/* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_rewrite.rr,v 1.3 2006/03/12 00:27:20 noro Exp $ */

/*
 * test functions for rewriting by rules 
 *
 * usage : qt_rewrite(Expr,Rules,0|1|2) 0 : do not expand, 1 : expand 
 *
 */

/* commutativity */
#if 0
Rc0=[`X*Y,`!qt_is_number(X) && nqt_comp(X,Y)<0,`Y*X]$
#else
Rc0=[`X*Y,`nqt_comp(Y*X,X*Y)>0,`Y*X]$
#endif
Rcomm = [Rc0]$

/* alternativity */
Ra0=[`X*Y,`qt_is_var(X) && qt_is_var(Y) && nqt_comp(Y,X)>0,`-Y*X]$
Ra1=[`X^N,`eval_quote(N)>=2,`0]$
Ra2=[`X*X,`0]$
Ralt = [Ra0,Ra1,Ra2]$

/* simplifier of exp() */
Re1=[`exp(X)*exp(Y),`exp(X+Y)]$
Re2=[`exp(X)^K,`exp(K*X)]$
Re3=[`exp(0),`1]$
Re4=[`exp(N*p*i),`qt_is_integer(N) && eval_quote(N)%2==0,`1]$
Rexp = [Re1,Re2,Re3,Re4]$

R5=[`(V^N)^M,`V^(N*M)]$

/* integration */
Ri1=[`int(F+G,X),`int(F,X)+int(G,X)]$
Ri2=[`int(N*F,X),`qt_is_number(N),`N*int(F,X)]$
Ri3=[`int(F,X),`qt_is_number(F), `F*X]$
Ri4=[`int(X^N,X),`qt_is_number(N) && eval_quote(N)!=-1,`X^(N+1)/(N+1)]$
Ri5=[`int(X^(-1),X),`log(X)]$
Ri6=[`int((A*X+B)^(-1),X),`1/A*log(A*X+B)]$
Rint = [Ri1,Ri2,Ri3,Ri4,Ri5,Ri6]$

/* derivation */
Rd0=[`d(N*X),`qt_is_number(N),`N*d(X)]$
Rd1=[`d(X+Y),`d(X)+d(Y)]$
Rd2=[`d(X*Y),`d(X)*Y+X*d(Y)]$
Rd3=[`d(N),`qt_is_number(N),`0]$
Rd=[Rd1,Rd2,Rd3]$

/* representing an expression as a polynomial w.r.t. x */
/* T = qt_rewrite(qt_rewrite(Expr,[Ru0],1),[Ru1],0) */
Ru0=[`x^N*X,`X*x^N]$
Ru1=[`F*x^N+G*x^N,`(F+G)*x^N]$
#define O_LIST 4
#define O_QUOTE 17

ctrl("print_quote",2)$

def normalize_rule(R,Expand)
{
	return map(qt_normalize,R,Expand);
}

def qt_rewrite(F,Rules,Expand)
{
	F = qt_normalize(F,Expand);
	Rules = map(normalize_rule,Rules,Expand);

	/* rewrite chidren */
	F00 = F0 = F;
	while ( 1 ) {
		FA = quote_to_funargs(F);
		for ( R = [FA[0]], T = cdr(FA); T != []; T = cdr(T) ) {
			E = car(T); TE = type(E);
			if ( TE == O_QUOTE )
				E1 = qt_rewrite(E,Rules,Expand);
			else if ( TE == O_LIST )
				E1 = map(qt_rewrite,E,Rules,Expand);
			else
				E1 = E;
			R = cons(E1,R);
		}
		F = qt_normalize(funargs_to_quote(reverse(R)),Expand);
		if ( F == F0 ) break;
		else F0 = F;
	}
	F0 = F;
	while ( 1 ) {
		for ( T = Rules; T != []; T = cdr(T) ) {
			F1 = nqt_match_rewrite(F,car(T),Expand);
			if ( F1 != F ) {
				F = F1; break;
			}
		}
		if ( F == F0 ) break;
		else F0 = F;
	}
	if ( F00 == F ) return F;
	else return qt_normalize(qt_rewrite(F,Rules,Expand),Expand);
}
end$