static void graph_InternSCC(GRAPH Graph, GRAPHNODE Node)
/**************************************************************
INPUT: A graph and a node of the graph.
RETURNS: Nothing.
EFFECT: This is an internal function used by
graph_StronglyConnnectedComponents.
It sets information in the graph structure which
specifies the strongly connected components of
the graph.
***************************************************************/
{
GRAPHNODE n;
LIST scan;
NAT act_dfs;
act_dfs = (Graph->dfscount)++;
graph_NodeSetDfsNum(Node, act_dfs);
graph_UNFINISHED = list_Push(Node, graph_UNFINISHED);
graph_ROOTS = list_Push(Node, graph_ROOTS);
/* putchar('\n'); list_Apply(graph_NodePrint, graph_UNFINISHED);
putchar('\n'); list_Apply(graph_NodePrint, graph_ROOTS);
fflush(stdout); DBG */
for (scan = graph_NodeNeighbors(Node);
!list_Empty(scan); scan = list_Cdr(scan)) {
n = list_Car(scan);
if (!graph_NodeVisited(n)) {
graph_InternSCC(Graph, n); /* Visit <n> */
} else if (!graph_NodeCompleted(n)) {
/* <n> was visited but is not yet in a permanent component */
NAT dfs_num_of_n = graph_NodeDfsNum(n);
while (!list_StackEmpty(graph_ROOTS) &&
graph_NodeDfsNum(list_Top(graph_ROOTS)) > dfs_num_of_n)
graph_ROOTS = list_Pop(graph_ROOTS);
/* putchar('\n'); list_Apply(symbol_Print, graph_UNFINISHED);
putchar('\n'); list_Apply(symbol_Print, graph_ROOTS);
fflush(stdout); DBG */
}
}
/* printf("\nDFS(%u) complete.", graph_NodeNumber(Node)); DBG */
if (Node == list_Top(graph_ROOTS)) {
/* Node is root of a component, so make this component permanent */
while (!list_StackEmpty(graph_UNFINISHED) &&
graph_NodeDfsNum(list_Top(graph_UNFINISHED)) >= act_dfs) {
n = list_Top(graph_UNFINISHED);
graph_UNFINISHED = list_Pop(graph_UNFINISHED);
graph_NodeSetCompNum(n, Graph->compcount);
}
Graph->compcount++;
graph_ROOTS = list_Pop(graph_ROOTS);
}
/* putchar('\n'); list_Apply(graph_NodePrint, graph_UNFINISHED);
putchar('\n'); list_Apply(graph_NodePrint, graph_ROOTS); fflush(stdout); DBG */
}
void graph_Delete(GRAPH Graph)
/**************************************************************
INPUT: A graph.
RETURNS: Nothing.
EFFECT: All memory required by the graph and its nodes
is freed.
***************************************************************/
{
for ( ; !list_Empty(Graph->nodes); Graph->nodes = list_Pop(Graph->nodes)) {
list_Delete(graph_NodeNeighbors(list_Car(Graph->nodes)));
memory_Free(list_Car(Graph->nodes), sizeof(GRAPHNODE_STRUCT));
}
memory_Free(Graph, sizeof(GRAPH_STRUCT));
}
void graph_Print(GRAPH Graph)
/**************************************************************
INPUT: A graph.
RETURNS: Nothing.
EFFECT: The adjacency list representation of the graph
is printed to stdout.
***************************************************************/
{
LIST scan1, scan2;
for (scan1 = graph_Nodes(Graph); !list_Empty(scan1); scan1 = list_Cdr(scan1)) {
printf("\n%u -> ", graph_NodeNumber(list_Car(scan1)));
for (scan2 = graph_NodeNeighbors(list_Car(scan1)); !list_Empty(scan2);
scan2 = list_Cdr(scan2)) {
printf("%u,", graph_NodeNumber(list_Car(scan2)));
}
}
}
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;
}
