void graph_NodePrint(GRAPHNODE Node)
/**************************************************************
INPUT: A graph node.
RETURNS: Nothing.
EFFECT: Prints some node information to stdout.
***************************************************************/
{
printf("(%d,%d,%d) ", graph_NodeNumber(Node), graph_NodeDfsNum(Node),
graph_NodeCompNum(Node));
}
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;
}
static LIST ana_CalculatePredicatePrecedence(LIST Predicates, LIST Clauses)
/**************************************************************
INPUT: A list of predicates and a list of clauses.
RETURNS: A list of predicate symbols, which should be used
for setting the symbol precedence. The list is sorted
in descending order, that means predicates with highest
precedence come first.
EFFECT: Analyze the clause list to build a directed graph G where
the predicates are vertices. There's an edge (P,Q) in
G iff a clause exists where P is a negative literal
and Q is a positive literal and P != Q. Apply DFS to
find the strongly connected components of this graph.
The <Predicates> list is deleted.
CAUTION: The predicate list must contain ALL predicates
occurring in the clause list!
***************************************************************/
{
GRAPH graph;
LIST result, scan;
int i, j;
NAT count;
SYMBOL s;
/* clause_ListPrint(Clauses); DBG */
if (list_Empty(Predicates)) {
return Predicates;
}
graph = graph_Create();
/* First create the nodes: one node for every predicate symbol. */
for ( ; !list_Empty(Predicates); Predicates = list_Pop(Predicates))
graph_AddNode(graph, symbol_Index((SYMBOL)list_Car(Predicates)));
/* Now scan the clause clause list to create the edges */
/* An edge (P,Q) means P is smaller than Q */
for (scan = Clauses; !list_Empty(scan); scan = list_Cdr(scan)) {
CLAUSE c = list_Car(scan);
for (i = clause_FirstLitIndex(); i < clause_FirstSuccedentLitIndex(c); i++) {
SYMBOL negPred = term_TopSymbol(clause_GetLiteralAtom(c, i));
if (!symbol_Equal(negPred, fol_Equality())) { /* negative predicate */
for (j = clause_FirstSuccedentLitIndex(c); j < clause_Length(c); j++) {
SYMBOL posPred = term_TopSymbol(clause_GetLiteralAtom(c, j));
if (!symbol_Equal(posPred, fol_Equality()) && /* positive predicate */
negPred != posPred) { /* No self loops! */
graph_AddEdge(graph_GetNode(graph, symbol_Index(negPred)),
graph_GetNode(graph, symbol_Index(posPred)));
}
}
}
}
}
/* graph_Print(graph); fflush(stdout); DBG */
/* Calculate the strongly connected components of the graph */
count = 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();
for (i = count - 1; i >= 0; i--) {
for (scan = graph_Nodes(graph); !list_Empty(scan); scan = list_Cdr(scan)) {
GRAPHNODE n = list_Car(scan);
if (graph_NodeCompNum(n) == i) {
/* The symbol represented by the node <<n> belongs to component <i> */
s = symbol_GetSigSymbol(graph_NodeNumber(n));
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);
putchar(' ');
}
putchar('\n'); fflush(stdout); DBG */
graph_Delete(graph);
return result;
}