Annotation of OpenXM/src/asir-contrib/testing/tr-ja.oxt, Revision 1.3
1.1 takayama 1: /*&generate-prologue
2: */
1.3 ! takayama 3: $Id: tr.oxt,v 1.5 2005/04/02 05:55:37 taka Exp $
! 4: $OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.2 2005/04/01 11:34:21 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.
1.3 ! takayama 29: example: qt_child(quote(1+2*3),0) quote(1) $B$rLa$9(B.
1.1 takayama 30: end: */
31:
32: @c --------------------------------------------------------------------
33: @subsection quote $B$KBP$9$k=R8l(B
34:
35: /*&usage begin: qt_is_integer(Q)
36: quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
37: example: qt_is_integer(quote(0))
38: end: */
39:
40: /*&usage begin: qt_depend(Q,x)
41: quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
42: example: qt_depend(quote(1+1/x),x)
43: end: */
44:
45: @c --------------------------------------------------------------------
46: @subsection quote $B$KBP$9$k%3%s%9%H%i%/%?(B
47:
48: /*&usage begin: qt_zero()
49: quote 0 $B$rLa$9(B.
50: end: */
51:
52: /*&usage begin: qt_id(Qobj)
53: quote object {Qobj} $B$r$=$N$^$^La$9(B.
54: end: */
55:
56: /*&usage begin: qt_replace(Qobj,[[x,Valuex],[y,Valuey],...])
57: quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
58: quote object $B$rLa$9(B.
1.3 ! takayama 59: example: qt_replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
1.1 takayama 60: end: */
61:
1.3 ! takayama 62: qt_replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
! 63: quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.
! 64:
1.1 takayama 65: /*&usage begin: qt_parenthesis(Qobj)
66: quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
67: quote object $B$r:n$k(B.
1.3 ! takayama 68: +, *, /, ^, - $BEy$K$D$$$F(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
1.1 takayama 69: end: */
70:
1.2 takayama 71: /*&usage begin: qt_eval(Qobj,type)
72: Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
73: end: */
74:
75: /*&usage begin: qt_(Obj)
76: asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.
77: end: */
78:
1.1 takayama 79:
80: @c --------------------------------------------------------------------
81: @section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B
82:
83: /*&usage begin: tr_match0(Qobj,P)
84: 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
85: $B$rLa$9(B.
1.3 ! takayama 86: example: tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))
! 87: x $B$K(B quote(1), y $B$K(B quote(2*3)
! 88: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,y)))
! 89: qt_is_integer(2*3) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
1.1 takayama 90: end: */
91:
92: pn(x) $B$OG$0U$N(B quote object $B$K%^%C%A$7(B, $BL>A0(B x $B$r$D$1$k(B.
93: tr_match0(quote(1+2*3),quote(pn(x)+pn(y))) $B$O(B 1 $B$rLa$9$,(B,
94: tr_match0(quote(1+2*3),quote(pn(x)+pn(y,tr_is_integer,x))) $B$O(B 0 $B$r$b$I$9(B.
95: 2*3 $B$O(B integer $B$+$i:n$i$l$?(B fnode $B$G$O$"$k$,(B integer $B$G$O$J$$$N$G(B qt_is_integer
96: $B$,(B 0 $B$rLa$9$?$a(B.
97:
1.3 ! takayama 98: /*&usage begin: tr_match_act(Qobj,P,Act)
1.1 takayama 99: 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.
100: $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.
101:
1.3 ! takayama 102: example: tr_match_act(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])
1.1 takayama 103: end: */
104:
105: /*&usage begin: tr_or_match1(Qobj,Rules)
106: end: */
107:
108: /*&usage begin: tr_apply_rule1(Qobj,P,Act)
109: quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B,
110: $B%Q%?!<%s(B {P} $B$KE,9g$9$k$b$N$,$"$k$H$-$O(B {Act} $B$r8F$S=P$7$=$NCM$rLa$9(B.
111: $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
1.3 ! takayama 112: tr_apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr_match_act $B$H$O0[$J$k(B).
1.1 takayama 113: $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).
114:
115: example: tr_apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
116: end: */
117:
1.3 ! takayama 118: $B$3$3$G(B sin_int(X) $B$O(B X $B$,(B integer $B$N;~$O(B quote(0) $B$rLa$7(B,
! 119: $B$=$&$G$J$$$H$-$O(B quote(sin(X*@pi)) $B$rLa$9(B.
1.1 takayama 120: $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
121: $B$h$$(B.
122:
123: /*&usage begin: tr_apply_or_rules(Qobj,Rules)
124: end: */
125:
1.2 takayama 126: @subsection $BFbIt4X?t(B
127:
1.3 ! takayama 128: /*&usage begin: tr_apply_function0(Qobj,BindingTable)
1.2 takayama 129: end: */
130:
131: /*&usage begin: tr_rp(Qobj,P,A)
132: end: */
133:
134: /*&usage begin: tr_make_binding(Qobj,P)
135: end: */
136:
1.1 takayama 137: @c ---------------------------------------------------------
138: @section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B
139:
140: $BNc(B:
1.2 takayama 141: pn(x) $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
1.1 takayama 142: pn(x,qt_is_integer(x))
1.2 takayama 143: fn(f) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
144: fn(f,pn(x),pn(y)) $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
145: f $B$N0z?t$r(B x, y $B$K(B bind
1.1 takayama 146:
147: @c ---------------------------------------------------------
148: @section $B%Q%?!<%s(B
149:
150: $B%Q%?!<%s$O(B quote $B$GM?$($k(B.
151: $BM=Ls8l(B tr_and, tr_or, tr_not $B$O%Q%?!<%s$N%^%C%A$K4X$7$FO@M}1i;;$r$*$3$J$&(B.
152: $B$?$H$($P(B
1.3 ! takayama 153: quote(tr_and(pn(x,qt_is_integer),pn(x,qt_is_non_negative(x))))
1.1 takayama 154: $B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.
155:
156: @c ---------------------------------------------------------
157: @section $BNcBj(B sin($B@0?t(B*@pi) $B$r(B 0 $B$K(B.
158:
1.2 takayama 159: /* $B=`Hw(B */
160: extern P,A;
161: P=quote(sin(pn(x)*@pi)); /* $B%Q%?!<%s(B */
162: A=[sin_int,x] /* action, action $B4X?t(B */
163: def sin_int(X) {
164: X = tr_apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */
165: if (qt_is_integer(X)) return qt_zero();
166: else qt_replace(sin(y*@pi),[[y,X]]); /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/
167: }
168:
169: /* $B7W;;(B */
170: Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
171: tr_apply_rule1(Qobj,P,A);
172:
1.1 takayama 173:
174: @c ---------------------------------------------------------
175: @section $BNcBj(B $BITDj@QJ,(B
176:
1.2 takayama 177: /* integral(f+g) => integral(f)+integral(g) */
178: S1=[quote(integral(pn(f)+pn(g))),
179: [int_linear1,f,g]];
180: def int_linear1(X,Y) {
181: return qt_replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
182: }
183:
184: /* integral(c*f) => c*integral(f) */
185: def qt_independent(F,X) { return !qt_dependent(F,X); }
186: S2=[quote(integral(pn(c,qt_independent(c,x))*f)),
187: [int_linear2,c,f]];
188: def int_linear2(X,Y) {
189: return qt_replace(quote(c*integral(f)),[[c,X],[f,Y]]);
190: }
191:
192: apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
193: $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
194: $B$3$N%k!<%k$N>l9gEz$($O(B
195: a*integral(x^2)+integral(x)+integral(2/x);
196:
197: quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.
198:
1.1 takayama 199: @c ---------------------------------------------------------
200: @section $BNcBj(B $B4JC1$J9=J82r@O(B
201:
1.2 takayama 202: $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
203:
204: extern R1,R2,R3,R4,S1,S2,S3,S4;
205: /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
206: R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
207: R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
208: R3=[quote((pn(x,is_expression(x)))), 1];
209: R4=[quote(pn(x,qt_is_integer(x))), 1];
210: def is_expression(Qobj) {
211: R = [R1,R2,R3,R4];
212: A = apply_or_match0(Qobj,R);
213: if (A == 0) return 0; else return 1;
214: }
215:
216: /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
217: S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
218: S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
219: S3=[quote((pn(x,is_expression(x)))), [qt_id,x]];
220: S4=[quote(pn(x,qt_is_integer(x))), [qt_id,x]];
221:
222: def eval_expression(Qobj) {
223: S = [S1,S2,S3,S4];
224: return apply_or_rules(Qobj,S);
225: }
226:
227: def myadd(X,Y) {
228: return qt_(qt_eval(X,1)+qt_eval(Y,1));
229: }
230:
231: def mymul(X,Y) {
232: return qt_(qt_eval(X,1)*qt_eval(Y,1));
233: }
234:
235: /* $B7W;;(B */
236: tr_eval_expression(quote(1+2*(3+15)));
1.1 takayama 237:
238: @c ---------------------------------------------------------
239: @section $BNcBj(B $BHs2D494D$N4JC1$J9=J82r@O(B
240:
241:
242:
1.3 ! takayama 243: @section Todo:
! 244: $BNc(B. Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
! 245: nn(sin(cos(@pi)+sqrt(2)))
! 246: --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
! 247: $BG$0U4X?t$H$N(B match.
! 248:
! 249: $BNc(B: $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
! 250: sort $B$d(B expand $B$OAH$_9~$_$G(B.
! 251:
! 252: $BNc(B: Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.
! 253:
! 254: $BNc(B: D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.
! 255:
! 256: $BNc(B: (x^(1/n))^n --> x $BEy(B.
! 257:
! 258: $BNc(B: $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
! 259: y''+xy=0, y''=y^2+x $BEy(B.
! 260:
! 261: $BNc(B: QE, $BO@M}<0(B.
! 262:
! 263: @section $B9M$(J}$K$D$$$F$N35@b(B
! 264:
! 265: $B%H%C%W%l%Y%k$N4X?tC#(B. (stylesheet $B$N9M$($K;w$F$k(B.)
! 266: iterator $B$N0l<o(B.
! 267:
! 268: @c ------------------------------------------------
! 269: @section $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B
! 270:
! 271: qt_ltor, qt_rtol : $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)
! 272:
! 273: idxtov(x,i) x_i $B$r@8@.(B. x_i $B$N(B index (idx) $BB0@-(B $B$r(B i $B$K(B.
! 274: base_name $BB0@-$r(B x $B$K(B.
! 275: idxtov(x,[i,j]) x_i_j $B$r@8@.(B. x_i_i $B$N(B index (idx) $BB0@-(B $B$r(B [i,j] $B$K(B.
! 276: vtoidx(x_i) $B$O(B i $B$rLa$9(B. $BB0@-$N8!:w$J$N$G9bB.(B. idx $BB0@-$,L5$$>l9g$O(B i $B$r@_Dj(B.
! 277:
! 278: idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B --> $BHyJ,4DBP1~(B.
! 279:
! 280: qt_function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.
! 281: index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.
! 282:
! 283: $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
! 284: qt_qttodp(Qobj | vlist, order?) quote $B$+$i(B dp $B$r:n$k(B.
! 285: exponent $B$,?t$G$J$$$H:n$l$:(B.
! 286: qt_dptoqt(Qobj | vlist) dp $B$+$i(B quote $B$r:n$k(B. vlist $B$OB0@-$GBP1~(B?
1.1 takayama 287:
1.3 ! takayama 288: qt_expand, qt_sort, qt_ht, qt_rest, qt_mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.
1.1 takayama 289:
290: /*&generate-epilogue
291: */
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