public VcPhaseLemmaManager(VCInstantiation <Block> vcinst,
BoogieMethodData methodData,
IEnumerable <Function> vcFunctions,
IsaBlockInfo isaBlockInfo,
IVariableTranslationFactory variableFactory)
{
this.vcinst = vcinst;
this.methodData = methodData;
programVariables = methodData.AllVariables();
initState = IsaBoogieTerm.Normal(normalInitState);
this.isaBlockInfo = isaBlockInfo;
this.variableFactory = variableFactory;
boogieContext = new BoogieContextIsa(
IsaCommonTerms.TermIdentFromName("A"),
IsaCommonTerms.TermIdentFromName("M"),
IsaCommonTerms.TermIdentFromName("\\<Lambda>"),
IsaCommonTerms.TermIdentFromName("\\<Gamma>"),
IsaCommonTerms.TermIdentFromName("\\<Omega>")
);
var typeDeclTranslation = new ConcreteTypeDeclTranslation(boogieContext);
declToVCMapping = LemmaHelper.DeclToTerm(
((IEnumerable <NamedDeclaration>)methodData.Functions).Union(programVariables),
vcFunctions,
typeDeclTranslation,
uniqueNamer);
//separate unique namer for function interpretations (since they already have a name in uniqueNamer): possible clashes
funToInterpMapping = LemmaHelper.FunToTerm(methodData.Functions, new IsaUniqueNamer());
assmManager = new AssumptionManager(methodData.Functions, programVariables, variableFactory);
}
public VcAxiomLemmaManager(
VCInstantiation <VCExpr> vcAxiomInst,
BoogieMethodData methodData,
IEnumerable <Function> vcFunctions,
VcRewriteLemmaGen vcRewriteLemmaGen,
IVariableTranslationFactory variableFactory)
{
this.vcAxiomInst = vcAxiomInst;
this.methodData = methodData;
this.vcRewriteLemmaGen = vcRewriteLemmaGen;
this.variableFactory = variableFactory;
basicCmdIsaVisitor = new BasicCmdIsaVisitor(variableFactory);
boogieContext = new BoogieContextIsa(IsaCommonTerms.TermIdentFromName("A"),
IsaCommonTerms.TermIdentFromName("M"), IsaCommonTerms.TermIdentFromName("\\<Lambda>"),
IsaCommonTerms.TermIdentFromName("\\<Gamma>"), IsaCommonTerms.TermIdentFromName("\\<Omega>"));
var typeDeclTranslation = new ConcreteTypeDeclTranslation(boogieContext);
declToVCMapping =
LemmaHelper.DeclToTerm(
((IEnumerable <NamedDeclaration>)methodData.Functions).Union(methodData.Constants), vcFunctions,
typeDeclTranslation, uniqueNamer);
//separate unique namer for function interpretations (since they already have a name in uniqueNamer): possible clashes
funToInterpMapping = LemmaHelper.FunToTerm(methodData.Functions, new IsaUniqueNamer());
assmManager = new AssumptionManager(methodData.Functions, methodData.Constants, variableFactory);
}
public LemmaDecl GenerateEmptyBlockLemma(Block block, IEnumerable <Block> finalCfgSuccessors, string lemmaName)
{
//Term cmds = new TermList(cmdIsaVisitor.Translate(block.Cmds));
var blockDefName = isaBlockInfo.CmdsQualifiedName(block);
Term blockDefTerm = IsaCommonTerms.TermIdentFromName(blockDefName);
var cmdsReduce = IsaBoogieTerm.RedCmdList(boogieContext, blockDefTerm, initState, finalState);
var assumptions = new List <Term> {
cmdsReduce
};
if (finalCfgSuccessors.Any())
{
assumptions.Add(LemmaHelper.ConjunctionOfSuccessorBlocks(finalCfgSuccessors, declToVCMapping, vcinst));
}
var conclusion = ConclusionBlock(finalCfgSuccessors, normalInitState, finalState, declToVCMapping, vcinst);
var proof = new Proof(
new List <string>
{
"using assms",
"unfolding " + blockDefName + "_def",
"apply cases",
"by auto"
}
);
return(new LemmaDecl(lemmaName, ContextElem.CreateWithAssumptions(assumptions), conclusion, proof));
}
/// <summary>The returned list in-sync with <see cref="AllAssumptionLabels" />.</summary>
public IList <Term> AllAssumptions(
IDictionary <Function, TermIdent> funInterpMapping,
IDictionary <NamedDeclaration, Term> declToVCMapping,
Term state,
BoogieContextIsa boogieContext,
IVariableTranslation <Variable> varTranslation
)
{
var assumptions = new List <Term>();
foreach (var obj in _assumptionLabelMap.Keys)
{
if (obj is Function f)
{
assumptions.Add(LemmaHelper.FunctionCtxtWfAssm(f, funInterpMapping, boogieContext));
assumptions.Add(LemmaHelper.FunctionVcCorresAssm(f, funInterpMapping, declToVCMapping,
boogieContext));
}
else if (obj is Variable v)
{
assumptions.Add(LemmaHelper.LocalStateVariableAssumption(v, boogieContext.varContext, state,
declToVCMapping, varTranslation));
if (!TypeUtil.IsPrimitive(v.TypedIdent.Type))
{
assumptions.Add(LemmaHelper.VariableTypeAssumption(
v,
declToVCMapping[v],
new TypeIsaVisitor(_factory.CreateEmptyTranslation().TypeVarTranslation),
boogieContext.absValTyMap));
}
}
else if (obj is SpecialAssumptionsKind kind)
{
switch (kind)
{
case SpecialAssumptionsKind.TypeValClosed:
assumptions.Add(EndToEndAssumptions.ClosednessAssumption(boogieContext.absValTyMap));
break;
default:
throw new ArgumentOutOfRangeException();
}
}
}
return(assumptions);
}
private static Term ConclusionBlock(
IEnumerable <Block> b_successors,
Term normalInitState,
Term finalState,
IDictionary <NamedDeclaration, Term> declToVCMapping,
VCInstantiation <Block> vcinst,
bool useMagicFinalState = false)
{
if (useMagicFinalState)
{
return(new TermBinary(finalState, IsaBoogieTerm.Magic(), TermBinary.BinaryOpCode.Eq));
}
Term nonFailureConclusion =
new TermBinary(finalState, IsaBoogieTerm.Failure(), TermBinary.BinaryOpCode.Neq);
var normalFinalState = IsaCommonTerms.TermIdentFromName("n_s'");
Term ifNormalConclusionLhs = new TermBinary(finalState, IsaBoogieTerm.Normal(normalFinalState),
TermBinary.BinaryOpCode.Eq);
Term ifNormalConclusionRhs1 = new TermBinary(normalFinalState, normalInitState, TermBinary.BinaryOpCode.Eq);
var ifNormalConclusionRhs =
!b_successors.Any()
? ifNormalConclusionRhs1
: new TermBinary(
ifNormalConclusionRhs1,
LemmaHelper.ConjunctionOfSuccessorBlocks(b_successors, declToVCMapping, vcinst),
TermBinary.BinaryOpCode.And);
Term ifNormalConclusion =
new TermQuantifier(
TermQuantifier.QuantifierKind.ALL,
new List <Identifier> {
normalFinalState.Id
},
new TermBinary(
ifNormalConclusionLhs,
ifNormalConclusionRhs,
TermBinary.BinaryOpCode.Implies)
);
return(new TermBinary(nonFailureConclusion, ifNormalConclusion, TermBinary.BinaryOpCode.And));
}
public LemmaDecl GenerateBlockLemma(Block block, Block finalCfgBlock, IEnumerable <Block> finalCfgSuccessors,
string lemmaName, string vcHintsName)
{
var cmdsReduce = IsaBoogieTerm.RedCmdList(boogieContext,
IsaCommonTerms.TermIdentFromName(isaBlockInfo.CmdsQualifiedName(block)),
initState, finalState);
var vcAssm = vcinst.GetVCObjInstantiation(finalCfgBlock, declToVCMapping);
//do not use separate assumption, leads to issues
var conclusion = ConclusionBlock(finalCfgSuccessors, normalInitState, finalState, declToVCMapping, vcinst,
LemmaHelper.FinalStateIsMagic(block));
Term statement = TermBinary.MetaImplies(cmdsReduce, TermBinary.MetaImplies(vcAssm, conclusion));
var proof = BlockCorrectProof(block, finalCfgBlock, vcHintsName);
return(new LemmaDecl(lemmaName, ContextElem.CreateEmptyContext(), statement, proof));
}
public static IList <Tuple <TermIdent, TypeIsa> > GlobalFixedVariables(
BoogieContextIsa boogieContext,
IEnumerable <Function> functions,
IEnumerable <Variable> variables,
TermIdent normalInitState,
IDictionary <Function, TermIdent> funToInterpMapping,
IsaUniqueNamer uniqueNamer)
{
var absValType = new VarType("a");
var pureTyIsaTransformer = LemmaHelper.ConretePureTyIsaTransformer(absValType);
var result = new List <Tuple <TermIdent, TypeIsa> >
{
Tuple.Create((TermIdent)boogieContext.absValTyMap, IsaBoogieType.AbstractValueTyFunType(absValType)),
Tuple.Create((TermIdent)boogieContext.varContext, IsaBoogieType.VarContextType()),
Tuple.Create((TermIdent)boogieContext.funContext, IsaBoogieType.FunInterpType(absValType)),
Tuple.Create(normalInitState, IsaBoogieType.NormalStateType(absValType))
};
foreach (var kv in funToInterpMapping)
{
result.Add(Tuple.Create(kv.Value, IsaBoogieType.BoogieFuncInterpType(absValType)));
var boogieFun = kv.Key;
//get untyped version, maybe should precompute this somewhere and re-use or get the data from the VC
TypeUtil.SplitTypeParams(boogieFun.TypeParameters, boogieFun.InParams.Select(v => v.TypedIdent.Type),
out var explicitTypeVars, out _);
var typeIsa = pureTyIsaTransformer.Translate(new Function(null, boogieFun.Name,
explicitTypeVars, boogieFun.InParams, boogieFun.OutParams[0]));
result.Add(Tuple.Create(
IsaCommonTerms.TermIdentFromName(uniqueNamer.GetName(boogieFun, boogieFun.Name)), typeIsa));
}
foreach (var v in variables)
{
var typeIsa = pureTyIsaTransformer.Translate(v);
result.Add(Tuple.Create(IsaCommonTerms.TermIdentFromName(uniqueNamer.GetName(v, v.Name)), typeIsa));
}
return(result);
}
private static HashSet <Block> ReachableBlocks(CFGRepr cfg)
{
var reachableBlocks = new HashSet <Block>();
var queue = new Queue <Block>();
reachableBlocks.Add(cfg.entry);
queue.Enqueue(cfg.entry);
while (queue.TryDequeue(out var b))
{
if (!LemmaHelper.FinalStateIsMagic(b))
{
//b's successors are not trivially unreachable
var successors = cfg.GetSuccessorBlocks(b);
foreach (var suc in successors)
{
reachableBlocks.Add(suc);
queue.Enqueue(suc);
}
}
}
return(reachableBlocks);
}
public LemmaDecl GenerateCfgLemma(
Block block,
Block finalCfgBlock,
bool isContainedInFinalCfg,
IEnumerable <Block> successors,
IEnumerable <Block> finalCfgSuccessors,
Term cfg,
Func <Block, string> cfgLemmaName,
LemmaDecl BlockLemma)
{
var red = IsaBoogieTerm.RedCFGMulti(
boogieContext,
cfg,
IsaBoogieTerm.CFGConfigNode(new NatConst(isaBlockInfo.BlockIds[block]),
IsaBoogieTerm.Normal(normalInitState)),
IsaBoogieTerm.CFGConfig(finalNode, finalState));
var assumption = new List <Term> {
red
};
var hasVcAssm = false;
if (isContainedInFinalCfg)
{
assumption.Add(vcinst.GetVCObjInstantiation(finalCfgBlock, declToVCMapping));
hasVcAssm = true;
}
else
{
//vc assumption is conjunction of reachable successors in final cfg
if (finalCfgSuccessors.Any())
{
assumption.Add(
LemmaHelper.ConjunctionOfSuccessorBlocks(finalCfgSuccessors, declToVCMapping, vcinst));
hasVcAssm = true;
}
}
Term conclusion = new TermBinary(finalState, IsaBoogieTerm.Failure(), TermBinary.BinaryOpCode.Neq);
var nodeLemma = isaBlockInfo.BlockCmdsMembershipLemma(block);
var outEdgesLemma = isaBlockInfo.OutEdgesMembershipLemma(block);
var proofMethods = new List <string>();
var eruleLocalBlock =
"erule " + (hasVcAssm ? ProofUtil.OF(BlockLemma.Name, "_", "assms(2)") : BlockLemma.Name);
if (isContainedInFinalCfg && LemmaHelper.FinalStateIsMagic(block))
{
proofMethods.Add("apply (rule converse_rtranclpE2[OF assms(1)], fastforce)");
proofMethods.Add(ProofUtil.Apply("rule " +
ProofUtil.OF("red_cfg_multi_backwards_step_magic", "assms(1)",
nodeLemma)));
proofMethods.Add(ProofUtil.By(eruleLocalBlock));
return(new LemmaDecl(cfgLemmaName(block), ContextElem.CreateWithAssumptions(assumption), conclusion,
new Proof(proofMethods)));
}
if (successors.Any())
{
proofMethods.Add("apply (rule converse_rtranclpE2[OF assms(1)], fastforce)");
var cfg_lemma = finalCfgSuccessors.Any()
? "red_cfg_multi_backwards_step"
: "red_cfg_multi_backwards_step_2";
proofMethods.Add(ProofUtil.Apply("rule " +
ProofUtil.OF(cfg_lemma, "assms(1)", nodeLemma)));
proofMethods.Add(ProofUtil.Apply(eruleLocalBlock));
proofMethods.Add("apply (" + ProofUtil.Simp(outEdgesLemma) + ")");
foreach (var bSuc in successors)
{
proofMethods.Add("apply (erule member_elim, simp)");
proofMethods.Add("apply (erule " + cfgLemmaName(bSuc) + ", simp?" + ")");
}
proofMethods.Add("by (simp add: member_rec(2))");
}
else
{
proofMethods.Add("apply (rule converse_rtranclpE2[OF assms(1)], fastforce)");
proofMethods.Add("apply (rule " + ProofUtil.OF("red_cfg_multi_backwards_step_no_succ", "assms(1)",
nodeLemma, outEdgesLemma) + ")");
if (isContainedInFinalCfg)
{
proofMethods.Add("using " + ProofUtil.OF(BlockLemma.Name, "_", "assms(2)") + " by blast");
}
else
{
proofMethods.Add("using " + BlockLemma.Name + " by blast");
}
}
return(new LemmaDecl(cfgLemmaName(block), ContextElem.CreateWithAssumptions(assumption), conclusion,
new Proof(proofMethods)));
}
