private static String getAxioms(Definition definition) {
StringBuilder sb = new StringBuilder();
for (Rule rule : definition.functionRules().values()) {
if (rule.containsAttribute(Attribute.SMT_LEMMA_KEY)) {
try {
KILtoSMTLib transformer = new KILtoSMTLib(false);
String leftExpression =
((SMTLibTerm) rule.leftHandSide().accept(transformer)).expression();
String rightExpression =
((SMTLibTerm) rule.rightHandSide().accept(transformer)).expression();
sb.append("(assert (forall (");
sb.append(getQuantifiedVariables(transformer.variables()));
sb.append(") (! (= ");
sb.append(leftExpression);
sb.append(" ");
sb.append(rightExpression);
sb.append(") :pattern(");
sb.append(leftExpression);
sb.append("))))\n");
} catch (UnsupportedOperationException e) {
}
}
}
return sb.toString();
}
/** Partially evaluate the right-hand side and the conditions for each rule. */
private static Definition evaluateDefinition(TermContext termContext) {
Definition definition = termContext.global().getDefinition();
/* replace the unevaluated rules defining functions with their partially evaluated counterparts */
ArrayList<Rule> partiallyEvaluatedRules = new ArrayList<>();
/* iterate until a fixpoint is reached, because the evaluation with functions uses Term#substituteAndEvalaute */
while (true) {
boolean change = false;
partiallyEvaluatedRules.clear();
for (Rule rule :
Iterables.concat(
definition.functionRules().values(), definition.anywhereRules().values())) {
Rule freshRule = rule.getFreshRule(termContext);
Rule evaluatedRule = evaluateRule(freshRule, termContext);
partiallyEvaluatedRules.add(evaluatedRule);
if (!evaluatedRule.equals(freshRule)) {
change = true;
}
}
if (!change) {
break;
}
definition.functionRules().clear();
definition.anywhereRules().clear();
definition.addRuleCollection(partiallyEvaluatedRules);
}
/* replace the unevaluated rules and macros with their partially evaluated counterparts */
partiallyEvaluatedRules.clear();
Iterable<Rule> rules =
Iterables.concat(
definition.rules(),
definition.macros(),
definition.patternRules().values(),
definition.patternFoldingRules());
for (Rule rule : rules) {
partiallyEvaluatedRules.add(evaluateRule(rule, termContext));
}
definition.rules().clear();
definition.macros().clear();
definition.patternRules().clear();
definition.patternFoldingRules().clear();
definition.addRuleCollection(partiallyEvaluatedRules);
return definition;
}
// apply rule by matching
private void rewriteByRule(Term term, Rule rule) {
stopwatch.reset();
stopwatch.start();
termResults = new ArrayList<Term>();
TermContext context = TermContext.of(definition);
ConstrainedTerm constrainedTerm = new ConstrainedTerm(term, context);
SymbolicConstraint leftHandSideConstraint = new SymbolicConstraint(context);
leftHandSideConstraint.addAll(rule.requires());
for (Variable variable : rule.freshVariables()) {
leftHandSideConstraint.add(variable, IntToken.fresh());
}
ConstrainedTerm leftHandSide =
new ConstrainedTerm(
rule.leftHandSide(),
rule.lookups().getSymbolicConstraint(context),
leftHandSideConstraint,
context);
for (SymbolicConstraint constraint : constrainedTerm.unify(leftHandSide)) {
if (!constraint.isMatching(leftHandSide)) {
continue;
}
constraint.orientSubstitution(leftHandSide.variableSet());
Term result = rule.rightHandSide();
/* apply the constraints substitution on the rule RHS */
result = result.substituteAndEvaluate(constraint.substitution(), context);
/* compute all results */
termResults.add(result);
}
stopwatch.stop();
}
@Override
public void visit(Rule rule) {
rule.leftHandSide().accept(this);
rule.rightHandSide().accept(this);
rule.lookups().accept(this);
for (Term term : rule.requires()) {
term.accept(this);
}
for (Term term : rule.ensures()) {
term.accept(this);
}
for (Variable variable : rule.freshVariables()) {
variable.accept(this);
}
}
private void narrowByRule(ConstrainedTerm constrainedTerm, Rule rule) {
stopwatch.reset();
stopwatch.start();
constrainedTermResults = new ArrayList<ConstrainedTerm>();
SymbolicConstraint leftHandSideConstraint =
new SymbolicConstraint(constrainedTerm.termContext());
leftHandSideConstraint.addAll(rule.requires());
for (Variable variable : rule.freshVariables()) {
leftHandSideConstraint.add(variable, IntToken.fresh());
}
ConstrainedTerm leftHandSide =
new ConstrainedTerm(
rule.leftHandSide(),
rule.lookups().getSymbolicConstraint(constrainedTerm.termContext()),
leftHandSideConstraint,
constrainedTerm.termContext());
for (SymbolicConstraint constraint : constrainedTerm.unify(leftHandSide)) {
constraint.addAll(rule.ensures());
/* rename rule variables in the constraints */
Map<Variable, Variable> freshSubstitution = constraint.rename(rule.variableSet());
Term result = rule.rightHandSide();
/* rename rule variables in the rule RHS */
result = result.substituteWithBinders(freshSubstitution, constrainedTerm.termContext());
/* apply the constraints substitution on the rule RHS */
result =
result.substituteWithBinders(constraint.substitution(), constrainedTerm.termContext());
/* evaluate pending functions in the rule RHS */
result = result.evaluate(constrainedTerm.termContext());
/* eliminate anonymous variables */
constraint.eliminateAnonymousVariables();
/* compute all results */
constrainedTermResults.add(
new ConstrainedTerm(result, constraint, constrainedTerm.termContext()));
}
stopwatch.stop();
}
@Override
public KRunProofResult<Set<org.kframework.kil.Term>> prove(Module module)
throws KRunExecutionException {
TermContext termContext = TermContext.of(globalContext);
List<Rule> rules = new ArrayList<Rule>();
for (org.kframework.kil.ModuleItem moduleItem : module.getItems()) {
if (!(moduleItem instanceof org.kframework.kil.Rule)) {
continue;
}
Rule rule = transformer.transformAndEval((org.kframework.kil.Rule) moduleItem);
Rule freshRule = rule.getFreshRule(termContext);
rules.add(freshRule);
}
CounterGetter counterGetter = new CounterGetter(context);
counterGetter.visitNode(module);
BigInteger counter = counterGetter.counter.add(BigInteger.ONE);
SymbolicRewriter symbolicRewriter = executor.getSymbolicRewriter();
List<ConstrainedTerm> proofResults = new ArrayList<>();
for (org.kframework.kil.ModuleItem moduleItem : module.getItems()) {
if (!(moduleItem instanceof org.kframework.kil.Rule)
|| moduleItem.containsAttribute(Attribute.TRUSTED_KEY)) {
continue;
}
termContext.setCounter(counter);
Rule rule = transformer.transformAndEval((org.kframework.kil.Rule) moduleItem);
ConstrainedTerm initialTerm =
new ConstrainedTerm(
rule.leftHandSide(), ConjunctiveFormula.of(termContext).addAll(rule.requires()));
ConstrainedTerm targetTerm =
new ConstrainedTerm(
rule.rightHandSide(), ConjunctiveFormula.of(termContext).addAll(rule.ensures()));
proofResults.addAll(symbolicRewriter.proveRule(initialTerm, targetTerm, rules));
}
return new KRunProofResult<>(
proofResults.isEmpty(), Collections.<org.kframework.kil.Term>emptySet());
}
/** Partially evaluate the right-hand side and the conditions of a specified rule. */
private static Rule evaluateRule(Rule rule, TermContext termContext) {
try {
// TODO(AndreiS): some evaluation is required in the LHS as well
// TODO(YilongL): cannot simply uncomment the following code because it
// may evaluate the LHS using the rule itself
// Term leftHandSide = rule.leftHandSide().evaluate(termContext);
Rule origRule = rule;
Term rightHandSide = rule.rightHandSide().evaluate(termContext);
List<Term> requires = new ArrayList<>();
for (Term term : rule.requires()) {
requires.add(term.evaluate(termContext));
}
List<Term> ensures = new ArrayList<>();
for (Term term : rule.ensures()) {
ensures.add(term.evaluate(termContext));
}
ConjunctiveFormula lookups = ConjunctiveFormula.of(termContext);
for (Equality equality : rule.lookups().equalities()) {
lookups =
lookups.add(
equality.leftHandSide().evaluate(termContext),
equality.rightHandSide().evaluate(termContext));
}
Map<CellLabel, Term> rhsOfWriteCell = null;
if (rule.isCompiledForFastRewriting()) {
rhsOfWriteCell = new HashMap<>();
for (Map.Entry<CellLabel, Term> entry : rule.rhsOfWriteCell().entrySet()) {
rhsOfWriteCell.put(entry.getKey(), entry.getValue().evaluate(termContext));
}
}
Rule newRule =
new Rule(
rule.label(),
rule.leftHandSide(),
rightHandSide,
requires,
ensures,
rule.freshConstants(),
rule.freshVariables(),
lookups,
rule.isCompiledForFastRewriting(),
rule.lhsOfReadCell(),
rhsOfWriteCell,
rule.cellsToCopy(),
rule.matchingInstructions(),
rule,
termContext);
return newRule.equals(rule) ? origRule : newRule;
} catch (KEMException e) {
e.exception.addTraceFrame(
"while compiling rule at location " + rule.getSource() + rule.getLocation());
throw e;
}
}
@Override
public ASTNode visit(org.kframework.kil.Rule node, Void _void) {
try {
assert node.getBody() instanceof org.kframework.kil.Rewrite;
JavaBackendRuleData ruleData = node.getAttribute(JavaBackendRuleData.class);
if (ruleData == null) {
ruleData = new JavaBackendRuleData();
}
concreteCollectionSize = ruleData.getConcreteDataStructureSize();
org.kframework.kil.Rewrite rewrite = (org.kframework.kil.Rewrite) node.getBody();
Term leftHandSide = (Term) this.visitNode(rewrite.getLeft());
Term rightHandSide = (Term) this.visitNode(rewrite.getRight());
List<Term> requires = new ArrayList<>();
if (node.getRequires() != null) {
transformConjunction(requires, (Term) this.visitNode(node.getRequires()));
}
List<Term> ensures = new ArrayList<>();
if (node.getEnsures() != null) {
transformConjunction(ensures, (Term) this.visitNode(node.getEnsures()));
}
ConjunctiveFormula lookups = ConjunctiveFormula.of(termContext);
for (org.kframework.kil.BuiltinLookup lookup : ruleData.getLookups()) {
Variable base = (Variable) this.visitNode(lookup.base());
Term key = (Term) this.visitNode(lookup.key());
if (lookup instanceof org.kframework.kil.SetLookup) {
if (lookup.choice()) {
lookups = lookups.add(DataStructures.choice(base, termContext), key);
} else {
lookups = lookups.add(DataStructures.lookup(base, key, termContext), BoolToken.TRUE);
}
} else {
Term value = (Term) this.visitNode(lookup.value());
if (lookup instanceof org.kframework.kil.MapLookup) {
if (lookup.choice()) {
lookups = lookups.add(DataStructures.choice(base, termContext), key);
}
lookups = lookups.add(DataStructures.lookup(base, key, termContext), value);
} else { // ListLookup
lookups = lookups.add(DataStructures.lookup(base, key, termContext), value);
}
}
}
// TODO(AndreiS): check !Variable only appears in the RHS
Set<Variable> freshConstants =
node.getBody()
.variables()
.stream()
.filter(v -> v.isFreshConstant())
.map(v -> (Variable) this.visitNode(v))
.collect(Collectors.toSet());
Set<Variable> freshVariables =
node.getBody()
.variables()
.stream()
.filter(v -> v.isFreshVariable())
.map(v -> (Variable) this.visitNode(v))
.collect(Collectors.toSet());
assert leftHandSide.kind() == rightHandSide.kind()
|| leftHandSide.kind().isComputational() && rightHandSide.kind().isComputational();
concreteCollectionSize = Collections.emptyMap();
java.util.Map<CellLabel, Term> lhsOfReadCell = null;
java.util.Map<CellLabel, Term> rhsOfWriteCell = null;
if (ruleData.isCompiledForFastRewriting()) {
lhsOfReadCell = Maps.newHashMap();
for (java.util.Map.Entry<String, org.kframework.kil.Term> entry :
ruleData.getLhsOfReadCell().entrySet()) {
lhsOfReadCell.put(CellLabel.of(entry.getKey()), (Term) this.visitNode(entry.getValue()));
}
rhsOfWriteCell = Maps.newHashMap();
for (java.util.Map.Entry<String, org.kframework.kil.Term> entry :
ruleData.getRhsOfWriteCell().entrySet()) {
rhsOfWriteCell.put(CellLabel.of(entry.getKey()), (Term) this.visitNode(entry.getValue()));
}
}
java.util.Set<CellLabel> cellsToCopy = null;
if (ruleData.getCellsToCopy() != null) {
cellsToCopy = Sets.newHashSet();
for (String cellLabelName : ruleData.getCellsToCopy()) {
cellsToCopy.add(CellLabel.of(cellLabelName));
}
}
Rule rule =
new Rule(
node.getLabel(),
leftHandSide,
rightHandSide,
requires,
ensures,
freshConstants,
freshVariables,
lookups,
ruleData.isCompiledForFastRewriting(),
lhsOfReadCell,
rhsOfWriteCell,
cellsToCopy,
ruleData.getMatchingInstructions(),
node,
termContext);
if (freshRules) {
return rule.getFreshRule(termContext);
}
return rule;
} catch (KEMException e) {
e.exception.addTraceFrame(
"while compiling rule at " + node.getSource() + node.getLocation() + " to backend");
throw e;
}
}
@Override
public ASTNode transform(org.kframework.kil.Rule node) throws TransformerException {
assert node.getBody() instanceof org.kframework.kil.Rewrite;
org.kframework.kil.Rewrite rewrite = (org.kframework.kil.Rewrite) node.getBody();
Term leftHandSide = (Term) rewrite.getLeft().accept(this);
Term rightHandSide = (Term) rewrite.getRight().accept(this);
Collection<Term> requires = new ArrayList<Term>();
Collection<Variable> freshVariables = new ArrayList<Variable>();
// TODO: Deal with Ensures
if (node.getRequires() != null) {
Term term = (Term) node.getRequires().accept(this);
if (term instanceof KItem && ((KItem) term).kLabel().toString().equals("'_andBool_")) {
for (Term item : ((KItem) term).kList().getItems()) {
if (item instanceof KItem && ((KItem) item).kLabel().toString().equals("'fresh(_)")) {
freshVariables.add((Variable) ((KItem) item).kList().get(0));
} else {
requires.add(item);
}
}
} else {
if (term instanceof KItem && ((KItem) term).kLabel().toString().equals("'fresh(_)")) {
freshVariables.add((Variable) ((KItem) term).kList().get(0));
} else {
requires.add(term);
}
}
}
SymbolicConstraint lookups = new SymbolicConstraint(new TermContext(definition));
for (org.kframework.kil.BuiltinLookup lookup : node.getLookups()) {
Variable base = (Variable) lookup.base().accept(this);
Term key = (Term) lookup.key().accept(this);
if (lookup instanceof org.kframework.kil.SetLookup) {
lookups.add(new SetLookup(base, key), BoolToken.TRUE);
} else {
Term value = (Term) lookup.value().accept(this);
if (lookup instanceof org.kframework.kil.MapLookup) {
lookups.add(new MapLookup(base, key), value);
} else { // ListLookup
lookups.add(new ListLookup(base, key), value);
}
}
}
assert leftHandSide.kind() == rightHandSide.kind()
|| ((leftHandSide.kind() == Kind.KITEM
|| leftHandSide.kind() == Kind.K
|| leftHandSide.kind() == Kind.KLIST)
&& (rightHandSide.kind() == Kind.KITEM
|| rightHandSide.kind() == Kind.K
|| rightHandSide.kind() == Kind.KLIST));
Rule rule =
new Rule(
leftHandSide, rightHandSide, requires, freshVariables, lookups, node.getAttributes());
return rule.getFreshRule(new TermContext(definition));
}
@Override
public void buildIndex() {
/* populate the table of rules rewriting the top configuration */
List<Index> indices = new ArrayList<Index>();
indices.add(TopIndex.TOP);
indices.add(BottomIndex.BOTTOM);
for (KLabelConstant kLabel : definition.kLabels()) {
indices.add(new KLabelIndex(kLabel));
indices.add(new FreezerIndex(kLabel, -1));
if (!kLabel.productions().isEmpty()) {
int maxArity = getMaxArityForProductions(kLabel.productions());
for (int i = 0; i < maxArity; ++i) {
indices.add(new FreezerIndex(kLabel, i));
}
}
}
// for (KLabelConstant frozenKLabel : definition.frozenKLabels()) {
// for (int i = 0; i < frozenKLabel.productions().get(0).getArity(); ++i) {
// indices.add(new FreezerIndex(frozenKLabel, i));
// }
// }
for (String sort : definition.builtinSorts()) {
indices.add(new TokenIndex(sort));
}
/* Map each index to a list of rules unifiable with that index */
/* Heating rules and regular rules have their first index checked */
/* Cooling rules have their second index checked */
ImmutableMap.Builder<Index, List<Rule>> mapBuilder = ImmutableMap.builder();
ImmutableMap.Builder<Index, List<Rule>> heatingMapBuilder = ImmutableMap.builder();
ImmutableMap.Builder<Index, List<Rule>> coolingMapBuilder = ImmutableMap.builder();
ImmutableMap.Builder<Index, List<Rule>> simulationMapBuilder = ImmutableMap.builder();
for (Index index : indices) {
ImmutableList.Builder<Rule> listBuilder = ImmutableList.builder();
ImmutableList.Builder<Rule> heatingListBuilder = ImmutableList.builder();
ImmutableList.Builder<Rule> coolingListBuilder = ImmutableList.builder();
ImmutableList.Builder<Rule> simulationListBuilder = ImmutableList.builder();
for (Rule rule : definition.rules()) {
if (rule.containsAttribute("heat")) {
if (index.isUnifiable(rule.indexingPair().first)) {
heatingListBuilder.add(rule);
}
} else if (rule.containsAttribute("cool")) {
if (index.isUnifiable(rule.indexingPair().second)) {
coolingListBuilder.add(rule);
}
} else if (rule.containsAttribute("alphaRule")) {
if (index.isUnifiable(rule.indexingPair().first)) {
simulationListBuilder.add(rule);
}
} else {
if (index.isUnifiable(rule.indexingPair().first)) {
listBuilder.add(rule);
}
}
}
ImmutableList<Rule> rules = listBuilder.build();
if (!rules.isEmpty()) {
mapBuilder.put(index, rules);
}
rules = heatingListBuilder.build();
if (!rules.isEmpty()) {
heatingMapBuilder.put(index, rules);
}
rules = coolingListBuilder.build();
if (!rules.isEmpty()) {
coolingMapBuilder.put(index, rules);
}
rules = simulationListBuilder.build();
if (!rules.isEmpty()) {
simulationMapBuilder.put(index, rules);
}
}
heatingRuleTable = heatingMapBuilder.build();
coolingRuleTable = coolingMapBuilder.build();
ruleTable = mapBuilder.build();
simulationRuleTable = simulationMapBuilder.build();
ImmutableList.Builder<Rule> listBuilder = ImmutableList.builder();
for (Rule rule : definition.rules()) {
if (!rule.containsKCell()) {
listBuilder.add(rule);
}
}
unindexedRules = listBuilder.build();
}