ord_RESULT rpos_GreaterEqual(TERM T1, TERM T2, BOOL VarIsConst)
/**************************************************************
INPUT: Two terms.
RETURNS: ord_GREATER_THAN if <T1> is greater than <T2>
ord_EQUAL if both terms are equal
ord_UNCOMPARABLE otherwise.
CAUTION: The precedence from the order module is used to determine
the precedence of symbols!
If <VarIsConst> is set then variables are interpreted as constants
with lowest precedence. They are ranked to each other using
their variable index.
***************************************************************/
{
LIST scan;
if (term_IsVariable(T1)) {
if (term_EqualTopSymbols(T1, T2))
return ord_Equal(); /* T2 is the same variable */
else if(VarIsConst && term_IsVariable(T2)) {
if(term_TopSymbol(T1) > term_TopSymbol(T2))
return ord_GreaterThan();
else
return ord_Uncomparable();
}
else
/* A variable can't be greater than another term */
return ord_Uncomparable();
} else if (!VarIsConst && term_IsVariable(T2)) { /* T1 isn't a variable */
if (term_ContainsSymbol(T1, term_TopSymbol(T2)))
return ord_GreaterThan();
else
return ord_Uncomparable();
} else if(VarIsConst && term_IsVariable(T2)){
return ord_GreaterThan();
} else if (term_EqualTopSymbols(T1, T2)) {
if (symbol_HasProperty(term_TopSymbol(T1), ORDMUL))
return rpos_MulGreaterEqual(T1, T2, VarIsConst);
else
return rpos_LexGreaterEqual(T1, T2, VarIsConst);
} else {
if (symbol_PrecedenceGreater(ord_PRECEDENCE, term_TopSymbol(T1),
term_TopSymbol(T2))) {
/* Different top symbols, symbol of T1 > symbol of T2. */
/* Try if T1 > each argument of T2. */
for (scan = term_ArgumentList(T2); !list_Empty(scan); scan = list_Cdr(scan))
if (!rpos_Greater(T1, list_Car(scan), VarIsConst))
return ord_Uncomparable();
return ord_GreaterThan();
} else {
/* Try to find an argument of T1 that is >= T2 */
for (scan = term_ArgumentList(T1); !list_Empty(scan); scan = list_Cdr(scan))
if (!ord_IsUncomparable(rpos_GreaterEqual(list_Car(scan), T2, VarIsConst)))
return ord_GreaterThan(); /* Argument of T1 >= T2 */
return ord_Uncomparable();
}
}
}
ord_RESULT rpos_ContGreaterEqual(CONTEXT C1, TERM T1, CONTEXT C2, TERM T2)
/**************************************************************
INPUT: Two contexts and two terms.
RETURNS: ord_GREATER_THAN if <T1> is greater than <T2>
ord_EQUAL if both terms are equal
ord_UNCOMPARABLE otherwise.
EFFECT: Variable bindings are considered.
CAUTION: The precedence from the order module is used to determine
the precedence of symbols!
***************************************************************/
{
LIST scan;
T1 = cont_Deref(&C1, T1);
T2 = cont_Deref(&C2, T2);
if (term_IsVariable(T1)) {
if (term_EqualTopSymbols(T1, T2))
return ord_Equal(); /* T2 is the same variable */
else
/* A variable can't be greater than another term */
return ord_Uncomparable();
} else if (term_IsVariable(T2)) { /* T1 isn't a variable */
if (cont_TermContainsSymbol(C1, T1, term_TopSymbol(T2)))
return ord_GreaterThan();
else
return ord_Uncomparable();
} else if (term_EqualTopSymbols(T1, T2)) {
if (symbol_HasProperty(term_TopSymbol(T1), ORDMUL))
return rpos_ContMulGreaterEqual(C1, T1, C2, T2);
else
return rpos_ContLexGreaterEqual(C1, T1, C2, T2);
} else {
if (symbol_PrecedenceGreater(ord_PRECEDENCE, term_TopSymbol(T1),
term_TopSymbol(T2))) {
/* Different top symbols, symbol of T1 > symbol of T2. */
/* Try if T1 > each argument of T2. */
for (scan = term_ArgumentList(T2); !list_Empty(scan); scan = list_Cdr(scan))
if (!rpos_ContGreater(C1, T1, C2, list_Car(scan)))
return ord_Uncomparable();
return ord_GreaterThan();
} else {
/* Try to find an argument of T1 that is >= T2 */
for (scan = term_ArgumentList(T1); !list_Empty(scan); scan = list_Cdr(scan))
if (!ord_IsUncomparable(rpos_ContGreaterEqual(C1,list_Car(scan),C2,T2)))
return ord_GreaterThan(); /* Argument of T1 >= T2 */
return ord_Uncomparable();
}
}
}
BOOL rpos_ContEqual(CONTEXT C1, TERM T1, CONTEXT C2, TERM T2)
/**************************************************************
INPUT: Two contexts and two terms.
RETURNS: TRUE, if <T1> is equal to <T2> and
FALSE otherwise.
EFFECT: Variable bindings are considered.
***************************************************************/
{
LIST l1, l2;
T1 = cont_Deref(&C1, T1);
T2 = cont_Deref(&C2, T2);
if (!term_EqualTopSymbols(T1, T2))
return FALSE;
else if (!term_IsComplex(T1))
return TRUE;
else {
if (symbol_HasProperty(term_TopSymbol(T1), ORDMUL)) {
l1 = rpos_ContMultisetDifference(C1, T1, C2, T2);
if (list_Empty(l1))
return TRUE;
else {
list_Delete(l1);
return FALSE;
}
} else { /* LEX case */
for (l1 = term_ArgumentList(T1), l2 = term_ArgumentList(T2);
!list_Empty(l1) && rpos_ContEqual(C1,list_Car(l1),C2,list_Car(l2));
l1 = list_Cdr(l1), l2 = list_Cdr(l2)); /* empty body */
return list_Empty(l1); /* All arguments were equal */
}
}
}
BOOL rpos_Equal(TERM T1, TERM T2)
/**************************************************************
INPUT: Two terms.
RETURNS: TRUE, if <T1> is equal to <T2> and
FALSE otherwise.
***************************************************************/
{
LIST l1, l2;
if (!term_EqualTopSymbols(T1, T2))
return FALSE;
else if (!term_IsComplex(T1)) /* Equal variable or constant */
return TRUE;
else {
if (symbol_HasProperty(term_TopSymbol(T1), ORDMUL)) { /* MUL case */
l1 = rpos_MultisetDifference(T1, T2);
if (list_Empty(l1))
return TRUE;
else {
list_Delete(l1);
return FALSE;
}
} else { /* LEX case */
for (l1 = term_ArgumentList(T1), l2 = term_ArgumentList(T2);
!list_Empty(l1) && rpos_Equal(list_Car(l1), list_Car(l2));
l1 = list_Cdr(l1), l2 = list_Cdr(l2))
/* empty */;
return list_Empty(l1); /* All arguments were equal */
}
}
}
BOOL cont_TermEqual(CONTEXT Context1, TERM Term1, CONTEXT Context2, TERM Term2)
/*********************************************************
INPUT: Two terms and two contexts.
RETURNS: TRUE iff the two terms are equal, where
variables are interpreted with respect to
the bindings in the contexts.
********************************************************/
{
#ifdef CHECK
if (!(term_IsTerm(Term1) && term_IsTerm(Term2))) {
misc_StartErrorReport();
misc_ErrorReport("\n In cont_TermEqual: Input terms are corrupted.\n");
misc_FinishErrorReport();
}
#endif
Term1 = cont_Deref(&Context1,Term1);
Term2 = cont_Deref(&Context2,Term2);
if (!term_EqualTopSymbols(Term1, Term2))
return FALSE;
else if (term_ArgumentList(Term1)) {
LIST Scan1, Scan2;
for (Scan1=term_ArgumentList(Term1), Scan2=term_ArgumentList(Term2);
list_Exist(Scan1) && list_Exist(Scan2);
Scan1=list_Cdr(Scan1), Scan2=list_Cdr(Scan2))
if (!cont_TermEqual(Context1,list_Car(Scan1), Context2,list_Car(Scan2)))
return FALSE;
return (list_Empty(Scan1) ? list_Empty(Scan2) : FALSE);
} else
return TRUE;
}
BOOL cont_TermEqual(CONTEXT GlobalContext1, CONTEXT TermContext1, TERM Term1,
CONTEXT GlobalContext2, CONTEXT TermContext2, TERM Term2)
/*********************************************************
INPUT: Two terms and two local contexts for the terms and
two global contexts
RETURNS: TRUE iff the two terms are equal, where
variables are interpreted with respect to
the bindings in the contexts.
CAUTION: Variables of <Term1> and <Term2> are bound in
<TermContext1> and <TermContext2> respectively and
the index variables are bound in <GlobalContext1>
and <GlobalContext2> respectively.
********************************************************/
{
#ifdef CHECK
if (!(term_IsTerm(Term1) && term_IsTerm(Term2))) {
misc_StartErrorReport();
misc_ErrorReport("\n In cont_TermEqual: Input terms are corrupted.\n");
misc_FinishErrorReport();
}
#endif
Term1 = cont_Deref(GlobalContext1,&TermContext1,Term1);
Term2 = cont_Deref(GlobalContext2,&TermContext2,Term2);
if (!term_EqualTopSymbols(Term1, Term2))
return FALSE;
else if (term_ArgumentList(Term1)) {
LIST Scan1, Scan2;
for (Scan1=term_ArgumentList(Term1), Scan2=term_ArgumentList(Term2);
list_Exist(Scan1) && list_Exist(Scan2);
Scan1=list_Cdr(Scan1), Scan2=list_Cdr(Scan2))
if (!cont_TermEqual(GlobalContext1, TermContext1,list_Car(Scan1),
GlobalContext2, TermContext2,list_Car(Scan2)))
return FALSE;
return (list_Empty(Scan1) ? list_Empty(Scan2) : FALSE);
} else
return TRUE;
}
static LIST ana_CalculateFunctionPrecedence(LIST Functions, LIST Clauses,
FLAGSTORE Flags)
/**************************************************************
INPUT: A list of functions, a list of clauses and
a flag store.
RETURNS: A list of function symbols, which should be used
for setting the symbol precedence. The list is sorted
in descending order, that means function with highest
precedence come first.
EFFECT: Analyzes the clauses to build a directed graph G with
function symbol as nodes. An edge (f,g) or in G means
f should have lower precedence than g.
An edge (f,g) or (g,f) is created if there's an equation
equal(f(...), g(...)) in the clause list.
The direction of the edge depends on the degree of the
nodes and the symbol arity.
Then find the strongly connected components of this
graph.
The "Ordering" flag will be set in the flag store.
CAUTION: The value of "ana_PEQUATIONS" must be up to date.
***************************************************************/
{
GRAPH graph;
GRAPHNODE n1, n2;
LIST result, scan, scan2, distrPairs;
int i, j;
SYMBOL s, Add, Mult;
if (list_Empty(Functions))
return Functions; /* Problem contains no functions */
else if (!ana_PEQUATIONS) {
Functions = list_NumberSort(Functions, (NAT (*)(POINTER)) symbol_PositiveArity);
return Functions;
}
graph = graph_Create();
/* First create the nodes: one node for every function symbol. */
for (; !list_Empty(Functions); Functions = list_Pop(Functions))
graph_AddNode(graph, symbol_Index((SYMBOL)list_Car(Functions)));
/* Now sort the node list wrt descending symbol arity. */
graph_SortNodes(graph, ana_NodeGreater);
/* A list of pairs (add, multiply) of distributive symbols */
distrPairs = list_Nil();
/* Now add undirected edges: there's an undirected edge between */
/* two nodes if the symbols occur as top symbols in a positive */
/* equation. */
for (scan = Clauses; !list_Empty(scan); scan = list_Cdr(scan)) {
CLAUSE c = list_Car(scan);
for (i = clause_FirstSuccedentLitIndex(c);
i <= clause_LastSuccedentLitIndex(c); i++) {
if (clause_LiteralIsEquality(clause_GetLiteral(c, i))) {
/* Consider only positive equations */
TERM t1, t2;
if (fol_DistributiveEquation(clause_GetLiteralAtom(c,i), &Add, &Mult)) {
/* Add a pair (Add, Mult) to <distrTerms> */
distrPairs = list_Cons(list_PairCreate((POINTER)Add, (POINTER)Mult),
distrPairs);
/*fputs("\nDISTRIBUTIVITY: ", stdout);
term_PrintPrefix(clause_GetLiteralAtom(c,i));
fputs(" Add=", stdout); symbol_Print(Add);
fputs(" Mult=", stdout); symbol_Print(Mult); fflush(stdout); DBG */
}
t1 = term_FirstArgument(clause_GetLiteralAtom(c, i));
t2 = term_SecondArgument(clause_GetLiteralAtom(c, i));
if (!term_IsVariable(t1) && !term_IsVariable(t2) &&
!term_EqualTopSymbols(t1, t2) && /* No self loops! */
!term_HasSubterm(t1, t2) && /* No subterm property */
!term_HasSubterm(t2, t1)) {
n1 = graph_GetNode(graph, symbol_Index(term_TopSymbol(t1)));
n2 = graph_GetNode(graph, symbol_Index(term_TopSymbol(t2)));
/* Create an undirected edge by adding two directed edges */
graph_AddEdge(n1, n2);
graph_AddEdge(n2, n1);
/* Use the node info for the degree of the node */
ana_IncNodeDegree(n1);
ana_IncNodeDegree(n2);
}
}
}
}
/* putchar('\n');
for (scan = graph_Nodes(graph); !list_Empty(scan); scan = list_Cdr(scan)) {
n1 = list_Car(scan);
printf("(%s,%d,%u), ",
symbol_Name(symbol_GetSigSymbol(graph_NodeNumber(n1))),
graph_NodeNumber(n1), ana_NodeDegree(n1));
}
graph_Print(graph); fflush(stdout); DBG */
graph_DeleteDuplicateEdges(graph);
/* Transform the undirected graph into a directed graph. */
for (scan = graph_Nodes(graph); !list_Empty(scan); scan = list_Cdr(scan)) {
n1 = list_Car(scan);
result = list_Nil(); /* Collect edges from n1 that shall be deleted */
for (scan2 = graph_NodeNeighbors(n1); !list_Empty(scan2);
scan2 = list_Cdr(scan2)) {
int a1, a2;
n2 = list_Car(scan2);
/* Get the node degrees in the undirected graph with multiple edges */
i = ana_NodeDegree(n1);
j = ana_NodeDegree(n2);
a1 = symbol_Arity(symbol_GetSigSymbol(graph_NodeNumber(n1)));
a2 = symbol_Arity(symbol_GetSigSymbol(graph_NodeNumber(n2)));
if (i > j || (i==j && a1 >= a2)) {
/* symbol2 <= symbol1, so remove edge n1 -> n2 */
result = list_Cons(n2, result);
}
if (i < j || (i==j && a1 <= a2)) {
/* symbol1 <= symbol2, so remove edge n2 -> n1 */
graph_DeleteEdge(n2, n1);
}
/* NOTE: If (i==j && a1==a2) both edges are deleted! */
}
/* Now delete edges from n1 */
for ( ; !list_Empty(result); result = list_Pop(result))
graph_DeleteEdge(n1, list_Car(result));
}
if (!list_Empty(distrPairs) && !ana_BidirectionalDistributivity(distrPairs)) {
/* Enable RPO ordering, otherwise the default KBO will be used. */
flag_SetFlagIntValue(Flags, flag_ORD, flag_ORDRPOS);
}
/* Now examine the list of distribute symbols */
/* since they've highest priority. */
for ( ; !list_Empty(distrPairs); distrPairs = list_Pop(distrPairs)) {
scan = list_Car(distrPairs); /* A pair (Add, Mult) */
/* Addition */
n1 = graph_GetNode(graph,
symbol_Index((SYMBOL)list_PairFirst(scan)));
/* Multiplication */
n2 = graph_GetNode(graph,
symbol_Index((SYMBOL)list_PairSecond(scan)));
/* Remove any edges between n1 and n2 */
graph_DeleteEdge(n1, n2);
graph_DeleteEdge(n2, n1);
/* Add one edge Addition -> Multiplication */
graph_AddEdge(n1, n2);
list_PairFree(scan);
}
/* fputs("\n------------------------",stdout);
graph_Print(graph); fflush(stdout); DBG */
/* Calculate the strongly connected components of the graph. */
/* <i> is the number of SCCs. */
i = graph_StronglyConnectedComponents(graph);
/* Now create the precedence list by scanning the nodes. */
/* If there's a link between two strongly connected components */
/* c1 and c2 then component_num(c1) > component_num(c2), so the */
/* following code creates a valid precedence list in descending */
/* order. */
result = list_Nil();
while (i-- > 0) { /* for i = numberOfSCCs -1 dowto 0 */
for (scan = graph_Nodes(graph); !list_Empty(scan); scan = list_Cdr(scan)) {
n1 = list_Car(scan);
if (graph_NodeCompNum(n1) == i) {
/* The symbol represented by the node <n> belongs to component <i> */
s = symbol_GetSigSymbol(graph_NodeNumber(n1));
result = list_Cons((POINTER)s, result);
}
}
}
/* putchar('\n');
for (scan = result; !list_Empty(scan); scan = list_Cdr(scan)) {
s = (SYMBOL) list_Car(scan);
symbol_Print(s);
fputs(" > ", stdout);
}
putchar('\n'); fflush(stdout); DBG */
graph_Delete(graph);
return result;
}
BOOL cont_TermEqualModuloBindings(CONTEXT IndexContext, CONTEXT CtL, TERM TermL,
CONTEXT CtR, TERM TermR)
/*********************************************************
INPUT: Two contexts, two terms.
RETURNS: The boolean value TRUE if the terms are equal.
CAUTION: EQUAL FUNCTION- OR PREDICATE SYMBOLS SHARE THE
SAME ARITY. THIS IS NOT VALID FOR JUNCTORS!
*******************************************************/
{
#ifdef CHECK
if (!(term_IsTerm(TermL) && term_IsTerm(TermR))) {
misc_StartErrorReport();
misc_ErrorReport("\n In cont_TermEqualModuloBindings: Input terms are corrupted.\n");
misc_FinishErrorReport();
}
#endif
while (term_IsVariable(TermL)) {
SYMBOL TermTop;
TermTop = term_TopSymbol(TermL);
if (symbol_IsIndexVariable(TermTop))
CtL = IndexContext;
else if (CtL == cont_InstanceContext())
break;
if (cont_VarIsBound(CtL, TermTop)) {
CONTEXT CHelp;
CHelp = cont_ContextBindingContext(CtL, TermTop);
TermL = cont_ContextBindingTerm(CtL, TermTop);
CtL = CHelp;
} else
break;
}
while (term_IsVariable(TermR)) {
SYMBOL TermTop;
TermTop = term_TopSymbol(TermR);
if (symbol_IsIndexVariable(TermTop))
CtR = IndexContext;
else if (CtR == cont_InstanceContext())
break;
if (cont_VarIsBound(CtR, TermTop)) {
CONTEXT CHelp;
CHelp = cont_ContextBindingContext(CtR, TermTop);
TermR = cont_ContextBindingTerm(CtR, TermTop);
CtR = CHelp;
} else
break;
}
if (!term_EqualTopSymbols(TermL, TermR))
return FALSE;
else
if (term_IsVariable(TermL)) {
if (CtL == CtR)
return TRUE;
else
return FALSE;
}
else
if (term_IsComplex(TermL)) {
LIST ScanL, ScanR;
for (ScanL=term_ArgumentList(TermL), ScanR=term_ArgumentList(TermR);
list_Exist(ScanL) && list_Exist(ScanR);
ScanL=list_Cdr(ScanL), ScanR=list_Cdr(ScanR))
if (!cont_TermEqualModuloBindings(IndexContext, CtL, list_Car(ScanL),
CtR, list_Car(ScanR)))
return FALSE;
return (list_Empty(ScanL) ? list_Empty(ScanR) : FALSE);
}
else
return TRUE;
}
ord_RESULT rpos_ContGreaterEqual(CONTEXT GlobalC1, CONTEXT TermC1, TERM T1,
CONTEXT GlobalC2, CONTEXT TermC2, TERM T2,
BOOL VarIsConst)
/**************************************************************
INPUT: Two contexts and two terms.
RETURNS: ord_GREATER_THAN if <T1> is greater than <T2>
ord_EQUAL if both terms are equal
ord_UNCOMPARABLE otherwise.
EFFECT: Variable bindings are considered.
CAUTION: The precedence from the order module is used to determine
the precedence of symbols!
If <VarIsConst> is set then variables are interpreted as constants
with lowest precedence. They are ranked to each other using
their variable index.
ASSUMPTION: All index variables of <T1> and <T2> are bound in
<GlobalC1> and <GlobalCt2>, respectively
***************************************************************/
{
LIST scan;
T1 = cont_Deref(GlobalC1, &TermC1, T1);
T2 = cont_Deref(GlobalC2, &TermC2, T2);
if (term_IsVariable(T1)) {
if (term_EqualTopSymbols(T1, T2))
return ord_Equal(); /* T2 is the same variable */
else
/* A variable can't be greater than another term */
return ord_Uncomparable();
} else if (term_IsVariable(T2)) { /* T1 isn't a variable */
if (cont_TermContainsSymbol(GlobalC1, TermC1, T1, term_TopSymbol(T2)))
return ord_GreaterThan();
else
return ord_Uncomparable();
} else if (term_EqualTopSymbols(T1, T2)) {
if (symbol_HasProperty(term_TopSymbol(T1), ORDMUL))
return rpos_ContMulGreaterEqual(GlobalC1, TermC1, T1,
GlobalC2, TermC2, T2, VarIsConst);
else
return rpos_ContLexGreaterEqual(GlobalC1, TermC1, T1,
GlobalC2, TermC2, T2, VarIsConst);
} else {
if (symbol_PrecedenceGreater(ord_PRECEDENCE, term_TopSymbol(T1),
term_TopSymbol(T2))) {
/* Different top symbols, symbol of T1 > symbol of T2. */
/* Try if T1 > each argument of T2. */
for (scan = term_ArgumentList(T2); !list_Empty(scan); scan = list_Cdr(scan))
if (!rpos_ContGreaterAux(GlobalC1, TermC1, T1,
GlobalC2, TermC2, list_Car(scan), VarIsConst))
return ord_Uncomparable();
return ord_GreaterThan();
} else {
/* Try to find an argument of T1 that is >= T2 */
for (scan = term_ArgumentList(T1); !list_Empty(scan); scan = list_Cdr(scan))
if (!ord_IsUncomparable(rpos_ContGreaterEqual(GlobalC1, TermC1,list_Car(scan),
GlobalC2, TermC2,T2,
VarIsConst)))
return ord_GreaterThan(); /* Argument of T1 >= T2 */
return ord_Uncomparable();
}
}
}
