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KILtoSMTLib.java
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KILtoSMTLib.java
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// Copyright (c) 2014-2019 K Team. All Rights Reserved.
package org.kframework.backend.java.symbolic;
import com.google.common.base.Joiner;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.ImmutableSet;
import com.google.common.collect.Sets;
import org.apache.commons.lang3.tuple.Pair;
import org.kframework.attributes.Att;
import org.kframework.backend.java.builtins.BitVector;
import org.kframework.backend.java.builtins.BoolToken;
import org.kframework.backend.java.builtins.FloatToken;
import org.kframework.backend.java.builtins.IntToken;
import org.kframework.backend.java.builtins.UninterpretedToken;
import org.kframework.backend.java.kil.BuiltinList;
import org.kframework.backend.java.kil.BuiltinMap;
import org.kframework.backend.java.kil.Definition;
import org.kframework.backend.java.kil.GlobalContext;
import org.kframework.backend.java.kil.JavaSymbolicObject;
import org.kframework.backend.java.kil.KItem;
import org.kframework.backend.java.kil.KLabelConstant;
import org.kframework.backend.java.kil.KList;
import org.kframework.backend.java.kil.Rule;
import org.kframework.backend.java.kil.SMTLibTerm;
import org.kframework.backend.java.kil.Sort;
import org.kframework.backend.java.kil.SortSignature;
import org.kframework.backend.java.kil.Term;
import org.kframework.backend.java.kil.Variable;
import org.kframework.builtin.Sorts;
import org.kframework.kore.KORE;
import org.kframework.krun.KRunOptions;
import org.kframework.utils.errorsystem.KEMException;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Formatter;
import java.util.LinkedHashMap;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Set;
import java.util.Stack;
public class KILtoSMTLib extends CopyOnWriteTransformer {
public static final ImmutableSet<Sort> SMTLIB_BUILTIN_SORTS = ImmutableSet.of(
Sort.BOOL,
Sort.INT,
Sort.BIT_VECTOR,
Sort.of(Sorts.Float()),
Sort.of(Sorts.String()),
Sort.of(KORE.Sort("IntSet")),
Sort.of(KORE.Sort("MIntSet")),
Sort.of(KORE.Sort("FloatSet")),
Sort.of(KORE.Sort("StringSet")),
Sort.of(KORE.Sort("IntSeq")),
Sort.of(KORE.Sort("MIntSeq")),
Sort.of(KORE.Sort("FloatSeq")),
Sort.of(KORE.Sort("StringSeq")));
public static final ImmutableSet<String> SMTLIB_BUILTIN_FUNCTIONS = ImmutableSet.of(
"forall",
"exists",
/* array theory */
"select",
"store",
/* core theory */
"not",
"and",
"or",
"xor",
"=>",
"=",
"distinct",
"ite",
/* int theory */
"+",
"-",
"*",
"div",
"mod",
"abs",
"<=",
"<",
">=",
">",
"^",
/* extra int theory */
"int_max",
"int_min",
"int_abs",
/* extra float theory */
"remainder",
"min",
"max",
"==",
/* bit vector theory */
"concat",
"extract",
"bvnot",
"bvneg",
"bvand",
"bvor",
"bvadd",
"bvmul",
"bvudiv",
"bvurem",
"bvshl",
"bvlshr",
"bvult",
/* z3-specific bit vector theory */
"bvsub",
"bvxor",
"bvslt",
"bvule",
"bvsle",
"bvugt",
"bvsgt",
"bvuge",
"bvsge",
"bv2int",
/* bit vector extras */
"mint_signed_of_unsigned",
/* string theory */
"string_lt",
"string_le",
"string_gt",
"string_ge",
/* set theory */
"smt_set_mem", "smt_miset_mem",
"smt_set_add", "smt_miset_add",
"smt_set_emp", "smt_miset_emp",
"smt_set_cup", "smt_miset_cup",
"smt_set_cap", "smt_miset_cap",
"smt_set_com", "smt_miset_com",
"smt_set_ele", "smt_miset_ele",
"smt_set_dif", "smt_miset_dif",
"smt_set_sub", "smt_miset_sub",
"smt_set_lt", "smt_miset_lt",
"smt_set_le", "smt_miset_le",
/* float set theory */
"float_set_mem",
"float_set_add",
"float_set_emp",
"float_set_cup",
"float_set_cap",
"float_set_com",
"float_set_ele",
"float_set_dif",
"float_set_sub",
"float_set_lt",
"float_set_le",
/* string set theory */
"string_set_mem",
"string_set_add",
"string_set_emp",
"string_set_cup",
"string_set_cap",
"string_set_com",
"string_set_ele",
"string_set_dif",
"string_set_sub",
"string_set_lt",
"string_set_le",
/* associative sequence theory */
"smt_seq_concat",
"smt_seq_elem",
"smt_seq_nil",
"smt_seq_len",
"smt_seq_sum",
"smt_seq2set",
"smt_seq_sorted",
"smt_seq_filter",
/* bool2int */
"smt_bool2int");
public static CharSequence translateConstraint(ConjunctiveFormula constraint) {
KILtoSMTLib kil2SMT = new KILtoSMTLib(true, constraint.globalContext());
//this line has side effects used later
CharSequence expression = kil2SMT.translate(constraint).expression();
StringBuilder sb = new StringBuilder(1024);
kil2SMT.appendSortAndFunctionDeclarations(sb, kil2SMT.variables());
kil2SMT.appendAxioms(sb);
kil2SMT.appendConstantDeclarations(sb, kil2SMT.variables());
sb.append("(assert ")
.append(expression)
.append(")");
return sb;
}
/**
* Generates the z3 query for "left /\ !right".
* left -> right <==> !(left /\ !right)
* => this query should be unsat for implication to be proven.
*/
public static CharSequence translateImplication(
ConjunctiveFormula leftHandSide,
ConjunctiveFormula rightHandSide,
Set<Variable> existentialQuantVars) {
KILtoSMTLib leftTransformer = new KILtoSMTLib(true, leftHandSide.globalContext());
// termAbstractionMap is shared between transformers
KILtoSMTLib rightTransformer = new KILtoSMTLib(false,
rightHandSide.globalContext().getDefinition(),
rightHandSide.globalContext().krunOptions,
rightHandSide.globalContext(), leftTransformer.termAbstractionMap);
CharSequence leftExpression = leftTransformer.translate(leftHandSide).expression();
String rightExpression = rightTransformer.translate(rightHandSide).expression().toString();
StringBuilder sb = new StringBuilder(1024);
Sets.SetView<Variable> allVars = Sets.union(leftTransformer.variables(), rightTransformer.variables());
Set<Variable> usedExistentialQuantVars = Sets.intersection(existentialQuantVars, rightTransformer.variables());
leftTransformer.appendSortAndFunctionDeclarations(sb, allVars);
leftTransformer.appendAxioms(sb);
leftTransformer.appendConstantDeclarations(sb, Sets.difference(allVars, usedExistentialQuantVars));
sb.append("(assert (and\n ");
sb.append(leftExpression);
sb.append("\n (not ");
if (!usedExistentialQuantVars.isEmpty()) {
sb.append("(exists (");
leftTransformer.appendQuantifiedVariables(sb, usedExistentialQuantVars);
sb.append(") ");
}
sb.append(rightExpression);
if (!usedExistentialQuantVars.isEmpty()) {
sb.append(")");
}
sb.append(")\n))");
return sb;
}
private final Definition definition;
private final GlobalContext globalContext;
private final KRunOptions krunOptions;
/**
* Flag indicating whether KItem terms and equalities that cannot be translated can be abstracted away into
* fresh variables. If the flag is false and untranslatable term is encountered, an exception will be thrown instead.
*/
private final boolean allowNewVars;
//All sets/maps are LinkedHashXXX, to avoid non-determinism when iterated and produce consistent logs.
private final LinkedHashSet<Variable> variables;
private final LinkedHashMap<Term, Variable> termAbstractionMap;
private final LinkedHashMap<UninterpretedToken, Integer> tokenEncoding;
private final Stack<Term> binders;
private KILtoSMTLib(boolean allowNewVars, GlobalContext global) {
this(allowNewVars, global.getDefinition(), global.krunOptions, global, new LinkedHashMap<>());
}
private KILtoSMTLib(boolean allowNewVars, Definition definition, KRunOptions krunOptions,
GlobalContext global) {
this(allowNewVars, definition, krunOptions, global, new LinkedHashMap<>());
}
/**
* @param allowNewVars If true, untranslatable terms not present in {@code termAbstractionMap} will be
* substituted with fresh vars. If false, only terms already present in the map will be
* substituted. Also, if true, substitutions will be translated into Z3 as equalities.
*/
private KILtoSMTLib(boolean allowNewVars, Definition definition, KRunOptions krunOptions,
GlobalContext global, LinkedHashMap<Term, Variable> termAbstractionMap) {
this.allowNewVars = allowNewVars;
this.definition = definition;
this.krunOptions = krunOptions;
this.globalContext = global;
this.termAbstractionMap = termAbstractionMap;
variables = new LinkedHashSet<>();
tokenEncoding = new LinkedHashMap<>();
binders = new Stack<>();
}
private SMTLibTerm translate(JavaSymbolicObject object) {
JavaSymbolicObject astNode = object.accept(this);
if (astNode instanceof SMTLibTerm) {
return (SMTLibTerm) astNode;
} else {
throw new SMTTranslationFailure("Attempting to translate an unsupported term of type " + object.getClass());
}
}
private StringBuilder appendSortAndFunctionDeclarations(StringBuilder sb, Set<Variable> variables) {
Set<Sort> sorts = new LinkedHashSet<>();
List<KLabelConstant> functions = new ArrayList<>();
for (KLabelConstant kLabel : definition.kLabels()) {
String smtlib = kLabel.getAttr(Att.SMTLIB());
Boolean inSmtPrelude = kLabel.getAttr(Att.SMT_PRELUDE()) != null;
if (smtlib != null && !inSmtPrelude && !SMTLIB_BUILTIN_FUNCTIONS.contains(smtlib) && !smtlib.startsWith("(")) {
functions.add(kLabel);
assert kLabel.signatures().size() == 1;
SortSignature signature = kLabel.signatures().iterator().next();
sorts.add(renameSort(signature.result()));
signature.parameters().stream()
.map(this::renameSort)
.forEach(sorts::add);
}
}
for (Variable variable : variables) {
sorts.add(renameSort(variable.sort()));
}
for (Sort sort : Sets.difference(sorts, Sets.union(SMTLIB_BUILTIN_SORTS, definition.smtPreludeSorts()))) {
if (sort.equals(Sort.MAP) && krunOptions.experimental.smt.mapAsIntArray) {
sb.append("(define-sort Map () (Array Int Int))");
} else {
sb.append("(declare-sort ");
sb.append(renameSort(sort).name());
sb.append(")\n");
}
}
for (KLabelConstant kLabel : functions) {
sb.append("(declare-fun ");
sb.append(kLabel.getAttr(Att.SMTLIB()));
sb.append(" (");
List<String> childrenSorts = new ArrayList<>();
for (Sort sort : kLabel.signatures().iterator().next().parameters()) {
childrenSorts.add(renameSort(sort).name());
}
Joiner.on(" ").appendTo(sb, childrenSorts);
sb.append(") ");
sb.append(renameSort(kLabel.signatures().iterator().next().result()).name());
sb.append(")\n");
}
return sb;
}
private CharSequence appendAxioms(StringBuilder sb) {
for (Rule rule : definition.functionRules().values()) {
if (rule.att().contains(Att.SMT_LEMMA())) {
try {
KILtoSMTLib kil2SMT = new KILtoSMTLib(false, globalContext);
CharSequence leftExpression = kil2SMT.translate(rule.leftHandSide()).expression();
CharSequence rightExpression = kil2SMT.translate(rule.rightHandSide()).expression();
List<CharSequence> requiresExpressions = new ArrayList<>();
for (Term term : rule.requires()) {
requiresExpressions.add(kil2SMT.translate(term).expression());
}
sb.append("(assert ");
if (!kil2SMT.variables().isEmpty()) {
sb.append("(forall (");
kil2SMT.appendQuantifiedVariables(sb, kil2SMT.variables());
sb.append(") ");
//sb.append(") (! ");
}
if (!requiresExpressions.isEmpty()) {
sb.append("(=> ");
sb.append("(and");
for (CharSequence cs : requiresExpressions) {
sb.append(" ");
sb.append(cs);
}
sb.append(") ");
}
sb.append("(= ");
sb.append(leftExpression);
sb.append(" ");
sb.append(rightExpression);
sb.append(")");
//sb.append(" :pattern(");
//sb.append(leftExpression);
//sb.append(")");
if (!requiresExpressions.isEmpty()) {
sb.append(")");
}
if (!kil2SMT.variables().isEmpty()) {
sb.append(")");
}
sb.append(")\n");
} catch (UnsupportedOperationException e) { }
}
}
return sb;
}
private CharSequence appendConstantDeclarations(StringBuilder sb, Set<Variable> variables) {
for (Variable variable : variables) {
sb.append("(declare-fun ");
sb.append("|").append(variable.longName()).append("|");
sb.append(" () ");
String sortName;
sortName = getSortName(variable);
sb.append(sortName);
sb.append(")\n");
}
return sb;
}
private CharSequence appendQuantifiedVariables(StringBuilder sb, Set<Variable> variables) {
for (Variable variable : variables) {
sb.append("(");
sb.append("|").append(variable.longName()).append("|");
sb.append(" ");
String sortName;
sortName = getSortName(variable);
sb.append(sortName);
sb.append(")");
}
return sb;
}
private String getSortName(Variable variable) {
return getParametricSortName(variable.att(), variable.sort());
}
private String getParametricSortName(Att att, Sort s) {
s = renameSort(s);
if (s == Sort.BIT_VECTOR) {
return "(_ BitVec " + BitVector.getBitwidthOrDie(att) + ")";
} else if (s == Sort.FLOAT && !krunOptions.experimental.smt.floatsAsPO) {
Pair<Integer, Integer> pair = FloatToken.getExponentAndSignificandOrDie(att);
return "(_ FP " + pair.getLeft() + " " + pair.getRight() + ")";
} else {
return s.name();
}
}
private Sort renameSort(Sort sort) {
sort = definition.smtSortFlattening().getOrDefault(sort, sort);
if (sort == Sort.LIST) {
return Sort.of(KORE.Sort("IntSeq"));
} else if (sort == Sort.of(Sorts.Id())) {
return Sort.INT;
} else {
return sort;
}
}
/**
* Returns an unmodifiable view of the set of variables occurring during the translation.
*/
public Set<Variable> variables() {
return Sets.union(variables, ImmutableSet.copyOf(termAbstractionMap.values()));
}
/**
* Translates the equalities of the given symbolic constraint into SMTLib format.
* Ignores the substitution of the symbolic constraint.
*/
@Override
public SMTLibTerm transform(ConjunctiveFormula constraint) {
if (!constraint.disjunctions().isEmpty()) {
throw KEMException.criticalError(
"disjunctions are not supported by SMT translation for:\n" + constraint.toStringMultiline());
}
Set<Equality> equalities = Sets.newLinkedHashSet(constraint.equalities());
if (!allowNewVars) {
constraint.substitution().entrySet().stream()
.map(entry -> new Equality(entry.getKey(), entry.getValue(), constraint.globalContext()))
.forEach(equalities::add);
}
if (equalities.isEmpty()) {
return new SMTLibTerm(Boolean.TRUE.toString());
}
StringBuilder sb = new StringBuilder();
sb.append("(and");
boolean isEmptyAdd = true;
for (Equality equality : equalities) {
try {
CharSequence left = translateTerm(equality.leftHandSide());
CharSequence right = translateTerm(equality.rightHandSide());
sb.append("\n\t(= ");
sb.append(left);
sb.append(" ");
sb.append(right);
sb.append(")");
isEmptyAdd = false;
} catch (UnsupportedOperationException e) {
// TODO(AndreiS): fix this translation and the exceptions
if (allowNewVars){
/* it is sound to skip the equalities that cannot be translated */
e.printStackTrace();
} else {
throw e;
}
}
}
if (isEmptyAdd) {
sb.append(" true");
}
sb.append(")");
return new SMTLibTerm(sb);
}
public CharSequence translateTerm(Term term) {
try {
return translate(term).expression();
} catch (SMTTranslationFailure | UnsupportedOperationException e) {
return abstractThroughAnonVariable(term, e);
}
}
private String abstractThroughAnonVariable(Term term, RuntimeException e) {
Variable variable = termAbstractionMap.get(term);
if (variable == null) {
if (allowNewVars) {
variable = Variable.getAnonVariable(term.sort());
termAbstractionMap.put(term, variable);
if (globalContext.javaExecutionOptions.debugZ3Queries) {
globalContext.log().format("\t%s ::= %s\n", variable.longName(), term);
}
} else {
throw e;
}
}
return variable.longName();
}
@Override
public SMTLibTerm transform(KItem kItem) {
if (!(kItem.kLabel() instanceof KLabelConstant)) {
throw new UnsupportedOperationException();
}
KLabelConstant kLabel = (KLabelConstant) kItem.kLabel();
if (!(kItem.kList() instanceof KList)) {
throw new UnsupportedOperationException();
}
KList kList = (KList) kItem.kList();
if (kList.hasFrame()) {
throw new UnsupportedOperationException();
}
if (kLabel.isBinder()) {
for (Integer keyIndex : kLabel.getBinderMap().keySet()) {
Term binderKVar = kList.get(keyIndex);
if (binderKVar instanceof UninterpretedToken && binderKVar.sort() == Sort.KVARIABLE) {
binders.push(binderKVar);
} else {
throw new UnsupportedOperationException();
}
}
}
SMTLibTerm smtLibTerm = transformSupportedKItem(kItem);
if (kLabel.isBinder()) {
for (Integer keyIndex : kLabel.getBinderMap().keySet()) {
binders.pop();
}
}
return smtLibTerm;
}
private SMTLibTerm transformSupportedKItem(KItem kItem) {
KLabelConstant kLabel = (KLabelConstant) kItem.kLabel();
KList kList = (KList) kItem.kList();
String label = kLabel.smtlib();
if (kLabel.label().equals("Map:lookup") && krunOptions.experimental.smt.mapAsIntArray) {
label = "select";
}
if (kLabel.label().equals("_[_<-_]") && krunOptions.experimental.smt.mapAsIntArray) {
label = "store";
}
if (label == null) {
return new SMTLibTerm(abstractThroughAnonVariable(kItem,
new SMTTranslationFailure("missing SMTLib translation for " + kLabel)));
}
if (krunOptions.experimental.smt.floatsAsPO) {
switch (kLabel.label()) {
case "_<Float_":
label = "float_lt";
break;
case "_<=Float_":
label = "float_le";
break;
case "_>Float_":
label = "float_gt";
break;
case "_>=Float_":
label = "float_ge";
break;
case "maxFloat":
label = "float_max";
break;
case "minFloat":
label = "float_min";
break;
case "_==Float_":
label = "=";
break;
case "_=/=Float_":
label = "(not (= #1 #2))";
break;
case "isNaN":
label = "(= #1 float_nan)";
break;
}
}
if (label.startsWith("(")) {
// smtlib expression instead of operator
String expression = label;
for (int i = 0; i < kList.getContents().size(); i++) {
expression = expression.replaceAll("#" + (i + 1) + "(?![0-9])",
translate(kList.get(i)).expression().toString());
}
return new SMTLibTerm(expression);
}
List<Term> arguments;
switch (label) {
case "exists":
Variable variable = (Variable) kList.get(0);
label = "exists ((" + variable.longName() + " " + variable.sort() + ")) ";
arguments = ImmutableList.of(kList.get(1));
break;
case "extract":
int beginIndex = ((IntToken) kList.get(1)).intValue();
int endIndex = ((IntToken) kList.get(2)).intValue() - 1;
label = "(_ extract " + endIndex + " " + beginIndex + ")";
arguments = ImmutableList.of(kList.get(0));
break;
default:
arguments = kList.getContents();
}
if (!arguments.isEmpty()) {
StringBuilder sb = new StringBuilder();
sb.append("(");
sb.append(label);
for (Term argument : arguments) {
sb.append(" ");
sb.append(translate(argument).expression());
}
sb.append(")");
return new SMTLibTerm(sb);
} else {
return new SMTLibTerm(label);
}
}
@Override
public JavaSymbolicObject transform(BuiltinMap builtinMap) {
return new SMTLibTerm(abstractThroughAnonVariable(builtinMap,
new SMTTranslationFailure("BuiltinMap can be translated to Z3 only through fresh var")));
}
@Override
public SMTLibTerm transform(BoolToken boolToken) {
return new SMTLibTerm(Boolean.toString(boolToken.booleanValue()));
}
@Override
public SMTLibTerm transform(IntToken intToken) {
return new SMTLibTerm(intToken.javaBackendValue());
}
@Override
public SMTLibTerm transform(FloatToken floatToken) {
if (krunOptions.experimental.smt.floatsAsPO
&& (floatToken.bigFloatValue().isPositiveZero() || floatToken.bigFloatValue().isNegativeZero())) {
return new SMTLibTerm("float_zero");
}
assert !krunOptions.experimental.smt.floatsAsPO;
StringBuilder sb = new StringBuilder();
new Formatter(sb).format(
"((_ asFloat %d %d) roundNearestTiesToEven %s 0)",
floatToken.exponent(), floatToken.bigFloatValue().precision(),
floatToken.bigFloatValue().toString("%f"));
return new SMTLibTerm(sb);
}
@Override
public SMTLibTerm transform(BitVector bitVector) {
StringBuilder sb = new StringBuilder();
sb.append("#b");
for (int i = bitVector.bitwidth() - 1; i >= 0; --i) {
BigInteger value = bitVector.unsignedValue();
sb.append(value.testBit(i) ? "1" : "0");
}
return new SMTLibTerm(sb);
}
@Override
public SMTLibTerm transform(UninterpretedToken uninterpretedToken) {
if (uninterpretedToken.sort() == Sort.KVARIABLE) {
if (binders.contains(uninterpretedToken)) {
return new SMTLibTerm(uninterpretedToken.javaBackendValue());
} else {
throw new SMTTranslationFailure("unbounded K variable: " + uninterpretedToken);
}
}
if (tokenEncoding.get(uninterpretedToken) == null) {
tokenEncoding.put(uninterpretedToken, tokenEncoding.size());
}
return new SMTLibTerm(Integer.toString(tokenEncoding.get(uninterpretedToken)));
}
@Override
public JavaSymbolicObject transform(BuiltinList builtinList) {
return builtinList.toKore().accept(this);
}
@Override
public SMTLibTerm transform(Variable variable) {
variables.add(variable);
return new SMTLibTerm("|" + variable.longName() + "|");
}
}