static CLAUSE inf_CreateURUnitResolvent(CLAUSE Clause, int i, SUBST Subst,
LIST FoundMap, FLAGSTORE Flags,
PRECEDENCE Precedence)
/**************************************************************
INPUT: A non-unit clause, a literal index from the clause,
a substitution, a list of pairs (l1, l2) of literals,
where l1 is from the non-unit clause and l2 is from a
unit clause, a flag store and a precedence.
RETURNS: The resolvent of this UR resolution inference. The
clause consists of the literal at index <i> in <Clause>
after application of <Subst>.
EFFECT: The flag store and the precedence are needed to create
the new clause.
***************************************************************/
{
CLAUSE Result, PClause;
LITERAL Lit;
TERM Atom;
LIST Parents;
NAT depth;
/* Create atom for resolvent */
Atom = subst_Apply(Subst, term_Copy(clause_GetLiteralAtom(Clause, i)));
/* Create clause */
Parents = list_List(Atom);
if (i <= clause_LastConstraintLitIndex(Clause))
Result = clause_Create(Parents, list_Nil(), list_Nil(), Flags, Precedence);
else if (i <= clause_LastAntecedentLitIndex(Clause))
Result = clause_Create(list_Nil(), Parents, list_Nil(), Flags, Precedence);
else
Result = clause_Create(list_Nil(), list_Nil(), Parents, Flags, Precedence);
list_Delete(Parents);
/* Get parent clauses and literals, calculate depth of resolvent */
Parents = list_List(Clause);
depth = clause_Depth(Clause);
for ( ; !list_Empty(FoundMap); FoundMap = list_Cdr(FoundMap)) {
Lit = list_PairSecond(list_Car(FoundMap)); /* Literal from unit */
PClause = clause_LiteralOwningClause(Lit);
Parents = list_Cons(PClause, Parents);
depth = misc_Max(depth, clause_Depth(PClause));
clause_AddParentClause(Result, clause_Number(PClause));
clause_AddParentLiteral(Result, clause_LiteralGetIndex(Lit));
Lit = list_PairFirst(list_Car(FoundMap)); /* Is from <Clause> */
clause_AddParentClause(Result, clause_Number(Clause));
clause_AddParentLiteral(Result, clause_LiteralGetIndex(Lit));
}
clause_SetFromURResolution(Result);
clause_SetDepth(Result, depth+1);
clause_SetSplitDataFromList(Result, Parents);
list_Delete(Parents);
return Result;
}
static CLAUSE red_CreateTerminatorEmptyClause(LIST FoundMap, FLAGSTORE Flags,
PRECEDENCE Precedence)
/**************************************************************
INPUT: A list of pairs (l1, l2), where l1 and l2 are unifiable
literals with complementary sign and a flag store.
More accurately, a substitution s exists,
such that l1 s = l2 s for all pairs (l1,l2) in
<FoundMap>.
For all literals l from the involved clauses
there exists one pair (l1,l2) in <FoundMap>
with l1=l or l2=l.
The flags store and the precedence are needed to create
the new clause.
RETURNS: A newly created empty clause, where the data
(parents,...) is set according to <FoundMap>.
***************************************************************/
{
CLAUSE Result, PClause;
LITERAL Lit;
LIST Parents;
NAT depth;
Result = clause_Create(list_Nil(), list_Nil(), list_Nil(), Flags, Precedence);
Parents = list_Nil();
depth = 0;
for (; !list_Empty(FoundMap); FoundMap = list_Cdr(FoundMap)) {
Lit = list_PairSecond(list_Car(FoundMap));
PClause = clause_LiteralOwningClause(Lit);
Parents = list_Cons(PClause, Parents);
depth = misc_Max(depth, clause_Depth(PClause));
clause_AddParentClause(Result, clause_Number(PClause));
clause_AddParentLiteral(Result, clause_LiteralGetIndex(Lit));
Lit = list_PairFirst(list_Car(FoundMap));
PClause = clause_LiteralOwningClause(Lit);
Parents = list_Cons(PClause, Parents);
depth = misc_Max(depth, clause_Depth(PClause));
clause_AddParentClause(Result, clause_Number(PClause));
clause_AddParentLiteral(Result, clause_LiteralGetIndex(Lit));
}
clause_SetFromTerminator(Result);
clause_SetDepth(Result, depth+1);
clause_SetSplitDataFromList(Result, Parents);
list_Delete(Parents);
return Result;
}
static void tab_ToSeqProofOrdered(TABLEAU T, LIST* Proof)
/**************************************************************
INPUT: A tableau <T>, a list of clauses <Proof> representing a
proof by reference
RETURNS: The sequential proof corresponding to the tableau.
***************************************************************/
{
LIST Scan;
BOOL RightSplitRead, LeftSplitRead;
if (tab_IsEmpty(T))
return;
Scan = tab_Clauses(T);
RightSplitRead = LeftSplitRead = FALSE;
while (!list_Empty(Scan)) {
/* insert left and right splits and descendants controlled by clause number */
if (!RightSplitRead && !tab_RightBranchIsEmpty(T) &&
clause_Number(list_Car(Scan)) <
clause_Number(list_Car(tab_RightSplitClauses(T)))) {
tab_ToSeqProofOrdered(tab_RightBranch(T), Proof);
RightSplitRead = TRUE;
}
if (!LeftSplitRead && !tab_LeftBranchIsEmpty(T) &&
clause_Number(list_Car(Scan)) <
clause_Number(tab_LeftSplitClause(T))) {
tab_ToSeqProofOrdered(tab_LeftBranch(T), Proof);
LeftSplitRead = TRUE;
}
(*Proof) = list_Cons(list_Car(Scan), *Proof);
Scan = list_Cdr(Scan);
}
/* if a split clause with descendants has not been inserted yet,
it been generated after all other clauses */
if (!RightSplitRead)
tab_ToSeqProofOrdered(tab_RightBranch(T), Proof);
if (!LeftSplitRead)
tab_ToSeqProofOrdered(tab_LeftBranch(T), Proof);
}
void tab_GetEarliestEmptyClauses(TABLEAU T, LIST* L)
/**************************************************************
INPUT : A tableau, a list of clauses by reference
RETURNS: Nothing.
EFFECTS: For each leaf node, adds empty clauses in
leaf nodes to <L>. If the leaf node contains only one
empty clause, it is added to <L> anyway.
If the leaf node contains more than one empty clause,
the earliest derived empty clause is added to <L>.
***************************************************************/
{
CLAUSE FirstEmpty;
LIST Scan;
if (tab_IsEmpty(T))
return;
if (tab_IsLeaf(T)) {
FirstEmpty = clause_Null();
for (Scan = tab_Clauses(T); !list_Empty(Scan); Scan = list_Cdr(Scan)) {
if (clause_IsEmptyClause(list_Car(Scan))) {
if (FirstEmpty == clause_Null())
FirstEmpty = list_Car(Scan);
else if (clause_Number(FirstEmpty) > clause_Number(list_Car(Scan)))
FirstEmpty = list_Car(Scan);
}
}
if (FirstEmpty != clause_Null())
(*L) = list_Cons(FirstEmpty, *L);
}
tab_GetEarliestEmptyClauses(tab_LeftBranch(T), L);
tab_GetEarliestEmptyClauses(tab_RightBranch(T), L);
}
void ana_AnalyzeProblem(PROOFSEARCH Search, LIST Clauses)
/**************************************************************
INPUT: A proofsearch object and a list of clauses.
RETURNS: Void.
EFFECT: Analyzes the clauses and sets the analyze variables.
Recomputes the weight for the clauses.
<Search> is modified according to clauses: non trivial domain number
is set
***************************************************************/
{
CLAUSE Clause;
ana_EQUATIONS = FALSE;
ana_PEQUATIONS = FALSE; /* Defaults for properties */
ana_NEQUATIONS = FALSE;
ana_FUNCTIONS = FALSE;
ana_FINDOMAIN = FALSE;
ana_NONTRIVDOMAIN = FALSE;
ana_MONADIC = FALSE;
ana_NONMONADIC = FALSE;
ana_PROP = FALSE;
ana_GROUND = FALSE;
ana_SORTRES = FALSE;
ana_USORTRES = FALSE;
ana_NONUNIT = FALSE;
ana_CONGROUND = TRUE;
ana_AXIOMCLAUSES = 0;
ana_CONCLAUSES = 0;
ana_NONHORNCLAUSES = 0;
list_Delete(ana_FINITEMONADICPREDICATES);
ana_FINITEMONADICPREDICATES = list_Nil();
if (list_Empty(Clauses))
return;
ana_FINITEMONADICPREDICATES = clause_FiniteMonadicPredicates(Clauses);
while (!list_Empty(Clauses)) {
Clause = (CLAUSE)list_Car(Clauses);
clause_UpdateWeight(Clause, prfs_Store(Search));
if (clause_GetFlag(Clause,CONCLAUSE))
ana_CONCLAUSES++;
else
ana_AXIOMCLAUSES++;
if (clause_NumOfSuccLits(Clause) > 1)
ana_NONHORNCLAUSES++;
if (ana_CONGROUND && clause_GetFlag(Clause,CONCLAUSE) &&
clause_MaxVar(Clause) != symbol_GetInitialStandardVarCounter())
ana_CONGROUND = FALSE;
if (!ana_PEQUATIONS && clause_ContainsPositiveEquations(Clause)) {
ana_PEQUATIONS = TRUE;
}
if (!ana_NEQUATIONS && clause_ContainsNegativeEquations(Clause)) {
ana_NEQUATIONS = TRUE;
}
if (!ana_MONADIC || !ana_NONMONADIC || !ana_PROP || !ana_GROUND)
clause_ContainsFolAtom(Clause,&ana_PROP,&ana_GROUND,&ana_MONADIC,&ana_NONMONADIC);
if (!ana_FUNCTIONS && clause_ContainsFunctions(Clause)) {
ana_FUNCTIONS = TRUE;
}
if (!ana_FINDOMAIN && clause_ImpliesFiniteDomain(Clause)) {
ana_FINDOMAIN = TRUE;
}
if (!ana_NONTRIVDOMAIN && clause_ImpliesNonTrivialDomain(Clause)) {
prfs_SetNonTrivClauseNumber(Search, clause_Number(Clause));
ana_NONTRIVDOMAIN = TRUE;
}
if (!ana_NONUNIT && clause_Length(Clause) > 1) {
ana_NONUNIT = TRUE;
}
if (!ana_SORTRES || !ana_USORTRES)
clause_ContainsSortRestriction(Clause,&ana_SORTRES,&ana_USORTRES);
Clauses = list_Cdr(Clauses);
}
ana_PUREEQUATIONAL = ((ana_PEQUATIONS || ana_NEQUATIONS) && !ana_MONADIC &&
!ana_NONMONADIC && !ana_PROP && !ana_GROUND);
ana_EQUATIONS = (ana_PEQUATIONS || ana_NEQUATIONS);
ana_PUREPROPOSITIONAL = (!ana_PEQUATIONS && !ana_NEQUATIONS &&!ana_MONADIC &&
!ana_NONMONADIC && ana_PROP);
}
LIST split_Backtrack(PROOFSEARCH PS, CLAUSE EmptyClause, CLAUSE* SplitClause)
/**************************************************************
INPUT: A proofsearch object, an empty clause and a pointer to a clause
used as return value.
RETURNS: A list of clauses deleted in the backtracked split levels.
<*SplitClause> is set to the split clause for the right branch
of the splitting step, or NULL, if the tableau is finished.
EFFECT: Backtracks the top of the split stack wrt the empty clause's level
***************************************************************/
{
SPLIT ActBacktrackSplit;
LIST RecoverList, Scan;
int Backtracklevel;
ActBacktrackSplit = (SPLIT)NULL;
RecoverList = split_RemoveUnnecessarySplits(PS, EmptyClause);
Backtracklevel = clause_SplitLevel(EmptyClause);
*SplitClause = NULL;
/* Backtrack all split levels bigger than the level of the empty clause */
while (!prfs_SplitStackEmpty(PS) && (prfs_ValidLevel(PS) > Backtracklevel)) {
ActBacktrackSplit = prfs_SplitStackTop(PS);
prfs_SplitStackPop(PS);
if (prfs_SplitFatherClause(ActBacktrackSplit) != (CLAUSE)NULL) {
RecoverList = list_Cons(prfs_SplitFatherClause(ActBacktrackSplit),
RecoverList);
prfs_SplitSetFatherClause(ActBacktrackSplit, NULL);
}
RecoverList = list_Nconc(prfs_SplitDeletedClauses(ActBacktrackSplit),
RecoverList);
clause_DeleteClauseList(prfs_SplitBlockedClauses(ActBacktrackSplit));
prfs_SplitFree(ActBacktrackSplit);
prfs_DecValidLevel(PS);
}
/* Backtrack further for all right branches on top of the stack */
while (!prfs_SplitStackEmpty(PS) &&
list_Empty(prfs_SplitBlockedClauses(prfs_SplitStackTop(PS)))) {
ActBacktrackSplit = prfs_SplitStackTop(PS);
prfs_SplitStackPop(PS);
if (prfs_SplitFatherClause(ActBacktrackSplit) != (CLAUSE)NULL)
RecoverList = list_Cons(prfs_SplitFatherClause(ActBacktrackSplit),
RecoverList);
RecoverList = list_Nconc(prfs_SplitDeletedClauses(ActBacktrackSplit),
RecoverList);
prfs_SplitFree(ActBacktrackSplit);
prfs_DecValidLevel(PS);
}
if (!prfs_SplitStackEmpty(PS)) {
/* Enter the right branch of the splitting step */
int SplitMinus1;
LIST RightClauses;
SplitMinus1 = prfs_ValidLevel(PS) - 1;
ActBacktrackSplit = prfs_SplitStackTop(PS);
RecoverList = list_Nconc(prfs_SplitDeletedClauses(ActBacktrackSplit),
RecoverList);
prfs_SplitSetDeletedClauses(ActBacktrackSplit, list_Nil());
RecoverList = split_DeleteInvalidClausesFromList(PS, SplitMinus1,
RecoverList);
RightClauses = prfs_SplitBlockedClauses(ActBacktrackSplit);
prfs_SplitSetBlockedClauses(ActBacktrackSplit, list_Nil());
for (Scan = RightClauses; !list_Empty(Scan); Scan = list_Cdr(Scan)) {
if (clause_Number(list_Car(Scan)) == 0) {
/* Found the right clause, the negation clauses have number -1. */
#ifdef CHECK
if (*SplitClause != NULL) {
misc_StartErrorReport();
misc_ErrorReport("\n In split_Backtrack:");
misc_ErrorReport(" Found two blocked clauses ");
misc_ErrorReport("\n with clause number 0 (this marks the clause ");
misc_ErrorReport("\n for the right branch of the tableau).");
misc_FinishErrorReport();
}
#endif
*SplitClause = list_Car(Scan);
}
clause_NewNumber((CLAUSE) list_Car(Scan));
clause_AddParentClause((CLAUSE) list_Car(Scan), clause_Number(EmptyClause));
clause_AddParentLiteral((CLAUSE) list_Car(Scan), 0); /* dummy literal */
}
#ifdef CHECK
if (*SplitClause == NULL) {
misc_StartErrorReport();
misc_ErrorReport("\n In split_Backtrack: Didn´t find a blocked clause");
misc_ErrorReport("\n with clause number 0. (this marks the clause ");
misc_ErrorReport("\n for the right branch of the tableau).");
misc_FinishErrorReport();
}
#endif
RecoverList = list_Nconc(RightClauses, RecoverList);
/* Then, delete clauses from current level (Hack) */
prfs_DecValidLevel(PS);
prfs_MoveInvalidClausesDocProof(PS);
split_DeleteInvalidClausesFromStack(PS);
prfs_IncValidLevel(PS);
} else {
/* Don't delete clauses from current level (split is top level) */
prfs_MoveInvalidClausesDocProof(PS);
for (Scan = RecoverList; !list_Empty(Scan); Scan = list_Cdr(Scan))
prfs_InsertDocProofClause(PS, list_Car(Scan));
list_Delete(RecoverList);
RecoverList = list_Nil();
}
prfs_SetLastBacktrackLevel(PS, prfs_ValidLevel(PS));
return RecoverList;
}
LIST dp_PrintProof(PROOFSEARCH Search, LIST Clauses, const char *FilePrefix)
/*********************************************************
INPUT: A proofsearch object, a list of empty clauses and
the prefix of the output file name.
RETURNS: The list of clauses required for the proof.
MEMORY: The returned list must be freed.
EFFECT: The proof is printed both to standard output and
to the file <FilePrefix>.prf.
**********************************************************/
{
LIST ProofClauses,Scan,EmptyClauses,AllClauses, ReducedProof;
LIST Missing, Incomplete, SplitClauses;
FLAGSTORE Flags;
Flags = prfs_Store(Search);
Missing = pcheck_ConvertParentsInSPASSProof(Search, Clauses);
if (!list_Empty(Missing)) {
puts("\nNOTE: clauses with following numbers have not been found:");
for (; !list_Empty(Missing); Missing = list_Pop(Missing))
printf("%d ", (int)list_Car(Missing));
putchar('\n');
}
EmptyClauses = list_Copy(Clauses);
ProofClauses = list_Nil();
AllClauses = list_Nconc(list_Copy(prfs_DocProofClauses(Search)),
list_Nconc(list_Copy(prfs_UsableClauses(Search)),
list_Copy(prfs_WorkedOffClauses(Search))));
/*
* collect proof clauses by noodling upward in the
* proof tree, starting from <EmptyClauses>.
* Before, add all splitting clauses to avoid gaps in split tree
*/
SplitClauses = list_Nil();
for (Scan = AllClauses; !list_Empty(Scan); Scan = list_Cdr(Scan))
if (clause_IsFromSplitting(list_Car(Scan)))
SplitClauses = list_Cons(list_Car(Scan), SplitClauses);
/* mark all needed clauses */
pcheck_ClauseListRemoveFlag(EmptyClauses, MARKED);
pcheck_ClauseListRemoveFlag(AllClauses, MARKED);
pcheck_MarkRecursive(EmptyClauses);
pcheck_MarkRecursive(SplitClauses);
/* collect all marked clauses */
ProofClauses = list_Nil();
for (Scan = AllClauses; !list_Empty(Scan); Scan = list_Cdr(Scan)) {
if (clause_GetFlag(list_Car(Scan), MARKED))
ProofClauses = list_Cons(list_Car(Scan), ProofClauses);
}
/* build reduced proof */
ProofClauses = list_Nconc(ProofClauses, list_Copy(EmptyClauses));
ProofClauses = pcheck_ClauseNumberMergeSort(ProofClauses);
ReducedProof = pcheck_ReduceSPASSProof(ProofClauses);
dp_SetProofDepth(pcheck_SeqProofDepth(ReducedProof));
pcheck_ParentPointersToParentNumbers(AllClauses);
pcheck_ParentPointersToParentNumbers(Clauses);
/* check reduced proof for clauses whose parents have been marked as
incomplete (HIDDEN flag) by ConvertParentsInSPASSProof */
Incomplete = list_Nil();
for (Scan = ReducedProof; !list_Empty(Scan); Scan = list_Cdr(Scan)) {
if (clause_GetFlag(list_Car(Scan), HIDDEN))
Incomplete = list_Cons(list_Car(Scan), Incomplete);
}
if (!list_Empty(Incomplete)) {
puts("NOTE: Following clauses in reduced proof have incomplete parent sets:");
for (Scan = Incomplete; !list_Empty(Scan); Scan = list_Cdr(Scan))
printf("%d ", clause_Number(list_Car(Scan)));
putchar('\n');
}
printf("\n\nHere is a proof with depth %d, length %d :\n",
dp_ProofDepth(), list_Length(ReducedProof));
clause_ListPrint(ReducedProof);
if (flag_GetFlagValue(Flags, flag_FPDFGPROOF))
dp_FPrintDFGProof(ReducedProof, FilePrefix, Flags, prfs_Precedence(Search));
fflush(stdout);
list_Delete(EmptyClauses);
list_Delete(AllClauses);
list_Delete(ProofClauses);
list_Delete(SplitClauses);
list_Delete(Incomplete);
return ReducedProof;
}
