private static IDictionary <Block, OuterDecl> GenerateCfgLemmas(
CFGRepr afterPassificationCfg,
CFGRepr finalCfg,
IDictionary <Block, Block> afterPassiveToFinalBlock,
HashSet <Block> reachableBlocks,
IDictionary <Block, IList <OuterDecl> > lemmaDecls,
VcPhaseLemmaManager vcPhaseLemmaManager,
Term cfgTerm,
IsaUniqueNamer lemmaNamer)
{
var blockToLemmaDecls = new Dictionary <Block, OuterDecl>();
foreach (var bAfterPassive in afterPassificationCfg.GetBlocksBackwards())
{
IEnumerable <Block> finalCfgSuccessors;
var isContainedInFinalCfg = afterPassiveToFinalBlock.TryGetValue(bAfterPassive, out var bFinal);
if (!isContainedInFinalCfg)
{
if (reachableBlocks.Contains(bAfterPassive))
{
finalCfgSuccessors =
GetNonEmptyReachableSuccessors(bAfterPassive, afterPassificationCfg, finalCfg,
afterPassiveToFinalBlock).Select(b => afterPassiveToFinalBlock[b]);
}
else
{
continue;
}
}
else
{
finalCfgSuccessors = finalCfg.GetSuccessorBlocks(bFinal);
}
var lemma = vcPhaseLemmaManager.GenerateCfgLemma(
bAfterPassive,
bFinal,
isContainedInFinalCfg,
afterPassificationCfg.GetSuccessorBlocks(bAfterPassive),
finalCfgSuccessors,
cfgTerm,
b => "cfg_" + lemmaNamer.GetName(b, b.Label),
(LemmaDecl)lemmaDecls[bAfterPassive].Last());
blockToLemmaDecls.Add(bAfterPassive, lemma);
}
return(blockToLemmaDecls);
}
public static Theory ProgramToVcProof(
string theoryName,
bool generateEndToEndProof,
CFGRepr finalCfg,
CFGRepr afterPassificationCfg,
IDictionary <Block, Block> afterPassiveToFinalBlock,
IDictionary <Block, Block> afterPassiveToOrigBlock,
IProgramAccessor passiveProgAccess,
IProgramAccessor beforePassiveProgAccess,
BoogieMethodData methodData,
ProgramVcProofData vcProofData,
IVariableTranslationFactory varFactory,
TypePremiseEraserFactory eraserFactory,
VCExpressionGenerator gen,
out Term vcAssm,
out LemmaDecl endToEndLemma)
{
var lemmaNamer = new IsaUniqueNamer();
var passiveLemmaManager = new VcPhaseLemmaManager(
vcProofData.VcBoogieInfo.VcInst,
methodData,
vcProofData.VcFunctions,
passiveProgAccess.BlockInfo(),
varFactory);
var afterPassiveReachableBlocks = ReachableBlocks(afterPassificationCfg);
var finalProgramLemmas =
GenerateVCLemmas(afterPassificationCfg, finalCfg, afterPassiveToFinalBlock, afterPassiveToOrigBlock,
afterPassiveReachableBlocks, passiveLemmaManager, vcProofData.VcHintManager, lemmaNamer);
var cfgProgramLemmas =
GenerateCfgLemmas(afterPassificationCfg, finalCfg, afterPassiveToFinalBlock,
afterPassiveReachableBlocks, finalProgramLemmas, passiveLemmaManager, passiveProgAccess.CfgDecl(),
lemmaNamer);
var afterPassificationDecls = new List <OuterDecl>();
foreach (var v in finalProgramLemmas.Values)
{
afterPassificationDecls.AddRange(v);
}
afterPassificationDecls.AddRange(cfgProgramLemmas.Values);
var afterPassificationLocale =
GenerateLocale("passification", passiveLemmaManager, afterPassificationDecls);
var passiveOuterDecls = new List <OuterDecl> {
vcProofData.VcLocale
};
passiveOuterDecls.Add(afterPassificationLocale);
//generate axiom
var axiomUniqueNamer = new IsaUniqueNamer();
var axId = 0;
var axiomToLemma = new Dictionary <Axiom, OuterDecl>();
var vcRewriteLemmaGen =
new VcRewriteLemmaGen(eraserFactory, VCExprToIsaTranslator.CreateNameBasedTranslator(new IsaUniqueNamer()));
var vcAxiomLemmaManager = new VcAxiomLemmaManager(
vcProofData.VcBoogieInfo.VcInstAxiom,
methodData,
vcProofData.VcFunctions,
vcRewriteLemmaGen, varFactory);
var axiomLocaleRequiredDecls = new List <OuterDecl>();
foreach (var axiom in vcProofData.VcBoogieInfo.VcAxiomsInfo)
{
if (axiom is VcBoogieAxiomInfo vcBoogieAxiom)
{
var axiomVcLemma =
vcAxiomLemmaManager.AxiomVcLemma(
axiomUniqueNamer.GetName(axiom, "axiom_vc_" + axId),
vcBoogieAxiom.Axiom,
vcBoogieAxiom.Expr,
out var requiredDecls);
axiomToLemma.Add(vcBoogieAxiom.Axiom, axiomVcLemma);
axiomLocaleRequiredDecls.AddRange(requiredDecls);
}
}
/* we add the required declarations for the axiom locale to the outer theory, since the axiom locale fixes variables that could clash
* with the declarations */
passiveOuterDecls.AddRange(axiomLocaleRequiredDecls);
var axiomLocale = GenerateLocale("axioms", vcAxiomLemmaManager, axiomToLemma.Values.ToList());
passiveOuterDecls.Add(axiomLocale);
if (generateEndToEndProof)
{
var endToEnd = new EndToEndVCProof(
methodData,
passiveProgAccess,
vcProofData.VcFunctions,
vcProofData.VcBoogieInfo,
afterPassificationCfg,
finalCfg,
afterPassificationLocale.Name + "." + cfgProgramLemmas[afterPassificationCfg.entry].Name,
axiomLocale.Name,
ax => axiomLocale.Name + "." + axiomToLemma[ax].Name,
varFactory,
vcProofData.VcTranslator,
eraserFactory,
gen);
passiveOuterDecls.AddRange(endToEnd.GenerateProof(out vcAssm, out endToEndLemma));
}
else
{
vcAssm = null;
endToEndLemma = null;
}
return
(new Theory(theoryName,
new List <string>
{
"Boogie_Lang.Semantics", "Boogie_Lang.Util", "Boogie_Lang.VCHints", "Boogie_Lang.VCPhaseML",
passiveProgAccess.TheoryName(), beforePassiveProgAccess.TheoryName()
},
passiveOuterDecls));
}
//assume that block identities in the two CFGs are the same (only edges may be different)
private static IDictionary <Block, IList <OuterDecl> > GenerateVCLemmas(
CFGRepr afterPassificationCfg,
CFGRepr finalCfg,
IDictionary <Block, Block> afterPassiveToFinalBlock,
IDictionary <Block, Block> afterPassiveToOrigBlock,
HashSet <Block> reachableBlocks,
VcPhaseLemmaManager vcPhaseLemmaManager,
VCHintManager vcHintManager,
IsaUniqueNamer lemmaNamer)
{
var blockToLemmaDecls = new Dictionary <Block, IList <OuterDecl> >();
foreach (var bAfterPassive in afterPassificationCfg.GetBlocksBackwards())
{
var result = new List <OuterDecl>();
if (afterPassiveToFinalBlock.TryGetValue(bAfterPassive, out var bFinal))
{
string vcHintsName = null;
if (vcHintManager.TryGetHints(afterPassiveToOrigBlock[bAfterPassive], out var hints,
out var requiredDecls))
{
//FIXME potential val name clash
vcHintsName = GetLemmaName(bAfterPassive, lemmaNamer) + "_hints";
var code = MLUtil.DefineVal(vcHintsName, MLUtil.MLList(hints));
//required declarations must be added first
result.AddRange(requiredDecls);
result.Add(new MLDecl(code));
}
result.Add(vcPhaseLemmaManager.GenerateBlockLemma(
bAfterPassive, bFinal, finalCfg.GetSuccessorBlocks(bFinal), GetLemmaName(bFinal, lemmaNamer),
vcHintsName));
//do not use identity of final CFG block to be consistent with other branches
blockToLemmaDecls.Add(bAfterPassive, result);
}
else if (reachableBlocks.Contains(bAfterPassive))
{
//block was removed after peephole but is reachable before peephole
if (bAfterPassive.Cmds.Count == 0)
{
//find the successors of b in the final cfg (i.e., the first non-empty reachable blocks)
var nonEmptyReachableSuccessors =
GetNonEmptyReachableSuccessors(bAfterPassive, afterPassificationCfg, finalCfg,
afterPassiveToFinalBlock);
//add lemma
var decls = new List <OuterDecl>
{
vcPhaseLemmaManager.GenerateEmptyBlockLemma(
bAfterPassive,
nonEmptyReachableSuccessors.Select(b => afterPassiveToFinalBlock[b]),
GetLemmaName(bAfterPassive, lemmaNamer))
};
blockToLemmaDecls.Add(bAfterPassive, decls);
}
else
{
throw new ProofGenUnexpectedStateException(
"Non-empty reachable block removed during peep-hole");
}
}
}
return(blockToLemmaDecls);
}
