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Implement first version of Unify2 with simple test

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JanUlrich 2021-01-21 03:02:47 +01:00
parent 9a0de3f193
commit 3019a0f513
7 changed files with 536 additions and 423 deletions
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108
src/main/java/de/dhbwstuttgart/unify2/MartelliMontanariUnify.java Normal file
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@ -0,0 +1,108 @@
package de.dhbwstuttgart.unify2;
import de.dhbwstuttgart.typeinference.unify.interfaces.IUnify;
import de.dhbwstuttgart.typeinference.unify.model.*;
import java.util.*;
import java.util.stream.Collectors;
/**
* Implementation of the Martelli-Montanari unification algorithm.
* @author Florian Steurer
*/
public class MartelliMontanariUnify {
/**
* Finds the most general unifier sigma of the set {t1 =. t1',...,tn =. tn'} so that
* sigma(t1) = sigma(t1') , ... sigma(tn) = sigma(tn').
* @param terms The set of terms to be unified
* @return An optional of the most general unifier if it exists or an empty optional if there is no unifier.
*/
public static Optional<Unifier> unify(UnifyType... terms) {
return unify(Arrays.stream(terms).collect(Collectors.toSet()));
}
public static Optional<Unifier> unify(Set<UnifyType> terms) {
// Sets with less than 2 terms are trivially unified
if(terms.size() < 2)
return Optional.of(Unifier.identity());
// For the the set of terms {t1,...,tn},
// build a list of equations {(t1 = t2), (t2 = t3), (t3 = t4), ....}
ArrayList<UnifyPair> termsList = new ArrayList<UnifyPair>();
Iterator<UnifyType> iter = terms.iterator();
UnifyType prev = iter.next();
while(iter.hasNext()) {
UnifyType next = iter.next();
termsList.add(new UnifyPair(prev, next, PairOperator.EQUALSDOT));
prev = next;
}
// Start with the identity unifier. Substitutions will be added later.
Unifier mgu = Unifier.identity();
// Apply rules while possible
int idx = 0;
while(idx < termsList.size()) {
UnifyPair pair = termsList.get(idx);
UnifyType rhsType = pair.getRhsType();
UnifyType lhsType = pair.getLhsType();
TypeParams rhsTypeParams = rhsType.getTypeParams();
TypeParams lhsTypeParams = lhsType.getTypeParams();
// REDUCE - Rule
if(!(rhsType instanceof PlaceholderType) && !(lhsType instanceof PlaceholderType)) {
Set<UnifyPair> result = new HashSet<>();
// f<...> = g<...> with f != g are not unifiable
if(!rhsType.getName().equals(lhsType.getName()))
return Optional.empty(); // conflict
// f<t1,...,tn> = f<s1,...,sm> are not unifiable
if(rhsTypeParams.size() != lhsTypeParams.size())
return Optional.empty(); // conflict
// f = g is not unifiable (cannot be f = f because erase rule would have been applied)
//if(rhsTypeParams.size() == 0)
//return Optional.empty();
// Unpack the arguments
for(int i = 0; i < rhsTypeParams.size(); i++)
result.add(new UnifyPair(rhsTypeParams.get(i), lhsTypeParams.get(i), PairOperator.EQUALSDOT));
termsList.remove(idx);
termsList.addAll(result);
continue;
}
// DELETE - Rule
if(pair.getRhsType().equals(pair.getLhsType())) {
termsList.remove(idx);
continue;
}
// SWAP - Rule
if(!(lhsType instanceof PlaceholderType) && (rhsType instanceof PlaceholderType)) {
termsList.remove(idx);
termsList.add(new UnifyPair(rhsType, lhsType, PairOperator.EQUALSDOT));
continue;
}
// OCCURS-CHECK
if(pair.getLhsType() instanceof PlaceholderType
&& pair.getRhsType().getTypeParams().occurs((PlaceholderType) pair.getLhsType()))
return Optional.empty();
// SUBST - Rule
if(lhsType instanceof PlaceholderType) {
mgu.add((PlaceholderType) lhsType, rhsType);
//PL 2018-04-01 nach checken, ob es richtig ist, dass keine Substitutionen uebergeben werden muessen.
termsList = termsList.stream().map(x -> mgu.apply(x)).collect(Collectors.toCollection(ArrayList::new));
idx = idx+1 == termsList.size() ? 0 : idx+1;
continue;
}
idx++;
}
return Optional.of(mgu);
}
}

78
src/main/java/de/dhbwstuttgart/unify2/RuleSet.java
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@ -28,7 +28,7 @@ public class RuleSet {
* This is step one of the unification algorithm. * This is step one of the unification algorithm.
* @return The set of pairs that results from repeated application of the inference rules. * @return The set of pairs that results from repeated application of the inference rules.
*/ */
protected Set<UnifyPair> applyTypeUnificationRules(Set<UnifyPair> eq, IFiniteClosure fc) { public static Set<UnifyPair> applyTypeUnificationRules(Set<UnifyPair> eq, IFiniteClosure fc) {
/* /*
* Rule Application Strategy: * Rule Application Strategy:
@ -683,82 +683,6 @@ public class RuleSet {
return succ ? permutation : new int[0]; return succ ? permutation : new int[0];
} }
static Optional<Set<UnifyPair>> subst(Set<UnifyPair> pairs) {
return subst(pairs, new ArrayList<>());
}
static Optional<Set<UnifyPair>> subst(Set<UnifyPair> pairs, List<Set<Constraint<UnifyPair>>> oderConstraints) {
HashMap<UnifyType, Integer> typeMap = new HashMap<>();
Stack<UnifyType> occuringTypes = new Stack<>();
for(UnifyPair pair : pairs) {
occuringTypes.push(pair.getLhsType());
occuringTypes.push(pair.getRhsType());
}
while(!occuringTypes.isEmpty()) {
UnifyType t1 = occuringTypes.pop();
if(!typeMap.containsKey(t1))
typeMap.put(t1, 0);
typeMap.put(t1, typeMap.get(t1)+1);
if(t1 instanceof ExtendsType)
occuringTypes.push(((ExtendsType) t1).getExtendedType());
if(t1 instanceof SuperType)
occuringTypes.push(((SuperType) t1).getSuperedType());
else
t1.getTypeParams().forEach(x -> occuringTypes.push(x));
}
Queue<UnifyPair> result1 = new LinkedList<UnifyPair>(pairs);
ArrayList<UnifyPair> result = new ArrayList<UnifyPair>();
boolean applied = false;
while(!result1.isEmpty()) {
UnifyPair pair = result1.poll();
PlaceholderType lhsType = null;
UnifyType rhsType;
if(pair.getPairOp() == PairOperator.EQUALSDOT
&& pair.getLhsType() instanceof PlaceholderType)
lhsType = (PlaceholderType) pair.getLhsType();
rhsType = pair.getRhsType(); //PL eingefuegt 2017-09-29 statt !((rhsType = pair.getRhsType()) instanceof PlaceholderType)
if(lhsType != null
//&& !((rhsType = pair.getRhsType()) instanceof PlaceholderType) //PL geloescht am 2017-09-29 Begründung: auch Typvariablen muessen ersetzt werden.
&& typeMap.get(lhsType) > 1 // The type occurs in more pairs in the set than just the recent pair.
&& !rhsType.getTypeParams().occurs(lhsType)
&& !((rhsType instanceof WildcardType) && ((WildcardType)rhsType).getWildcardedType().equals(lhsType))) //PL eigefuegt 2018-02-18
{
Unifier uni = new Unifier(lhsType, rhsType);
result = result.stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(ArrayList::new));
result1 = result1.stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(LinkedList::new));
Function<? super Constraint<UnifyPair>,? extends Constraint<UnifyPair>> applyUni = b -> b.stream().map(
x -> uni.apply(pair,x)).collect(Collectors.toCollection((b.getExtendConstraint() != null)
? () -> new Constraint<UnifyPair>(
b.isInherited(),
b.getExtendConstraint().stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(Constraint::new)))
: () -> new Constraint<UnifyPair>(b.isInherited())
));
oderConstraints.replaceAll(oc -> oc.stream().map(applyUni).collect(Collectors.toCollection(HashSet::new)));
/*
oderConstraints = oderConstraints.stream().map(
a -> a.stream().map(applyUni
//b -> b.stream().map(
// x -> uni.apply(pair,x)).collect(Collectors.toCollection(HashSet::new) )
).collect(Collectors.toCollection(HashSet::new))
).collect(Collectors.toList(ArrayList::new));
}
*/
applied = true;
}
result.add(pair);
}
return applied ? Optional.of(new HashSet<>(result)) : Optional.empty();
}
static Optional<UnifyPair> reduceWildcardLow(UnifyPair pair) { static Optional<UnifyPair> reduceWildcardLow(UnifyPair pair) {
if(pair.getPairOp() != PairOperator.SMALLERDOTWC) if(pair.getPairOp() != PairOperator.SMALLERDOTWC)
return Optional.empty(); return Optional.empty();

371
src/main/java/de/dhbwstuttgart/unify2/TypeUnify.java
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@ -1,375 +1,54 @@
package de.dhbwstuttgart.unify2; package de.dhbwstuttgart.unify2;
import de.dhbwstuttgart.typeinference.constraints.Constraint;
import de.dhbwstuttgart.typeinference.constraints.ConstraintSet;
import de.dhbwstuttgart.typeinference.unify.UnifyResultModel;
import de.dhbwstuttgart.typeinference.unify.interfaces.IFiniteClosure;
import de.dhbwstuttgart.typeinference.unify.model.*; import de.dhbwstuttgart.typeinference.unify.model.*;
import de.dhbwstuttgart.unify2.model.UnifyConstraintSet; import de.dhbwstuttgart.unify2.model.UnifyConstraintSet;
import de.dhbwstuttgart.unify2.model.UnifyConstraintSetBuilder;
import de.dhbwstuttgart.unify2.model.UnifyOderConstraint;
import java.util.*; import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.Stream;
public class TypeUnify { public class TypeUnify {
public void unifyOrConstraints(UnifyConstraintSet eq, FiniteClosure fc){ public static Optional<Set<UnifyPair>> unifyOrConstraints(UnifyConstraintSet eq, FiniteClosure fc){
return eq.cartesianProductParallel().map(eqPrime -> unify(eqPrime, fc)).filter(Optional::isPresent).map(Optional::get).findAny();
eq.cartesianProductParallel().map(eqPrime -> unify(eqPrime, fc));
} }
public Optional<UnifyResultModel> unify(Set<UnifyPair> eq, FiniteClosure fc){ public static Optional<Set<UnifyPair>> unify(Set<UnifyPair> eq, FiniteClosure fc){
/* /*
TODO: Hier könnte man prüfen, ob es überhaupt einen Sinn macht mit eq weiterzumachen TODO: Hier könnte man prüfen, ob es überhaupt einen Sinn macht mit eq weiterzumachen
Es könnte eine über threads geteiltes Objekt geben (Feld in TypeUnify), welches unmögliche Klauseln lernt Es könnte eine über threads geteiltes Objekt geben (Feld in TypeUnify), welches unmögliche Klauseln lernt
*/ */
//Apply Reduce und Apply rules //Apply Reduce und Apply rules
Set<UnifyPair> res = applyTypeUnificationRules(eq, fc); Set<UnifyPair> res = RuleSet.applyTypeUnificationRules(eq, fc);
//Split result //Split result
UnifyConstraintSet constraintSet = step4(res, fc);
return constraintSet.cartesianProductParallel().map(toSubst -> {
//TODO: try subst
toSubst = toSubst; //hier substituieren
//if it changed:
if (true) {
return unify(toSubst, fc);
}else{
//TODO: return the result
return Optional.<UnifyResultModel>empty();
}
}).filter(it -> it.isPresent()).map(Optional::get).findAny();
}
/**
* Repeatedly applies type unification rules to a set of equations.
* This is step one of the unification algorithm.
* @return The set of pairs that results from repeated application of the inference rules.
*/
protected Set<UnifyPair> applyTypeUnificationRules(Set<UnifyPair> eq, FiniteClosure fc) {
/* /*
* Rule Application Strategy: * Step 2 and 3: Create a subset eq1s of pairs where both sides are TPH and eq2s of the other pairs
*
* 1. Swap all pairs and erase all erasable pairs
* 2. Apply all possible rules to a single pair, then move it to the result set.
* Iterating over pairs first, then iterating over rules prevents the application
* of rules to a "finished" pair over and over.
* 2.1 Apply all rules repeatedly except for erase rules. If
* the application of a rule creates new pairs, check immediately
* against the erase rules.
*/ */
Set<UnifyPair> eq1s = new HashSet<>();
Set<UnifyPair> eq2s = new HashSet<>();
LinkedHashSet<UnifyPair> targetSet = new LinkedHashSet<UnifyPair>(); for(UnifyPair pair : res) {
LinkedList<UnifyPair> eqQueue = new LinkedList<>(); if (pair.getLhsType() instanceof PlaceholderType && pair.getRhsType() instanceof PlaceholderType)
eq1s.add(pair);
/*
* Swap all pairs and erase all erasable pairs
*/
eq.forEach(x -> swapAddOrErase(x, fc, eqQueue));
/*
* Apply rules until the queue is empty
*/
while(!eqQueue.isEmpty()) {
UnifyPair pair = eqQueue.pollFirst();
// ReduceUp, ReduceLow, ReduceUpLow
Optional<UnifyPair> opt = rules.reduceUpLow(pair);
opt = opt.isPresent() ? opt : rules.reduceLow(pair);
opt = opt.isPresent() ? opt : rules.reduceUp(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardLow(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardLowRight(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardUp(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardUpRight(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardLowUp(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardUpLow(pair);
opt = opt.isPresent() ? opt : rules.reduceWildcardLeft(pair);
// Reduce TPH
opt = opt.isPresent() ? opt : rules.reduceTph(pair);
// One of the rules has been applied
if(opt.isPresent()) {
swapAddOrErase(opt.get(), fc, eqQueue);
continue;
}
// Reduce1, Reduce2, ReduceExt, ReduceSup, ReduceEq
Optional<Set<UnifyPair>> optSet = rules.reduce1(pair, fc);
optSet = optSet.isPresent() ? optSet : rules.reduce2(pair);
optSet = optSet.isPresent() ? optSet : rules.reduceExt(pair, fc);
optSet = optSet.isPresent() ? optSet : rules.reduceSup(pair, fc);
optSet = optSet.isPresent() ? optSet : rules.reduceEq(pair);
// ReduceTphExt, ReduceTphSup
optSet = optSet.isPresent() ? optSet : rules.reduceTphExt(pair);
optSet = optSet.isPresent() ? optSet : rules.reduceTphSup(pair);
// FunN Rules
optSet = optSet.isPresent() ? optSet : rules.reduceFunN(pair);
optSet = optSet.isPresent() ? optSet : rules.greaterFunN(pair);
optSet = optSet.isPresent() ? optSet : rules.smallerFunN(pair);
// One of the rules has been applied
if(optSet.isPresent()) {
optSet.get().forEach(x -> swapAddOrErase(x, fc, eqQueue));
continue;
}
// Adapt, AdaptExt, AdaptSup
opt = rules.adapt(pair, fc);
opt = opt.isPresent() ? opt : rules.adaptExt(pair, fc);
opt = opt.isPresent() ? opt : rules.adaptSup(pair, fc);
// One of the rules has been applied
if(opt.isPresent()) {
swapAddOrErase(opt.get(), fc, eqQueue);
continue;
}
// None of the rules has been applied
targetSet.add(pair);
}
return targetSet;
}
/**
* Creates sets of pairs specified in the fourth step. Does not calculate cartesian products.
* @return The set of the eight cases (without empty sets). Each case is a set, containing sets generated
* from the pairs that matched the case. Each generated set contains singleton sets or sets with few elements
* (as in case 1 where sigma is added to the innermost set).
*/
protected UnifyConstraintSet step4(Set<UnifyPair> eq2s, FiniteClosure fc) {
Set<UnifyOderConstraint> result = new HashSet<>(8);
for(UnifyPair pair : eq2s) {
PairOperator pairOp = pair.getPairOp();
UnifyType lhsType = pair.getLhsType();
UnifyType rhsType = pair.getRhsType();
// Case 1: (a <. Theta')
if(pairOp == PairOperator.SMALLERDOT && lhsType instanceof PlaceholderType)
result.add(unifyCase1((PlaceholderType) pair.getLhsType(), pair.getRhsType(), fc));
// Case 2: (a <.? ? ext Theta')
else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType && rhsType instanceof ExtendsType)
result.add(unifyCase2((PlaceholderType) pair.getLhsType(), (ExtendsType) pair.getRhsType(), fc));
// Case 3: (a <.? ? sup Theta')
else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType && rhsType instanceof SuperType)
result.add(unifyCase3((PlaceholderType) lhsType, (SuperType) rhsType, fc));
// Case 4 was replaced by an inference rule
// Case 4: (a <.? Theta')
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType)
// result.get(3).add(unifyCase4((PlaceholderType) lhsType, rhsType, fc));
// Case 5: (Theta <. a)
else if(pairOp == PairOperator.SMALLERDOT && rhsType instanceof PlaceholderType)
result.add(unifyCase5(lhsType, (PlaceholderType) rhsType, fc));
// Case 6 was replaced by an inference rule.
// Case 6: (? ext Theta <.? a)
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof ExtendsType && rhsType instanceof PlaceholderType)
// result.get(5).add(unifyCase6((ExtendsType) lhsType, (PlaceholderType) rhsType, fc));
// Case 7 was replaced by an inference rule
// Case 7: (? sup Theta <.? a)
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof SuperType && rhsType instanceof PlaceholderType)
// result.get(6).add(unifyCase7((SuperType) lhsType, (PlaceholderType) rhsType, fc));
// Case 8: (Theta <.? a)
else if(pairOp == PairOperator.SMALLERDOTWC && rhsType instanceof PlaceholderType)
result.add(unifyCase8(lhsType, (PlaceholderType) rhsType, fc));
// Case unknown: If a pair fits no other case, then the type unification has failed.
// Through application of the rules, every pair should have one of the above forms.
// Pairs that do not have one of the aboves form are contradictory.
else {
break;
}
}
// Filter empty sets or sets that only contain an empty set.
//Andi: Why? Should they exist? this should be an error then
return new UnifyConstraintSet(result);
}
/**
* Cartesian product Case 1: (a <. Theta')
*/
protected UnifyOderConstraint unifyCase1(PlaceholderType a, UnifyType thetaPrime, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
boolean allGen = thetaPrime.getTypeParams().size() > 0;
for(UnifyType t : thetaPrime.getTypeParams())
if(!(t instanceof PlaceholderType) || !((PlaceholderType) t).isGenerated()) {
allGen = false;
break;
}
Set<UnifyType> cs = fc.getAllTypesByName(thetaPrime.getName());
cs.add(thetaPrime);
for(UnifyType c : cs) {
Set<UnifyType> thetaQs = fc.getChildren(c).stream().collect(Collectors.toCollection(HashSet::new));
//thetaQs.add(thetaPrime);
Set<UnifyType> thetaQPrimes = new HashSet<>();
TypeParams cParams = c.getTypeParams();
if(cParams.size() == 0)
thetaQPrimes.add(c);
else {
ArrayList<Set<UnifyType>> candidateParams = new ArrayList<>();
for(UnifyType param : cParams)
candidateParams.add(fc.grArg(param));
for(TypeParams tp : permuteParams(candidateParams))
thetaQPrimes.add(c.setTypeParams(tp));
}
for(UnifyType tqp : thetaQPrimes) {
Optional<Unifier> opt = stdUnify.unify(tqp, thetaPrime);
if (!opt.isPresent())
continue;
Unifier unifier = opt.get();
unifier.swapPlaceholderSubstitutions(thetaPrime.getTypeParams());
Set<UnifyPair> substitutionSet = new HashSet<>();
for (Entry<PlaceholderType, UnifyType> sigma : unifier)
substitutionSet.add(new UnifyPair(sigma.getKey(), sigma.getValue(), PairOperator.EQUALSDOT));
List<UnifyType> freshTphs = new ArrayList<>();
for (UnifyType tq : thetaQs) {
Set<UnifyType> smaller = fc.smaller(unifier.apply(tq));
for(UnifyType theta : smaller) {
Set<UnifyPair> resultPrime = new HashSet<>();
for(int i = 0; !allGen && i < theta.getTypeParams().size(); i++) {
if(freshTphs.size()-1 < i)
freshTphs.add(PlaceholderType.freshPlaceholder());
resultPrime.add(new UnifyPair(freshTphs.get(i), theta.getTypeParams().get(i), PairOperator.SMALLERDOTWC));
}
if(allGen)
resultPrime.add(new UnifyPair(a, theta, PairOperator.EQUALSDOT));
else
resultPrime.add(new UnifyPair(a, theta.setTypeParams(new TypeParams(freshTphs.toArray(new UnifyType[0]))), PairOperator.EQUALSDOT));
resultPrime.addAll(substitutionSet);
result.add(resultPrime);
}
}
}
}
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 2: (a <.? ? ext Theta')
*/
private UnifyOderConstraint unifyCase2(PlaceholderType a, ExtendsType extThetaPrime, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
UnifyType aPrime = PlaceholderType.freshPlaceholder();
UnifyType extAPrime = new ExtendsType(aPrime);
UnifyType thetaPrime = extThetaPrime.getExtendedType();
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, thetaPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, extAPrime, PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(aPrime, thetaPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 3: (a <.? ? sup Theta')
*/
private UnifyOderConstraint unifyCase3(PlaceholderType a, SuperType subThetaPrime, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
UnifyType aPrime = PlaceholderType.freshPlaceholder();
UnifyType supAPrime = new SuperType(aPrime);
UnifyType thetaPrime = subThetaPrime.getSuperedType();
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(thetaPrime, a, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, supAPrime, PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(thetaPrime, aPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 5: (Theta <. a)
*/
private UnifyOderConstraint unifyCase5(UnifyType theta, PlaceholderType a, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
boolean allGen = theta.getTypeParams().size() > 0;
for(UnifyType t : theta.getTypeParams())
if(!(t instanceof PlaceholderType) || !((PlaceholderType) t).isGenerated()) {
allGen = false;
break;
}
for(UnifyType thetaS : fc.greater(theta)) {
Set<UnifyPair> resultPrime = new HashSet<>();
UnifyType[] freshTphs = new UnifyType[thetaS.getTypeParams().size()];
for(int i = 0; !allGen && i < freshTphs.length; i++) {
freshTphs[i] = PlaceholderType.freshPlaceholder();
resultPrime.add(new UnifyPair(thetaS.getTypeParams().get(i), freshTphs[i], PairOperator.SMALLERDOTWC));
}
if(allGen)
resultPrime.add(new UnifyPair(a, thetaS, PairOperator.EQUALSDOT));
else else
resultPrime.add(new UnifyPair(a, thetaS.setTypeParams(new TypeParams(freshTphs)), PairOperator.EQUALSDOT)); eq2s.add(pair);
result.add(resultPrime);
} }
return new UnifyOderConstraint(result); Optional<UnifyConstraintSet> step4Res = Unify.step4(eq1s, eq2s, fc);
//Falls step4 etwas liefert, dann subst und rekursiver unify aufruf anwenden:
return step4Res.flatMap(constraintSet ->
constraintSet.cartesianProductParallel().map(toSubst -> {
Optional<Set<UnifyPair>> substitutionResult = Unify.subst(toSubst); //hier substituieren
//if it changed:
if (substitutionResult.isPresent()) {
return unify(substitutionResult.get(), fc);
}else{
//TODO: return the result
return Optional.of(toSubst);
}
}).filter(it -> it.isPresent()).map(Optional::get).findAny());
} }
/**
* Cartesian Product Case 8: (Theta <.? a)
*/
private UnifyOderConstraint unifyCase8(UnifyType theta, PlaceholderType a, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
//for(UnifyType thetaS : fc.grArg(theta)) {
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, theta, PairOperator.EQUALSDOT));
result.add(resultPrime);
UnifyType freshTph = PlaceholderType.freshPlaceholder();
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, new ExtendsType(freshTph), PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(theta, freshTph, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, new SuperType(freshTph), PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(freshTph, theta, PairOperator.SMALLERDOT));
result.add(resultPrime);
//}
return new UnifyOderConstraint(result);
}
} }

340
src/main/java/de/dhbwstuttgart/unify2/Unify.java Normal file
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@ -0,0 +1,340 @@
package de.dhbwstuttgart.unify2;
import de.dhbwstuttgart.typeinference.constraints.Constraint;
import de.dhbwstuttgart.typeinference.unify.interfaces.IFiniteClosure;
import de.dhbwstuttgart.typeinference.unify.model.*;
import de.dhbwstuttgart.unify2.model.UnifyConstraintSet;
import de.dhbwstuttgart.unify2.model.UnifyOderConstraint;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
public class Unify {
/**
* Creates sets of pairs specified in the fourth step. Does not calculate cartesian products.
* @return The set of the eight cases (without empty sets). Each case is a set, containing sets generated
* from the pairs that matched the case. Each generated set contains singleton sets or sets with few elements
* (as in case 1 where sigma is added to the innermost set).
*/
public static Optional<UnifyConstraintSet> step4(Set<UnifyPair> eq1s, Set<UnifyPair> eq2s, FiniteClosure fc) {
Set<UnifyOderConstraint> result = new HashSet<>(8);
for(UnifyPair pair : eq2s) {
PairOperator pairOp = pair.getPairOp();
UnifyType lhsType = pair.getLhsType();
UnifyType rhsType = pair.getRhsType();
// Case 1: (a <. Theta')
if(pairOp == PairOperator.SMALLERDOT && lhsType instanceof PlaceholderType)
result.add(unifyCase1((PlaceholderType) pair.getLhsType(), pair.getRhsType(), fc));
// Case 2: (a <.? ? ext Theta')
else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType && rhsType instanceof ExtendsType)
result.add(unifyCase2((PlaceholderType) pair.getLhsType(), (ExtendsType) pair.getRhsType(), fc));
// Case 3: (a <.? ? sup Theta')
else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType && rhsType instanceof SuperType)
result.add(unifyCase3((PlaceholderType) lhsType, (SuperType) rhsType, fc));
// Case 4 was replaced by an inference rule
// Case 4: (a <.? Theta')
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof PlaceholderType)
// result.get(3).add(unifyCase4((PlaceholderType) lhsType, rhsType, fc));
// Case 5: (Theta <. a)
else if(pairOp == PairOperator.SMALLERDOT && rhsType instanceof PlaceholderType)
result.add(unifyCase5(lhsType, (PlaceholderType) rhsType, fc));
// Case 6 was replaced by an inference rule.
// Case 6: (? ext Theta <.? a)
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof ExtendsType && rhsType instanceof PlaceholderType)
// result.get(5).add(unifyCase6((ExtendsType) lhsType, (PlaceholderType) rhsType, fc));
// Case 7 was replaced by an inference rule
// Case 7: (? sup Theta <.? a)
//else if(pairOp == PairOperator.SMALLERDOTWC && lhsType instanceof SuperType && rhsType instanceof PlaceholderType)
// result.get(6).add(unifyCase7((SuperType) lhsType, (PlaceholderType) rhsType, fc));
// Case 8: (Theta <.? a)
else if(pairOp == PairOperator.SMALLERDOTWC && rhsType instanceof PlaceholderType)
result.add(unifyCase8(lhsType, (PlaceholderType) rhsType, fc));
// Case unknown: If a pair fits no other case, then the type unification has failed.
// Through application of the rules, every pair should have one of the above forms.
// Pairs that do not have one of the aboves form are contradictory.
else {
return Optional.empty();
}
}
result.add(new UnifyOderConstraint(Set.of(eq1s)));
// Filter empty sets or sets that only contain an empty set.
//Andi: Why? Should they exist? this should be an error then
return Optional.of(new UnifyConstraintSet(result));
}
/**
* Cartesian product Case 1: (a <. Theta')
*/
static UnifyOderConstraint unifyCase1(PlaceholderType a, UnifyType thetaPrime, FiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
boolean allGen = thetaPrime.getTypeParams().size() > 0;
for(UnifyType t : thetaPrime.getTypeParams())
if(!(t instanceof PlaceholderType) || !((PlaceholderType) t).isGenerated()) {
allGen = false;
break;
}
Set<UnifyType> cs = fc.getAllTypesByName(thetaPrime.getName());
cs.add(thetaPrime);
for(UnifyType c : cs) {
Set<UnifyType> thetaQs = fc.getChildren(c).stream().collect(Collectors.toCollection(HashSet::new));
//thetaQs.add(thetaPrime);
Set<UnifyType> thetaQPrimes = new HashSet<>();
TypeParams cParams = c.getTypeParams();
if(cParams.size() == 0)
thetaQPrimes.add(c);
else {
ArrayList<Set<UnifyType>> candidateParams = new ArrayList<>();
for(UnifyType param : cParams)
candidateParams.add(fc.grArg(param, new HashSet<>()));
for(TypeParams tp : permuteParams(candidateParams))
thetaQPrimes.add(c.setTypeParams(tp));
}
for(UnifyType tqp : thetaQPrimes) {
Optional<Unifier> opt = MartelliMontanariUnify.unify(tqp, thetaPrime);
if (!opt.isPresent())
continue;
Unifier unifier = opt.get();
unifier.swapPlaceholderSubstitutions(thetaPrime.getTypeParams());
Set<UnifyPair> substitutionSet = new HashSet<>();
for (Map.Entry<PlaceholderType, UnifyType> sigma : unifier)
substitutionSet.add(new UnifyPair(sigma.getKey(), sigma.getValue(), PairOperator.EQUALSDOT));
List<UnifyType> freshTphs = new ArrayList<>();
for (UnifyType tq : thetaQs) {
Set<UnifyType> smaller = fc.smaller(unifier.apply(tq), new HashSet<>());
for(UnifyType theta : smaller) {
Set<UnifyPair> resultPrime = new HashSet<>();
for(int i = 0; !allGen && i < theta.getTypeParams().size(); i++) {
if(freshTphs.size()-1 < i)
freshTphs.add(PlaceholderType.freshPlaceholder());
resultPrime.add(new UnifyPair(freshTphs.get(i), theta.getTypeParams().get(i), PairOperator.SMALLERDOTWC));
}
if(allGen)
resultPrime.add(new UnifyPair(a, theta, PairOperator.EQUALSDOT));
else
resultPrime.add(new UnifyPair(a, theta.setTypeParams(new TypeParams(freshTphs.toArray(new UnifyType[0]))), PairOperator.EQUALSDOT));
resultPrime.addAll(substitutionSet);
result.add(resultPrime);
}
}
}
}
return new UnifyOderConstraint(result);
}
/**
* Takes a set of candidates for each position and computes all possible permutations.
* @param candidates The length of the list determines the number of type params. Each set
* contains the candidates for the corresponding position.
*/
static Set<TypeParams> permuteParams(ArrayList<Set<UnifyType>> candidates) {
Set<TypeParams> result = new HashSet<>();
permuteParams(candidates, 0, result, new UnifyType[candidates.size()]);
return result;
}
/**
* Takes a set of candidates for each position and computes all possible permutations.
* @param candidates The length of the list determines the number of type params. Each set
* contains the candidates for the corresponding position.
* @param idx Idx for the current permutatiton.
* @param result Set of all permutations found so far
* @param current The permutation of type params that is currently explored
*/
static void permuteParams(ArrayList<Set<UnifyType>> candidates, int idx, Set<TypeParams> result, UnifyType[] current) {
if(candidates.size() == idx) {
result.add(new TypeParams(Arrays.copyOf(current, current.length)));
return;
}
Set<UnifyType> localCandidates = candidates.get(idx);
for(UnifyType t : localCandidates) {
current[idx] = t;
permuteParams(candidates, idx+1, result, current);
}
}
/**
* Cartesian Product Case 2: (a <.? ? ext Theta')
*/
static UnifyOderConstraint unifyCase2(PlaceholderType a, ExtendsType extThetaPrime, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
UnifyType aPrime = PlaceholderType.freshPlaceholder();
UnifyType extAPrime = new ExtendsType(aPrime);
UnifyType thetaPrime = extThetaPrime.getExtendedType();
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, thetaPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, extAPrime, PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(aPrime, thetaPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 3: (a <.? ? sup Theta')
*/
static UnifyOderConstraint unifyCase3(PlaceholderType a, SuperType subThetaPrime, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
UnifyType aPrime = PlaceholderType.freshPlaceholder();
UnifyType supAPrime = new SuperType(aPrime);
UnifyType thetaPrime = subThetaPrime.getSuperedType();
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(thetaPrime, a, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, supAPrime, PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(thetaPrime, aPrime, PairOperator.SMALLERDOT));
result.add(resultPrime);
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 5: (Theta <. a)
*/
static UnifyOderConstraint unifyCase5(UnifyType theta, PlaceholderType a, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
boolean allGen = theta.getTypeParams().size() > 0;
for(UnifyType t : theta.getTypeParams())
if(!(t instanceof PlaceholderType) || !((PlaceholderType) t).isGenerated()) {
allGen = false;
break;
}
for(UnifyType thetaS : fc.greater(theta, new HashSet<>())) {
Set<UnifyPair> resultPrime = new HashSet<>();
UnifyType[] freshTphs = new UnifyType[thetaS.getTypeParams().size()];
for(int i = 0; !allGen && i < freshTphs.length; i++) {
freshTphs[i] = PlaceholderType.freshPlaceholder();
resultPrime.add(new UnifyPair(thetaS.getTypeParams().get(i), freshTphs[i], PairOperator.SMALLERDOTWC));
}
if(allGen)
resultPrime.add(new UnifyPair(a, thetaS, PairOperator.EQUALSDOT));
else
resultPrime.add(new UnifyPair(a, thetaS.setTypeParams(new TypeParams(freshTphs)), PairOperator.EQUALSDOT));
result.add(resultPrime);
}
return new UnifyOderConstraint(result);
}
/**
* Cartesian Product Case 8: (Theta <.? a)
*/
static UnifyOderConstraint unifyCase8(UnifyType theta, PlaceholderType a, IFiniteClosure fc) {
Set<Set<UnifyPair>> result = new HashSet<>();
//for(UnifyType thetaS : fc.grArg(theta)) {
Set<UnifyPair> resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, theta, PairOperator.EQUALSDOT));
result.add(resultPrime);
UnifyType freshTph = PlaceholderType.freshPlaceholder();
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, new ExtendsType(freshTph), PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(theta, freshTph, PairOperator.SMALLERDOT));
result.add(resultPrime);
resultPrime = new HashSet<>();
resultPrime.add(new UnifyPair(a, new SuperType(freshTph), PairOperator.EQUALSDOT));
resultPrime.add(new UnifyPair(freshTph, theta, PairOperator.SMALLERDOT));
result.add(resultPrime);
//}
return new UnifyOderConstraint(result);
}
static Optional<Set<UnifyPair>> subst(Set<UnifyPair> pairs) {
HashMap<UnifyType, Integer> typeMap = new HashMap<>();
Stack<UnifyType> occuringTypes = new Stack<>();
for(UnifyPair pair : pairs) {
occuringTypes.push(pair.getLhsType());
occuringTypes.push(pair.getRhsType());
}
while(!occuringTypes.isEmpty()) {
UnifyType t1 = occuringTypes.pop();
if(!typeMap.containsKey(t1))
typeMap.put(t1, 0);
typeMap.put(t1, typeMap.get(t1)+1);
if(t1 instanceof ExtendsType)
occuringTypes.push(((ExtendsType) t1).getExtendedType());
if(t1 instanceof SuperType)
occuringTypes.push(((SuperType) t1).getSuperedType());
else
t1.getTypeParams().forEach(x -> occuringTypes.push(x));
}
Queue<UnifyPair> result1 = new LinkedList<UnifyPair>(pairs);
ArrayList<UnifyPair> result = new ArrayList<UnifyPair>();
boolean applied = false;
while(!result1.isEmpty()) {
UnifyPair pair = result1.poll();
PlaceholderType lhsType = null;
UnifyType rhsType;
if(pair.getPairOp() == PairOperator.EQUALSDOT
&& pair.getLhsType() instanceof PlaceholderType)
lhsType = (PlaceholderType) pair.getLhsType();
rhsType = pair.getRhsType(); //PL eingefuegt 2017-09-29 statt !((rhsType = pair.getRhsType()) instanceof PlaceholderType)
if(lhsType != null
//&& !((rhsType = pair.getRhsType()) instanceof PlaceholderType) //PL geloescht am 2017-09-29 Begründung: auch Typvariablen muessen ersetzt werden.
&& typeMap.get(lhsType) > 1 // The type occurs in more pairs in the set than just the recent pair.
&& !rhsType.getTypeParams().occurs(lhsType)
&& !((rhsType instanceof WildcardType) && ((WildcardType)rhsType).getWildcardedType().equals(lhsType))) //PL eigefuegt 2018-02-18
{
Unifier uni = new Unifier(lhsType, rhsType);
result = result.stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(ArrayList::new));
result1 = result1.stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(LinkedList::new));
Function<? super Constraint<UnifyPair>,? extends Constraint<UnifyPair>> applyUni = b -> b.stream().map(
x -> uni.apply(pair,x)).collect(Collectors.toCollection((b.getExtendConstraint() != null)
? () -> new Constraint<UnifyPair>(
b.getExtendConstraint().stream().map(x -> uni.apply(pair,x)).collect(Collectors.toCollection(Constraint::new)))
: () -> new Constraint<UnifyPair>()
));
applied = true;
}
result.add(pair);
}
return applied ? Optional.of(new HashSet<>(result)) : Optional.empty();
}
}

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src/main/java/de/dhbwstuttgart/unify2/UnifyResult.java Normal file
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@ -0,0 +1,11 @@
package de.dhbwstuttgart.unify2;
import de.dhbwstuttgart.typeinference.unify.model.UnifyPair;
import java.util.Set;
public class UnifyResult {
public UnifyResult(Set<UnifyPair> toSubst) {
}
}

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src/test/java/unify/RuleSetTest.java Normal file
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package unify;
public class RuleSetTest {
}

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src/test/java/unify/TypeUnifyTest.java Normal file
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package unify;
import de.dhbwstuttgart.typeinference.unify.model.FiniteClosure;
import de.dhbwstuttgart.typeinference.unify.model.PairOperator;
import de.dhbwstuttgart.typeinference.unify.model.PlaceholderType;
import de.dhbwstuttgart.typeinference.unify.model.UnifyPair;
import de.dhbwstuttgart.unify2.TypeUnify;
import de.dhbwstuttgart.unify2.model.UnifyConstraintSet;
import de.dhbwstuttgart.unify2.model.UnifyOderConstraint;
import org.junit.Test;
import java.util.HashSet;
import java.util.Optional;
import java.util.Set;
public class TypeUnifyTest {
@Test
public void emptyInput(){
UnifyConstraintSet empty = new UnifyConstraintSet(new HashSet<>());
TypeUnify.unifyOrConstraints(empty, emptyFC());
}
@Test
public void singleOrConstraintOnlyTPHs(){
Set<UnifyPair> pairs = Set.of(new UnifyPair(PlaceholderType.freshPlaceholder(), PlaceholderType.freshPlaceholder(), PairOperator.EQUALSDOT));
UnifyOderConstraint orConstraint = new UnifyOderConstraint(Set.of(pairs));
UnifyConstraintSet input = new UnifyConstraintSet(Set.of(orConstraint));
Optional<Set<UnifyPair>> res = TypeUnify.unifyOrConstraints(input, emptyFC());
assert res.isPresent();
}
@Test
public void unifyTest1(){
PlaceholderType tph1 = PlaceholderType.freshPlaceholder();
PlaceholderType tph2 = PlaceholderType.freshPlaceholder();
UnifyPair p1 = new UnifyPair(tph1, tph2, PairOperator.SMALLERDOT);
Set<UnifyPair> pairs = Set.of(p1);
UnifyOderConstraint orConstraint = new UnifyOderConstraint(Set.of(pairs));
UnifyConstraintSet input = new UnifyConstraintSet(Set.of(orConstraint));
Optional<Set<UnifyPair>> res = TypeUnify.unifyOrConstraints(input, emptyFC());
assert res.isPresent();
}
private FiniteClosure emptyFC(){
return new FiniteClosure(new HashSet<>(), null);
}
}