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Annotation of OpenXM/src/asir-contrib/testing/noro/new_rewrite.rr, Revision 1.1

1.1     ! noro        1: $OpenXM$
        !             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: