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Annotation of OpenXM/src/asir-contrib/testing/noro/new_rewrite.rr, Revision 1.2

1.2     ! noro        1: /* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_rewrite.rr,v 1.1 2005/12/11 07:24:30 noro Exp $ */
1.1       noro        2:
                      3: /*
                      4:  * test functions for rewriting by rules
                      5:  *
                      6:  * usage : qt_rewrite(Expr,Rules,0|1|2) 0 : do not expand, 1 : expand
                      7:  *
                      8:  */
                      9:
                     10: /* commutativity */
                     11: #if 0
                     12: Rc0=[`_X*_Y,`!qt_is_number(_X) && nqt_comp(_X,_Y)<0,`_Y*_X]$
                     13: #else
                     14: Rc0=[`_X*_Y,`nqt_comp(_Y*_X,_X*_Y)>0,`_Y*_X]$
                     15: #endif
                     16: Rcomm = [Rc0]$
                     17:
                     18: /* alternativity */
                     19: Ra0=[`X*Y,`qt_is_var(X) && qt_is_var(Y) && nqt_comp(Y,X)>0,`-Y*X]$
                     20: Ra1=[`X^N,`eval_quote(N)>=2,`0]$
                     21: Ra2=[`X*X,`0]$
                     22: Ralt = [Ra0,Ra1,Ra2]$
                     23:
                     24: /* simplifier of exp() */
                     25: Re1=[`exp(_X)*exp(_Y),`exp(_X+_Y)]$
                     26: Re2=[`exp(_X)^_K,`exp(_K*_X)]$
                     27: Re3=[`exp(0),`1]$
                     28: Re4=[`exp(_N*p*i),`qt_is_integer(_N) && eval_quote(_N)%2==0,`1]$
                     29: Rexp = [Re1,Re2,Re3,Re4]$
                     30:
                     31: R5=[`(_V^_N)^_M,`_V^(_N*_M)]$
                     32:
                     33: /* integration */
                     34: Ri1=[`int(_F+_G,_X),`int(_F,_X)+int(_G,_X)]$
                     35: Ri2=[`int(_N*_F,_X),`qt_is_number(_N),`_N*int(_F,_X)]$
                     36: Ri3=[`int(_F,_X),`qt_is_number(_F), `_F*_X]$
                     37: Ri4=[`int(_X^_N,_X),`qt_is_number(_N) && eval_quote(_N)!=-1,`_X^(_N+1)/(_N+1)]$
                     38: Ri5=[`int(_X^(-1),_X),`log(_X)]$
                     39: Ri6=[`int((_A*_X+_B)^(-1),_X),`1/_A*log(_A*_X+_B)]$
                     40: Rint = [Ri1,Ri2,Ri3,Ri4,Ri5,Ri6]$
                     41:
                     42: /* derivation */
                     43: Rd0=[`d(_N*_X),`qt_is_number(_N),`_N*d(_X)]$
                     44: Rd1=[`d(X+Y),`d(X)+d(Y)]$
                     45: Rd2=[`d(X*Y),`d(X)*Y+X*d(Y)]$
                     46: Rd3=[`d(_N),`qt_is_number(_N),`0]$
                     47: Rd=[Rd0,Rd1,Rd2,Rd3]$
                     48:
                     49: /* representing an expression as a polynomial w.r.t. x */
                     50: /* T = qt_rewrite(qt_rewrite(Expr,[Ru0],1),[Ru1],0) */
                     51: Ru0=[`x^_N*_X,`_X*x^_N]$
                     52: Ru1=[`_F*x^_N+_G*x^_N,`(_F+_G)*x^_N]$
                     53: #define O_LIST 4
                     54: #define O_QUOTE 17
                     55:
                     56: ctrl("print_quote",2)$
                     57:
                     58: def normalize_rule(R,Expand)
                     59: {
                     60:        return map(qt_normalize,R,Expand);
                     61: }
                     62:
                     63: def qt_rewrite(F,Rules,Expand)
                     64: {
                     65:        F = qt_normalize(F,Expand);
                     66:        Rules = map(normalize_rule,Rules,Expand);
                     67:
                     68:        /* rewrite chidren */
                     69:        F00 = F0 = F;
                     70:        while ( 1 ) {
                     71:                FA = quote_to_funargs(F);
                     72:                for ( R = [FA[0]], T = cdr(FA); T != []; T = cdr(T) ) {
                     73:                        E = car(T); TE = type(E);
                     74:                        if ( TE == O_QUOTE )
                     75:                                E1 = qt_rewrite(E,Rules,Expand);
                     76:                        else if ( TE == O_LIST )
                     77:                                E1 = map(qt_rewrite,E,Rules,Expand);
                     78:                        else
                     79:                                E1 = E;
                     80:                        R = cons(E1,R);
                     81:                }
                     82:                F = qt_normalize(funargs_to_quote(reverse(R)),Expand);
                     83:                if ( F == F0 ) break;
                     84:                else F0 = F;
                     85:        }
                     86:        F0 = F;
                     87:        while ( 1 ) {
                     88:                for ( T = Rules; T != []; T = cdr(T) ) {
                     89:                        F1 = nqt_match_rewrite(F,car(T),Expand);
                     90:                        if ( F1 != F ) {
                     91:                                F = F1; break;
                     92:                        }
                     93:                }
                     94:                if ( F == F0 ) break;
                     95:                else F0 = F;
                     96:        }
                     97:        if ( F00 == F ) return F;
                     98:        else return qt_normalize(qt_rewrite(F,Rules,Expand),Expand);
                     99: }
                    100: end$
                    101: