Annotation of OpenXM/src/asir-contrib/testing/tr-ja.oxt, Revision 1.2
1.1 takayama 1: /*&generate-prologue
2: */
1.2 ! takayama 3: $Id: tr.oxt,v 1.3 2005/04/01 11:33:16 taka Exp $
! 4: $OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.1 2005/04/01 08:08:36 takayama Exp $
1.1 takayama 5:
6: $BCm0U(B: testing/tr.rr $B$G$O(B quote $B$r(B quotetolist $B$G(B list $B$KJQ49$7$F07$&$?$a(B,
7: $B2<$N;EMM$H$O$3$H$J$j(B, list $B7?$G%G!<%?$rLa$9>l9g$bB?$$(B.
8: $B%f!<%68@8l$G=q$$$F$$$k4X78>e(B pn(x) $B$r(B pn("x") $B$H$7$F$$$k(B.
9: $BB>$K$bF1MM$J4X?t$,$"$j(B.
10:
11: @c --------------------------------------------------------------------
12: @section quote $B$KBP$9$k4pK\4X?t(B
13:
14: /*&usage begin: qt_node(Q)
15: quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
16: example: qt_node(quote(1+2*3))
17: end: */
18:
19:
20: /*&usage begin: qt_nchild(Q)
21: quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
22: example: qt_nchild(quote(1+2*3)) 2 $B$rLa$9(B.
23: end: */
24:
25:
26: /*&usage begin: qt_child(Q,K)
27: quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
28: example: qt_child(quote(1+2*3),1) quote(2*3) $B$rLa$9(B.
29: end: */
30:
31: @c --------------------------------------------------------------------
32: @subsection quote $B$KBP$9$k=R8l(B
33:
34: /*&usage begin: qt_is_integer(Q)
35: quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
36: example: qt_is_integer(quote(0))
37: end: */
38:
39: /*&usage begin: qt_depend(Q,x)
40: quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
41: example: qt_depend(quote(1+1/x),x)
42: end: */
43:
44: @c --------------------------------------------------------------------
45: @subsection quote $B$KBP$9$k%3%s%9%H%i%/%?(B
46:
47: /*&usage begin: qt_zero()
48: quote 0 $B$rLa$9(B.
49: end: */
50:
51: /*&usage begin: qt_id(Qobj)
52: quote object {Qobj} $B$r$=$N$^$^La$9(B.
53: end: */
54:
55: /*&usage begin: qt_replace(Qobj,[[x,Valuex],[y,Valuey],...])
56: quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
57: quote object $B$rLa$9(B.
58: end: */
59:
60: /*&usage begin: qt_parenthesis(Qobj)
61: quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
62: quote object $B$r:n$k(B.
63: +, *, /, ^, - $BEy$K$D$$$F$N(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
64: end: */
65:
1.2 ! takayama 66: /*&usage begin: qt_eval(Qobj,type)
! 67: Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
! 68: end: */
! 69:
! 70: /*&usage begin: qt_(Obj)
! 71: asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.
! 72: end: */
! 73:
! 74: $B$=$NB>(B qt_expand, qt_sort, qt_ht, qt_rest, qt_mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.
1.1 takayama 75:
76: @c --------------------------------------------------------------------
77: @section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B
78:
79: /*&usage begin: tr_match0(Qobj,P)
80: quote $B%G!<%?(B {Qobj} $B$,(B $B%Q%?!<%s(B {P} $B$KE,9g$9$l$P(B 1 $B$rLa$7(B, $B$=$&$G$J$1$l$P(B 0
81: $B$rLa$9(B.
82: example: tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))
83: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,x)))
84: end: */
85:
86: pn(x) $B$OG$0U$N(B quote object $B$K%^%C%A$7(B, $BL>A0(B x $B$r$D$1$k(B.
87: tr_match0(quote(1+2*3),quote(pn(x)+pn(y))) $B$O(B 1 $B$rLa$9$,(B,
88: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,tr_is_integer,x))) $B$O(B 0 $B$r$b$I$9(B.
89: 2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt_is_integer
90: $B$,(B 0 $B$rLa$9$?$a(B.
91:
92: /*&usage begin: tr_match1(Qobj,P,Act)
93: quote $B%G!<%?(B {Qobj} $B$,(B $B%Q%?!<%s(B {P} $B$KE,9g$9$l$P(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
94: $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.
95:
96: example: tr_match1(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])
97: end: */
98:
99: /*&usage begin: tr_or_match1(Qobj,Rules)
100: end: */
101:
102: /*&usage begin: tr_apply_rule1(Qobj,P,Act)
103: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
104: $B%Q%?!<%s(B {P} $B$KE,9g$9$k$b$N$,$"$k$H$-$O(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
105: $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
106: tr_apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr_match1 $B$H$O0[$J$k(B).
107: $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).
108:
109: example: tr_apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
110: end: */
111:
112: $B?<$5M%@h$G=q$-49$($r$9$k$K$O(B $B4X?t(B sin_int $B$NCf$G$^$?(B tr_apply_rule1 $B$r8F$S=P$;$P(B
113: $B$h$$(B.
114:
115: /*&usage begin: tr_apply_or_rules(Qobj,Rules)
116: end: */
117:
1.2 ! takayama 118: @subsection $BFbIt4X?t(B
! 119:
! 120: /*&usage begin: tr_apply_function0(Qobj,Arg1,...)
! 121: end: */
! 122:
! 123: /*&usage begin: tr_rp(Qobj,P,A)
! 124: end: */
! 125:
! 126: /*&usage begin: tr_make_binding(Qobj,P)
! 127: end: */
! 128:
1.1 takayama 129: @c ---------------------------------------------------------
130: @section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B
131:
132: $BNc(B:
1.2 ! takayama 133: pn(x) $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
1.1 takayama 134: pn(x,qt_is_integer(x))
1.2 ! takayama 135: fn(f) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
! 136: fn(f,pn(x),pn(y)) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
! 137: f $B$N0z?t$r(B x, y $B$K(B bind
1.1 takayama 138:
139: @c ---------------------------------------------------------
140: @section $B%Q%?!<%s(B
141:
142: $B%Q%?!<%s$O(B quote $B$GM?$($k(B.
143: $BM=Ls8l(B tr_and, tr_or, tr_not $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
144: $B$?$H$($P(B
145: quote(tr_and(pn(x,qt_is_integer),pn(x,qt_is_non_negative)))
146: $B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.
147:
148: @c ---------------------------------------------------------
149: @section $BNcBj(B sin($B@0?t(B*@pi) $B$r(B 0 $B$K(B.
150:
1.2 ! takayama 151: /* $B=`Hw(B */
! 152: extern P,A;
! 153: P=quote(sin(pn(x)*@pi)); /* $B%Q%?!<%s(B */
! 154: A=[sin_int,x] /* action, action $B4X?t(B */
! 155: def sin_int(X) {
! 156: X = tr_apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */
! 157: if (qt_is_integer(X)) return qt_zero();
! 158: else qt_replace(sin(y*@pi),[[y,X]]); /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/
! 159: }
! 160:
! 161: /* $B7W;;(B */
! 162: Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
! 163: tr_apply_rule1(Qobj,P,A);
! 164:
1.1 takayama 165:
166: @c ---------------------------------------------------------
167: @section $BNcBj(B $BITDj@QJ,(B
168:
1.2 ! takayama 169: /* integral(f+g) => integral(f)+integral(g) */
! 170: S1=[quote(integral(pn(f)+pn(g))),
! 171: [int_linear1,f,g]];
! 172: def int_linear1(X,Y) {
! 173: return qt_replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
! 174: }
! 175:
! 176: /* integral(c*f) => c*integral(f) */
! 177: def qt_independent(F,X) { return !qt_dependent(F,X); }
! 178: S2=[quote(integral(pn(c,qt_independent(c,x))*f)),
! 179: [int_linear2,c,f]];
! 180: def int_linear2(X,Y) {
! 181: return qt_replace(quote(c*integral(f)),[[c,X],[f,Y]]);
! 182: }
! 183:
! 184: apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
! 185: $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
! 186: $B$3$N%k!<%k$N>l9gEz$($O(B
! 187: a*integral(x^2)+integral(x)+integral(2/x);
! 188:
! 189: quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
! 190:
1.1 takayama 191: @c ---------------------------------------------------------
192: @section $BNcBj(B $B4JC1$J9=J82r@O(B
193:
1.2 ! takayama 194: $B<0(B(expression) $B$O(B $B<0(B+$B<0(B | $B<0(B*$B<0(B | ($B<0(B) | $B@0?t(B
! 195:
! 196: extern R1,R2,R3,R4,S1,S2,S3,S4;
! 197: /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
! 198: R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
! 199: R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
! 200: R3=[quote((pn(x,is_expression(x)))), 1];
! 201: R4=[quote(pn(x,qt_is_integer(x))), 1];
! 202: def is_expression(Qobj) {
! 203: R = [R1,R2,R3,R4];
! 204: A = apply_or_match0(Qobj,R);
! 205: if (A == 0) return 0; else return 1;
! 206: }
! 207:
! 208: /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
! 209: S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
! 210: S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
! 211: S3=[quote((pn(x,is_expression(x)))), [qt_id,x]];
! 212: S4=[quote(pn(x,qt_is_integer(x))), [qt_id,x]];
! 213:
! 214: def eval_expression(Qobj) {
! 215: S = [S1,S2,S3,S4];
! 216: return apply_or_rules(Qobj,S);
! 217: }
! 218:
! 219: def myadd(X,Y) {
! 220: return qt_(qt_eval(X,1)+qt_eval(Y,1));
! 221: }
! 222:
! 223: def mymul(X,Y) {
! 224: return qt_(qt_eval(X,1)*qt_eval(Y,1));
! 225: }
! 226:
! 227: /* $B7W;;(B */
! 228: tr_eval_expression(quote(1+2*(3+15)));
1.1 takayama 229:
230: @c ---------------------------------------------------------
231: @section $BNcBj(B $BHs2D494D$N4JC1$J9=J82r@O(B
232:
233:
234:
235:
236:
237: /*&generate-epilogue
238: */
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