termToRewrite.CurrentSubTerm.CreateCopy()).ApplySubstitutions(composedUnifier.Unifier);
foreach (var native in nativeFunctions)
{
var processedTerm = native.Evaluate(nativeTermInHead);
if (processedTerm == null) throw new Exception(string.Format("Native function in type {0} returned null", native.GetType().FullName));
// If the rewrite result is the same, no rewriting took place ...
if (!nativeTermInHead.Equals(processedTerm))
{
var newTerm = termToRewrite.RootTerm.CreateCopyAndReplaceSubTerm(termToRewrite.CurrentSubTerm, processedTerm);
rewritingTookPlaceLocal = true;
var newTermWrapper = new InterpreterTerm(newTerm);
newTermWrapper.IsNewTerm = true;
executionCache.Add(newTermWrapper);
}
}
}
else
{
// Normal rewriting without native eval functions
var replacementTerm = ((TrsTermBase)rule.Tail.CreateCopy()).ApplySubstitutions(composedUnifier.Unifier);
if (!termToRewrite.CurrentSubTerm.Equals(replacementTerm))
{
var newTerm = termToRewrite.RootTerm.CreateCopyAndReplaceSubTerm(termToRewrite.CurrentSubTerm, replacementTerm);
rewritingTookPlaceLocal = true;
var newTermWrapper = new InterpreterTerm(newTerm);
newTermWrapper.IsNewTerm = true;
executionCache.Add(newTermWrapper);
}
}
}
if (rewritingTookPlaceLocal)
{
rewritingTookPlace = true; // stops rewriting on next rewrite step
termToRewrite.CacheSourceTerm.MustDeletFromCache = true;
}
}
/// <summary>
/// Combines a list of unifiers for the term product
/// </summary>
private UnificationResult ComposeUnifiers(IEnumerable<UnificationResult> unifierList)
{
if (unifierList.Count() == 1) return unifierList.First();
UnificationResult retVal = new UnificationResult();
var composedUnifier = new Dictionary<TrsVariable, TrsTermBase>();
foreach (var unifier in unifierList)
{
foreach (var substitution in unifier.Unifier)
{
TrsTermBase subValue = null;
if (!composedUnifier.TryGetValue(substitution.Variable, out subValue))
{
composedUnifier.Add(substitution.Variable, substitution.SubstitutionTerm);
}
else if (!subValue.Equals(substitution.SubstitutionTerm))
{
// Conflicting mapping found.
retVal.Succeed = false;
return retVal;
}
}
}
retVal.Succeed = true;
retVal.Unifier = new List<Substitution>();
retVal.Unifier.AddRange(composedUnifier.Select(pair => new Substitution
{
Variable = pair.Key,
SubstitutionTerm = pair.Value
}));
return retVal;
}
/// <summary>
/// NB: this is not a general solution, only for c = b + x where + can be -, / or * and, b and x can be swapped arround.
/// c is the match term. The rest is the head term.
/// </summary>
public List<UnificationResult> GetUnifier(TrsTermBase termHead, TrsTermBase matchTerm)
{
UnificationResult result = new UnificationResult();
result.Succeed = false;
// Check input
Substitution sRhs = new Substitution
{
Variable = new TrsVariable("exp_r"),
SubstitutionTerm = termHead
};
Substitution sLhs = new Substitution
{
Variable = new TrsVariable("exp_l"),
SubstitutionTerm = matchTerm
};
var headTerm = termHead as TrsTerm;
if (!interpreter.TypeChecker.IsSubstitutionValid(sLhs) ||
!interpreter.TypeChecker.IsSubstitutionValid(sRhs))
{
return new List<UnificationResult> { result };
}
// Load problem
interpreter.ClearExecutionCache();
interpreter.LoadTerms(new []
{
new TrsTerm("rhs",new [] { termHead }),
new TrsTerm("lhs",new [] { matchTerm })
});
// Solve
while (interpreter.ExecuteRewriteStep()) { };
// Extract answer
var runResults = interpreter.GetCurrentRewriteResult();
foreach (var stm in runResults.ProgramOut.Statements)
{
var resEq = stm as TrsTerm;
if (resEq != null
&& resEq.Name == "eq"
&& resEq.Arguments.Count == 2
&& resEq.Arguments[0] is TrsNumber
&& resEq.Arguments[1] is TrsVariable)
{
result.Succeed = true;
result.Unifier = new List<Substitution>();
result.Unifier.Add(new Substitution()
{
Variable = resEq.Arguments[1] as TrsVariable,
SubstitutionTerm = resEq.Arguments[0]
});
}
}
return new List<UnificationResult> { result };
}
