===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v
retrieving revision 1.55
retrieving revision 1.71
diff -u -p -r1.55 -r1.71
--- OpenXM_contrib2/asir2000/builtin/strobj.c	2005/07/26 01:33:46	1.55
+++ OpenXM_contrib2/asir2000/builtin/strobj.c	2005/10/12 14:43:36	1.71
@@ -45,7 +45,7 @@
  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
  *
- * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.54 2005/07/15 00:23:26 noro Exp $
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.70 2005/10/12 03:31:04 noro Exp $
 */
 #include "ca.h"
 #include "parse.h"
@@ -63,6 +63,8 @@ struct TeXSymbol {
 	char *symbol;
 };
 
+#define OPNAME(f) (((ARF)FA0(f))->name[0])
+
 extern char *parse_strp;
 
 void Psprintf();
@@ -77,8 +79,15 @@ void Pquotetotex_tb();
 void Pquotetotex();
 void Pquotetotex_env();
 void Pflatten_quote();
+
+void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number();
+void Pquote_is_dependent(),Pquote_is_function();
+void Pquote_normalize();
+
 void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name();
-void Pquote_unify();
+void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite();
+void Pquote_to_nary(),Pquote_to_bin();
+void do_assign(NODE arg);
 void fnodetotex_tb(FNODE f,TB tb);
 char *symbol_name(char *name);
 char *conv_rule(char *name);
@@ -88,7 +97,7 @@ void tb_to_string(TB tb,STRING *rp);
 void fnodenodetotex_tb(NODE n,TB tb);
 void fargstotex_tb(char *opname,FNODE f,TB tb);
 int top_is_minus(FNODE f);
-NODE quote_unify(Obj f,Obj pat);
+int quote_unify(Obj f,Obj pat,NODE *rp);
 
 struct ftab str_tab[] = {
 	{"sprintf",Psprintf,-99999999},
@@ -104,12 +113,25 @@ struct ftab str_tab[] = {
 	{"clear_tb",Pclear_tb,1},
 	{"tb_to_string",Ptb_to_string,1},
 	{"string_to_tb",Pstring_to_tb,1},
+	{"get_quote_id",Pget_quote_id,1},
+
+	{"quote_is_number",Pquote_is_number,1},
+	{"quote_is_rational",Pquote_is_rational,1},
+	{"quote_is_integer",Pquote_is_integer,1},
+	{"quote_is_function",Pquote_is_function,1},
+	{"quote_is_dependent",Pquote_is_dependent,2},
+
+	{"quote_normalize",Pquote_normalize,1},
+
+	{"quote_to_nary",Pquote_to_nary,1},
+	{"quote_to_bin",Pquote_to_bin,2},
 	{"quotetotex_tb",Pquotetotex_tb,2},
 	{"quotetotex",Pquotetotex,1},
 	{"quotetotex_env",Pquotetotex_env,-99999999},
-	{"flatten_quote",Pflatten_quote,2},
+	{"flatten_quote",Pflatten_quote,-2},
 	{"quote_to_funargs",Pquote_to_funargs,1},
 	{"quote_unify",Pquote_unify,2},
+	{"quote_match_rewrite",Pquote_match_rewrite,-4},
 	{"funargs_to_quote",Pfunargs_to_quote,1},
 	{"get_function_name",Pget_function_name,1},
 	{0,0,0},
@@ -507,24 +529,189 @@ void Pwrite_to_tb(NODE arg,Q *rp)
 	*rp = 0;	
 }
 
-void Pquote_unify(NODE arg,LIST *rp)
+FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int);
+FNODE fnode_normalize(FNODE);
+
+void Pquote_to_nary(NODE arg,QUOTE *rp)
 {
+	FNODE f;
+
+	f = fnode_to_nary(BDY((QUOTE)ARG0(arg)));
+	MKQUOTE(*rp,f);	
+}
+
+void Pquote_to_bin(NODE arg,QUOTE *rp)
+{
+	FNODE f;
+	int direction;
+
+	direction = QTOS((Q)ARG1(arg));
+	f = fnode_to_bin(BDY((QUOTE)ARG0(arg)),direction);
+
+	MKQUOTE(*rp,f);	
+}
+
+void Pquote_is_number(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_number");
+	ret = fnode_is_number(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_rational(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_rational");
+	ret = fnode_is_rational(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_integer(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_integer");
+	ret = fnode_is_integer(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_function(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_function");
+	if ( q->id == I_FUNC || q->id == I_IFUNC )
+		ret = 1;
+	else
+		ret = 0;
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_dependent(NODE arg,Q *rp)
+{
+	P x;
+	QUOTE q,v;
+	int ret;
+	V var;
+
+	q = (QUOTE)ARG0(arg);
+	v = (QUOTE)ARG1(arg);
+	asir_assert(q,O_QUOTE,"quote_is_dependent");
+	asir_assert(v,O_QUOTE,"quote_is_dependent");
+	x = (P)eval(BDY(v));
+	if ( !x || OID(x) != O_P )
+		*rp = 0;
+	var = VR(x);
+	ret = fnode_is_dependent(BDY(q),var);
+	STOQ(ret,*rp);
+}
+
+
+void Pquote_unify(NODE arg,Q *rp)
+{
+	FNODE f,g;
+	Obj obj;
+	QUOTE q;
 	NODE r;
+	int ret;
 
-	r = quote_unify((Obj)ARG0(arg),(Obj)ARG1(arg));
-	MKLIST(*rp,r);
+#if 0
+	g = partial_eval(BDY(((QUOTE)ARG0(arg))));
+	MKQUOTE(q,g);
+	ret = quote_unify((Obj)q,(Obj)ARG1(arg),&r);
+#else
+	obj = (Obj)ARG0(arg);
+	ret = quote_unify(obj,(Obj)ARG1(arg),&r);
+#endif
+	if ( ret ) {
+		do_assign(r);
+		*rp = ONE;
+	} else
+		*rp = 0;
 }
 
+FNODE rewrite_fnode(FNODE,NODE);
+
+extern Obj VOIDobj;
+
+void Pquote_match_rewrite(NODE arg,Obj *rp)
+{
+	FNODE f,g,h,c,value;
+	Obj obj;
+	QUOTE q;
+	NODE r,t,s,s0,pair;
+	int ret,ind,ac;
+
+	obj = (Obj)ARG0(arg);
+	ret = quote_unify(obj,(Obj)ARG1(arg),&r);
+	if ( ret ) {
+		for ( t = r, s0 = 0; t; t = NEXT(t) ) {
+			NEXTNODE(s0,s);
+			pair = BDY((LIST)BDY(t));
+			ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair)));
+			value = mkfnode(1,I_FORMULA,BDY(NEXT(pair)));
+			BDY(s) = mknode(2,ind,value);
+		}
+		if ( s0 ) NEXT(s) = 0;
+		switch ( ac = argc(arg) ) {
+			case 3:
+				h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0);
+				*rp = eval(h);
+				break;
+			case 4:
+				c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0);
+				if ( eval(c) ) {
+					h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0);
+					*rp = eval(h);
+				} else
+					*rp = VOIDobj;
+				break;
+			default:
+				error("quote_match_rewrite : invalid argument");
+		}
+	} else
+		*rp = VOIDobj;
+}
+
+void do_assign(NODE arg)
+{
+	NODE t,pair;
+	int pv;
+
+	QUOTE value;
+
+	for ( t = arg; t; t = NEXT(t) ) {
+		pair = BDY((LIST)BDY(t));
+		pv = (int)FA0((FNODE)BDY((QUOTE)BDY(pair)));
+		value = (QUOTE)(BDY(NEXT(pair)));
+		ASSPV(pv,value);
+	}
+}
+
 /* 
-/* consistency check and merge */
+/* consistency check and merge
+ */
 
-NODE merge_matching_node(NODE n,NODE a)
+int merge_matching_node(NODE n,NODE a,NODE *rp)
 {
 	NODE ta,ba,tn,bn;
 	QUOTE pa,va,pn,vn;
 
-	if ( !n )
-		return a;
+	if ( !n ) {
+		*rp = a;
+		return 1;
+	}
 	for ( ta = a; ta; ta = NEXT(ta) ) {
 		ba = BDY((LIST)BDY(ta));
 		if ( !ba ) continue;
@@ -543,23 +730,61 @@ NODE merge_matching_node(NODE n,NODE a)
 			n = tn;
 		}
 	}
-	return n;
+	*rp = n;
+	return 1;
 }
 
-NODE quote_unify_node(NODE f,NODE pat) {
-	NODE r,a,tf,tp;
+int quote_unify_node(NODE f,NODE pat,NODE *rp) {
+	NODE r,a,tf,tp,r1;
+	int ret;
 
 	if ( length(f) != length(pat) ) return 0;
 	r = 0;
 	for ( tf = f, tp = pat; tf; tf = NEXT(tf), tp = NEXT(tp) ) {
-		a = quote_unify((Obj)BDY(tf),(Obj)BDY(tp));
-		if ( !a ) return 0;
-		r = merge_matching_node(r,a);
-		if ( !r ) return 0;
+		ret = quote_unify((Obj)BDY(tf),(Obj)BDY(tp),&a);
+		if ( !ret ) return 0;
+		ret = merge_matching_node(r,a,&r1);
+		if ( !ret ) return 0;
+		else r = r1;
 	}
-	return r;
+	*rp = r;
+	return 1;
 }
 
+/* f = [a,b,c,...] pat = [X,Y,...] rpat matches the rest of f */
+
+int quote_unify_cons(NODE f,NODE pat,Obj rpat,NODE *rp) {
+	QUOTE q;
+	Q id;
+	FNODE fn;
+	NODE r,a,tf,tp,r1,arg;
+	int ret;
+	LIST list,alist;
+
+	/* matching of the head part */
+	if ( length(f) < length(pat) ) return 0;
+	r = 0;
+	for ( tf = f, tp = pat; tp; tf = NEXT(tf), tp = NEXT(tp) ) {
+		ret = quote_unify((Obj)BDY(tf),(Obj)BDY(tp),&a);
+		if ( !ret ) return 0;
+		ret = merge_matching_node(r,a,&r1);
+		if ( !ret ) return 0;
+		else r = r1;
+	}
+	/* matching of the rest */
+	MKLIST(list,tf);
+	STOQ(I_LIST,id); a = mknode(2,id,list);
+	MKLIST(alist,a);
+	arg = mknode(1,alist);
+	Pfunargs_to_quote(arg,&q);
+	ret = quote_unify((Obj)q,rpat,&a);
+	if ( !ret ) return 0;
+	ret = merge_matching_node(r,a,&r1);
+	if ( !ret ) return 0;
+	*rp = r1;
+	return 1;
+}
+
 void get_quote_id_arg(QUOTE f,int *id,NODE *r)
 {
 	LIST fa;
@@ -569,62 +794,110 @@ void get_quote_id_arg(QUOTE f,int *id,NODE *r)
 	*id = QTOS((Q)BDY(fab)); *r = NEXT(fab);
 }
 
-/* ret : [[quote(A),quote(1)],...] */
+/* *rp : [[quote(A),quote(1)],...] */
 
-NODE quote_unify(Obj f, Obj pat)
+int quote_unify(Obj f, Obj pat, NODE *rp)
 {
 	NODE tf,tp,head,body;
 	NODE parg,farg,r;
+	Obj rpat;
 	LIST fa,l;
 	int pid,id;
 	FUNC ff,pf;
+	int ret;
+	QUOTE q;
+	FNODE g;
 
-	if ( OID(pat) == O_LIST ) {
+	if ( !f )
+		if ( !pat ) {
+			*rp = 0; return 1;
+		} else
+			return 0;
+	else if ( OID(pat) == O_LIST ) {
 		if ( OID(f) == O_LIST )
-			return quote_unify_node(BDY((LIST)f),BDY((LIST)pat));
+			return quote_unify_node(BDY((LIST)f),BDY((LIST)pat),rp);
 		else
 			return 0;
 	} else if ( OID(pat) == O_QUOTE ) {
-		if ( OID(f) != O_QUOTE ) return 0;
-		get_quote_id_arg((QUOTE)pat,&pid,&parg);
-		get_quote_id_arg((QUOTE)f,&id,&farg);
+		pid = ((FNODE)BDY((QUOTE)pat))->id;
 		switch ( pid ) {
 			case I_FORMULA:
 				if ( compquote(CO,f,pat) )
 					return 0;
 				else {
-					MKLIST(l,0);
-					return mknode(1,l);
+					*rp = 0; return 1;
 				}
 				break;
-			case I_LIST:
-				return quote_unify_node(BDY((LIST)BDY(farg)),BDY((LIST)BDY(parg)));
+
+			case I_LIST: case I_CONS:
+				get_quote_id_arg((QUOTE)pat,&pid,&parg);
+				if ( OID(f) == O_LIST )
+					tf = BDY((LIST)f);
+				else if ( OID(f) == O_QUOTE 
+					&& ((FNODE)BDY((QUOTE)f))->id == pid ) {
+					get_quote_id_arg((QUOTE)f,&id,&farg);
+					tf = BDY((LIST)BDY(farg));
+				} else
+					return 0;
+
+				tp = BDY((LIST)BDY(parg));
+				if ( pid == I_LIST )
+					return quote_unify_node(tf,tp,rp);
+				else {
+					rpat = (Obj)BDY(NEXT(parg));
+					return quote_unify_cons(tf,tp,rpat,rp);
+				}
+
 			case I_PVAR:
 				/* [[pat,f]] */
 				r = mknode(2,pat,f); MKLIST(l,r);
-				return mknode(1,l);
+				*rp =  mknode(1,l);
+				return 1;
+
 			case I_IFUNC:
 				/* F(X,Y,...) = ... */
+				get_quote_id_arg((QUOTE)f,&id,&farg);
+				get_quote_id_arg((QUOTE)pat,&pid,&parg);
 				if ( id == I_FUNC ) {
 					r = mknode(2,BDY(parg),BDY(farg)); MKLIST(l,r);
 					head = mknode(1,l);
-					body = quote_unify(BDY(NEXT(farg)),BDY(NEXT(parg)));
-					if ( !body ) return 0;
-					return merge_matching_node(head,body);
+					ret = quote_unify(BDY(NEXT(farg)),
+								BDY(NEXT(parg)),&body);
+					if ( !ret ) return 0;
+					else return merge_matching_node(head,body,rp);
 				} else
 					return 0;
-			case I_BOP:
-			case I_FUNC:
+
+			case I_NARYOP: case I_BOP: case I_FUNC:
 				/* X+Y = ... */
 				/* f(...) = ... */
+				if ( OID(f) != O_QUOTE ) return 0;
+				id = ((FNODE)BDY((QUOTE)f))->id;
+				if ( pid == I_FUNC )
+					;
+				else {
+					/* XXX converting to I_BOP */
+					if ( pid == I_NARYOP ) {
+						g = fnode_to_bin(BDY((QUOTE)pat),1);
+						MKQUOTE(q,g); pat = (Obj)q;
+					}
+					if ( id == I_NARYOP ) {
+						g = fnode_to_bin(BDY((QUOTE)f),1);
+						MKQUOTE(q,g); f = (Obj)q;
+					}
+				}
+				get_quote_id_arg((QUOTE)pat,&pid,&parg);
+				get_quote_id_arg((QUOTE)f,&id,&farg);
 				if ( compqa(CO,BDY(farg),BDY(parg)) ) return 0;
-				return quote_unify_node(NEXT(farg),NEXT(parg));
-				break;
+				return quote_unify_node(NEXT(farg),NEXT(parg),rp);
+
 			default:
-				if ( pid == id )
-					return quote_unify_node(farg,parg);
-				else
-					return 0;
+				if ( OID(f) != O_QUOTE ) return 0;
+				id = ((FNODE)BDY((QUOTE)f))->id;
+				if ( id != pid ) return 0;
+				get_quote_id_arg((QUOTE)pat,&pid,&parg);
+				get_quote_id_arg((QUOTE)f,&id,&farg);
+				return quote_unify_node(farg,parg,rp);
 		}
 	}
 }
@@ -1027,47 +1300,56 @@ void fnodetotex_tb(FNODE f,TB tb)
 		/* otherwise   => FA1(f), FA2(f) */
 		case I_BOP:
 			opname = ((ARF)FA0(f))->name;
-			if ( !strcmp(opname,"+") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"-") ) {
-				if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(opname,tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"*") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(" ",tb);
-				/* XXX special care for DP */
-				f2 = (FNODE)FA2(f);
-				if ( f2->id == I_EV ) {
-					n = (NODE)FA0(f2);
-					for ( i = 0; n; n = NEXT(n), i++ ) {
-						fi = (FNODE)BDY(n);
-						if ( fi->id != I_FORMULA || FA0(fi) )
-							break;
-					}
-					if ( n )
+			switch ( opname[0] ) {
+				case '+':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				case '-':
+					if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(opname,tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				case '*':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(" ",tb);
+					/* XXX special care for DP */
+					f2 = (FNODE)FA2(f);
+					if ( f2->id == I_EV ) {
+						n = (NODE)FA0(f2);
+						for ( i = 0; n; n = NEXT(n), i++ ) {
+							fi = (FNODE)BDY(n);
+							if ( fi->id != I_FORMULA || FA0(fi) )
+								break;
+						}
+						if ( n )
+							fnodetotex_tb((FNODE)FA2(f),tb);
+					} else
 						fnodetotex_tb((FNODE)FA2(f),tb);
-				} else
+					break;
+				case '/':
+					write_tb("\\frac{",tb);
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb("} {",tb);
 					fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"/") ) {
-				write_tb("\\frac{",tb);
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb("} {",tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-				write_tb("}",tb);
-			} else if ( !strcmp(opname,"^") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb("^{",tb);
-				fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb);
-				write_tb("} ",tb);
-			} else if ( !strcmp(opname,"%") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(" {\\rm mod}\\, ",tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else
-				error("invalid binary operator");
+					write_tb("}",tb);
+					break;
+				case '^':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb("^{",tb);
+					fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb);
+					write_tb("} ",tb);
+					break;
+				case '%':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(" {\\rm mod}\\, ",tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				default:
+					error("invalid binary operator");
+					break;
+			}
 			break;
 
 		case I_COP:
@@ -1475,13 +1757,30 @@ void Pflatten_quote(NODE arg,Obj *rp)
 
 	if ( !ARG0(arg) || OID((Obj)ARG0(arg)) != O_QUOTE )
 		*rp = (Obj)ARG0(arg);
-	else {
+	else if ( argc(arg) == 1 ) {
+		f = flatten_fnode(BDY((QUOTE)ARG0(arg)),"+");
+		f = flatten_fnode(f,"*");
+		MKQUOTE(q,f);
+		*rp = (Obj)q;
+	} else {
 		f = flatten_fnode(BDY((QUOTE)ARG0(arg)),BDY((STRING)ARG1(arg)));
 		MKQUOTE(q,f);
 		*rp = (Obj)q;
 	}
 }
 
+void Pget_quote_id(NODE arg,Q *rp)
+{
+	FNODE f;
+	QUOTE q;
+
+	q = (QUOTE)ARG0(arg);
+	if ( !q || OID(q) != O_QUOTE )
+		error("get_quote_id : invalid argument");
+	f = BDY(q);
+	STOQ((int)f->id,*rp);
+}
+
 void Pquote_to_funargs(NODE arg,LIST *rp)
 {
 	fid_spec_p spec;
@@ -1620,4 +1919,457 @@ void Pfunargs_to_quote(NODE arg,QUOTE *rp)
 		}
 	}
 	MKQUOTE(*rp,f);
+}
+
+FNODE fnode_apply(FNODE f,FNODE (*func)());
+FNODE fnode_normalize(FNODE f);
+FNODE fnode_normalize_nary(FNODE f);
+
+void Pquote_normalize(NODE arg,QUOTE *rp)
+{
+	QUOTE q,r;
+	FNODE f;
+
+	q = (QUOTE)ARG0(arg);
+	if ( !q || OID(q) != O_QUOTE ) {
+		*rp = q;
+		return;
+	} else {
+#if 0
+		f = flatten_fnode(BDY(q),"+");
+		f = flatten_fnode(f,"*");
+#endif
+		f = fnode_normalize(BDY(q));
+		f = fnode_to_nary(f);
+		f = fnode_normalize_nary(f); 
+		MKQUOTE(r,f);
+		*rp = r;
+	}
+}
+
+int fnode_is_number(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_number(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_number(BDY((QUOTE)obj));
+			else if ( NUM(obj) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			return fnode_is_number(FA1(f)) && fnode_is_number(FA2(f));
+		
+		default:
+			return 0;
+	}
+}
+
+int fnode_is_rational(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_number(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_rational(BDY((QUOTE)obj));
+			else if ( NUM(obj) && RATN(obj) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			if ( !strcmp(((ARF)FA0(f))->name,"^")  )
+				return fnode_is_rational(FA1(f)) && fnode_is_integer(FA2(f));
+			else
+				return fnode_is_rational(FA1(f)) && fnode_is_rational(FA2(f));
+		
+		default:
+			return 0;
+	}
+}
+
+int fnode_is_integer(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_integer(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_integer(BDY((QUOTE)obj));
+			else if ( INT(obj)) return 1;
+			else return 0;
+		
+		case I_BOP:
+			switch ( ((ARF)FA0(f))->name[0] ) {
+				case '^':
+					return fnode_is_integer(FA1(f)) 
+						&& fnode_is_nonnegative_integer(FA2(f));
+				case '/':
+					return fnode_is_integer(FA1(f)) && 
+						( fnode_is_one(FA2(f)) || fnode_is_minusone(FA2(f)) );
+				default:
+					return fnode_is_integer(FA1(f)) && fnode_is_integer(FA2(f));
+			}
+			break;
+
+		default:
+			return 0;
+	}
+}
+
+int fnode_is_zero(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( !n ) return 1;
+	else return 0;
+}
+
+int fnode_is_nonnegative_integer(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( !n || (INT(n) && SGN(n) > 0) ) return 1;
+	else return 0;
+}
+
+int fnode_is_one(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( UNIQ(n) ) return 1;
+	else return 0;
+}
+
+int fnode_is_minusone(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( MUNIQ(n) ) return 1;
+	else return 0;
+}
+
+int fnode_is_dependent(FNODE f,V v)
+{
+	Obj obj;
+	FNODE arg;
+	NODE t;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_dependent(FA0(f),v);
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 0;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_dependent(BDY((QUOTE)obj),v);
+			else if ( obj_is_dependent(obj,v) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			return fnode_is_dependent(FA1(f),v) || fnode_is_dependent(FA2(f),v);
+	
+		case I_FUNC:
+			arg = (FNODE)FA1(f);
+			for ( t = FA0(arg); t; t = NEXT(t) )
+				if ( fnode_is_dependent(BDY(t),v) ) return 1;
+			return 0;
+
+		default:
+			return 0;
+	}
+}
+
+FNODE fnode_normalize(FNODE f)
+{
+	FNODE a2,mone;
+	Q q;
+	NODE n;
+
+	switch ( f->id ) {
+		case I_PAREN:
+			return fnode_normalize(FA0(f));
+		
+		case I_MINUS:
+			f = fnode_normalize(FA0(f));
+			return f->id==I_MINUS ? FA0(f) : mkfnode(1,I_MINUS,f);
+
+		case I_BOP:
+			/* arf fnode fnode */
+			f = fnode_apply(f,fnode_normalize);
+			switch ( ((ARF)FA0(f))->name[0] ) {
+				case '-':
+					a2 = mkfnode(1,I_MINUS,FA2(f));
+					return mkfnode(3,I_BOP,addfs,FA1(f),a2);
+				case '/':
+					STOQ(-1,q);
+					mone = mkfnode(1,I_FORMULA,q);
+					a2 = mkfnode(3,I_BOP,pwrfs,FA2(f),mone);
+					return mkfnode(3,I_BOP,mulfs,FA1(f),a2);
+				default:
+					return f;
+			}
+			break;
+	
+		default:
+			return fnode_apply(f,fnode_normalize);
+	}
+}
+
+FNODE fnode_simplify_add(FNODE f);
+FNODE fnode_simplify_mul(FNODE f);
+
+FNODE fnode_normalize_nary(FNODE f)
+{
+	NODE n;
+
+	switch ( f->id ) {
+		case I_PAREN:
+			return fnode_normalize_nary(FA0(f));
+				
+		case I_MINUS:
+			f = fnode_normalize_nary(FA0(f));
+			return f->id==I_MINUS ? FA0(f) : mkfnode(1,I_MINUS,f);
+
+		case I_NARYOP:
+			f = fnode_apply(f,fnode_normalize_nary);
+			switch ( ((ARF)FA0(f))->name[0] ) {
+				/* XXX */
+				case '+':
+					return fnode_simplify_add(f);
+				case '*':
+					return fnode_simplify_mul(f);
+				default:
+					return f;
+			}
+			break;
+	
+		default:
+			return fnode_apply(f,fnode_normalize_nary);
+			break;
+	}
+}
+
+FNODE fnode_apply(FNODE f,FNODE (*func)())
+{
+	fid_spec_p spec;
+	FNODE r;
+	int i,n;
+	NODE t,t0,s;
+
+	get_fid_spec(f->id,&spec);
+	for ( n = 0; spec->type[n] != A_end; n++ );
+	NEWFNODE(r,n); r->id = f->id;
+	for ( i = 0; i < n; i++ ) {
+		switch ( spec->type[i] ) {
+			case A_fnode:
+				r->arg[i] = func(f->arg[i]);
+				break;
+			case A_node:
+				s = (NODE)f->arg[i];
+				for ( t0 = 0; s; s = NEXT(s) ) {
+					NEXTNODE(t0,t);
+					BDY(t) = (pointer)func((FNODE)BDY(s));
+				}
+				if ( t0 ) NEXT(t) = 0;
+				r->arg[i] = t0;
+				break;
+			default:
+				r->arg[i] = f->arg[i];
+				break;
+		}
+	}
+	return r;
+}
+
+NODE2 fnode_add_monomial(NODE2 s0,FNODE g);
+
+FNODE fnode_simplify_add(FNODE f)
+{
+	NODE n;
+	NODE r0,r,t,u;
+	NODE2 s,s0;
+	FNODE g,m;
+	QUOTE q;
+
+	n = (NODE)FA1(f);
+	s0 = 0;
+	for ( t = n; t; t = NEXT(t) ) {
+		g = (FNODE)BDY(t);
+		s0 = fnode_add_monomial(s0,g);
+	}
+	if ( !s0 )
+		return mkfnode(1,I_FORMULA,0);
+	else {
+		for ( s = s0, r0 = 0; s; s = NEXT(s) ) {
+			NEXTNODE(r0,r);
+			if ( UNIQ(s->body1) )
+				BDY(r) = s->body2;
+			else if ( MUNIQ(s->body1) )
+				BDY(r) = mkfnode(1,I_MINUS,s->body2);
+			else {
+				objtoquote(s->body1,&q);
+				m = (FNODE)s->body2;
+				if ( m->id == I_NARYOP && OPNAME(m) == '*' ) {
+					MKNODE(u,BDY(q),FA1(m)); FA1(m) = u;
+					BDY(r) = m;
+				} else {
+					u = mknode(2,BDY(q),m);
+					BDY(r) = mkfnode(2,I_NARYOP,mulfs,u);
+				}
+			}
+		}
+		if ( r0 ) NEXT(r) = 0;
+		if ( length(r0) == 1 )
+			return (FNODE)BDY(r0);
+		else
+			return mkfnode(2,I_NARYOP,FA0(f),r0);
+	}
+}
+
+NODE2 fnode_add_monomial(NODE2 r,FNODE g)
+{
+	Num c,c1;
+	FNODE b;
+	NODE arg;
+	NODE2 prev,cur,t;
+	int a;
+
+	if ( fnode_is_number(g) ) {
+		c = (Num)eval(g);
+		b = mkfnode(1,I_FORMULA,ONE);
+	} else if ( g->id == I_NARYOP && OPNAME(g) == '*' ) {
+		arg = (NODE)FA1(g);
+		if ( fnode_is_number(BDY(arg)) ) {
+			c = (Num)eval(BDY(arg));
+			if ( length(arg) > 2 )
+				b = mkfnode(2,I_NARYOP,FA0(g),NEXT(arg));
+			else
+				b = BDY(NEXT(arg));
+		} else {
+			c = (Num)ONE;
+			b = g;
+		}
+	} else {
+		c = (Num)ONE;
+		b = g;
+	}
+
+	for ( prev = 0, cur = r; cur; prev = cur, cur = NEXT(cur) ) {
+		a = compfnode(b,cur->body2);
+		if ( a > 0 ) {
+			MKNODE2(t,c,b,cur);
+			if ( !prev )
+				return t;
+			else {
+				NEXT(prev) = t; return r;
+			}
+		} else if ( a == 0 ) {
+			addnum(0,cur->body1,c,&c1);
+			if ( !c1 ) {
+				if ( !prev )
+					return NEXT(cur);
+				else {
+					NEXT(prev) = NEXT(cur); return r;
+				}
+			} else {
+				cur->body1 = c1; return r;
+			}
+		}
+	}
+	MKNODE2(t,c,b,0);
+	if ( !r )
+		return t;
+	else {
+		NEXT(prev) = t; return r;
+	}
+}
+
+FNODE fnode_simplify_mul(FNODE f)
+{
+	int l,i,j;
+	FNODE *b;
+	Obj *e;
+	NODE n,t,r,r1;
+	FNODE g,base;
+	QUOTE q;
+	Obj exp,exp1;
+	Num c,c1;
+
+	n = (NODE)FA1(f);
+	for ( l = 0, t = n; t; t = NEXT(t), l++ );
+	b = (FNODE *)MALLOC(l*sizeof(FNODE));
+	e = (Obj *)MALLOC(l*sizeof(Obj));
+	c = (Num)ONE;
+	for ( i = 0, t = n; t; t = NEXT(t) ) {
+		g = (FNODE)BDY(t);
+		if ( fnode_is_number(g) ) {
+			if ( fnode_is_zero(g) )
+				return mkfnode(1,I_FORMULA,0);
+			else {
+				mulnum(0,c,(Num)eval(g),&c1); c = c1;
+			}
+		} else {
+			if ( g->id == I_MINUS ) {
+				chsgnnum(c,&c1); c = c1;
+				g = FA0(g);
+			}
+			if ( g->id == I_BOP && ((ARF)FA0(g))->name[0] == '^' ) {
+				base = FA1(g); 
+				exp = (Obj)eval(FA2(g));
+			} else {
+				base = g; exp = (Obj)ONE;
+			}
+			if ( i > 0 && !compfnode(b[i-1],base) ) {
+				arf_add(CO,e[i-1],exp,&exp1);
+				if ( !exp1 )
+					i--;
+				else
+					e[i-1] = exp1;
+			} else {
+				b[i] = base;
+				e[i] = exp;
+				i++;
+			}
+		}
+	}
+	if ( !i ) {
+		/* coeff only */
+		g = mkfnode(1,I_FORMULA,c);
+		return g;
+	} else {
+		r = 0;
+		for ( j = i-1; j >= 0; j-- ) {
+			if ( UNIQ(e[j]) )
+				g = b[j];
+			else {
+				objtoquote(e[j],&q);
+				g = mkfnode(3,I_BOP,pwrfs,b[j],BDY(q));
+			}
+			MKNODE(r1,g,r); r = r1;
+		}
+		g = mkfnode(1,I_FORMULA,c);
+		MKNODE(r1,g,r); r = r1;
+		return mkfnode(2,I_NARYOP,FA0(f),r);
+	}
 }