Return to tr-ja.oxt CVS log

Up to [local] / OpenXM / src / asir-contrib / testing

Added examples of
  sin(n*@pi) --> 0
  parsing of expressions,
  indefinite integral.

/*&generate-prologue
*/
$Id: tr.oxt,v 1.3 2005/04/01 11:33:16 taka Exp $
$OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.2 2005/04/01 11:34:21 takayama Exp $

$BCm0U(B: testing/tr.rr $B$G$O(B quote $B$r(B quotetolist $B$G(B list $B$KJQ49$7$F07$&$?$a(B,
      $B2<$N;EMM$H$O$3$H$J$j(B, list $B7?$G%G!<%?$rLa$9>l9g$bB?$$(B.
      $B%f!<%68@8l$G=q$$$F$$$k4X78>e(B pn(x) $B$r(B pn("x") $B$H$7$F$$$k(B. 
      $BB>$K$bF1MM$J4X?t$,$"$j(B.

@c --------------------------------------------------------------------
@section quote $B$KBP$9$k4pK\4X?t(B

/*&usage begin: qt_node(Q)
 quote $B%G!<%?(B {Q} $B$N(B node $B$r<h$j=P$9(B.
 example: qt_node(quote(1+2*3))     
end: */


/*&usage begin: qt_nchild(Q)
 quote $B%G!<%?(B {Q} $B$N(B $B;R6!$N?t$rLa$9(B.
 example: qt_nchild(quote(1+2*3))     2 $B$rLa$9(B.
end: */


/*&usage begin: qt_child(Q,K)
 quote $B%G!<%?(B {Q} $B$N(B {K} $BHVL\$N;R6!$rLa$9(B.
 example: qt_child(quote(1+2*3),1)     quote(2*3) $B$rLa$9(B.
end: */

@c --------------------------------------------------------------------
@subsection quote $B$KBP$9$k=R8l(B

/*&usage begin: qt_is_integer(Q)
 quote $B%G!<%?(B {Q} $B$,@0?t$J$i(B 1
 example: qt_is_integer(quote(0))     
end: */

/*&usage begin: qt_depend(Q,x)
 quote $B%G!<%?(B {Q} $B$,ITDj85(B {x} $B$r4^$`$H(B 1, $B4^$^$J$$$H(B 0.
 example: qt_depend(quote(1+1/x),x)
end: */

@c --------------------------------------------------------------------
@subsection quote $B$KBP$9$k%3%s%9%H%i%/%?(B

/*&usage begin: qt_zero()
 quote 0 $B$rLa$9(B.
end: */

/*&usage begin: qt_id(Qobj)
 quote object {Qobj} $B$r$=$N$^$^La$9(B.
end: */

/*&usage begin: qt_replace(Qobj,[[x,Valuex],[y,Valuey],...])
   quote object {Qobj} $B$NCf$N(B x $B$r(B Valuex, y $B$r(B Valuey, ... $B$KCV$-49$($?(B
   quote object $B$rLa$9(B.
end: */

/*&usage begin: qt_parenthesis(Qobj)
   quote object {Qobj} $B$NCf$N3g8L$,B-$j$J$$$H$-$K$OJd$$(B, $BB?$$$H$-$K$O<h$j5n$C$?(B
   quote object $B$r:n$k(B.
   +, *, /, ^, - $BEy$K$D$$$F$N(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
end: */

/*&usage begin: qt_eval(Qobj,type)
   Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
end: */

/*&usage begin: qt_(Obj)
   asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.  
end: */

$B$=$NB>(B qt_expand, qt_sort, qt_ht, qt_rest, qt_mtov $B$b4pAC4X?t$H$7$FM_$7$$(B.

@c --------------------------------------------------------------------
@section tr (term rewriting) $B$N%H%C%W%l%Y%k$N4X?t(B

/*&usage begin: tr_match0(Qobj,P)
 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
 $B$rLa$9(B. 
 example: tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))                   
          tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,x)))
end: */

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.
tr_match0(quote(1+2*3),quote(pn(x)+pn(y)))  $B$O(B 1 $B$rLa$9$,(B,
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.
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
$B$,(B 0 $B$rLa$9$?$a(B.
                 
/*&usage begin: tr_match1(Qobj,P,Act)
 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.
 $B%Q%?!<%s(B {P} $B$K%^%C%A$7$J$$$H$-$O(B 0.

 example: tr_match1(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])                   
end: */

/*&usage begin: tr_or_match1(Qobj,Rules)
end: */

/*&usage begin: tr_apply_rule1(Qobj,P,Act)
 quote $B%G!<%?(B {Qobj} $B$NLZ$rI}M%@hC5:w$7(B, 
 $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.
 $B$D$^$j(B top node $B$,(B {P} $B$KE,9g$9$k$+D4$Y(B, $BE,9g$7$J$$>l9g$O$=$N;R6!$K(B
  tr_apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr_match1 $B$H$O0[$J$k(B). 
 $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).

 example: tr_apply_rule1(quote(1+sin(2*@pi)),quote(sin(pn(x)*@pi)),[sin_int,x])
end: */

 $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
 $B$h$$(B.

/*&usage begin: tr_apply_or_rules(Qobj,Rules)
end: */

@subsection $BFbIt4X?t(B

/*&usage begin: tr_apply_function0(Qobj,Arg1,...)
end: */

/*&usage begin: tr_rp(Qobj,P,A)
end: */

/*&usage begin: tr_make_binding(Qobj,P)
end: */

@c ---------------------------------------------------------
@section $BJQ?t%Q%?!<%s$H4X?t%Q%?!<%s(B

$BNc(B:
pn(x)                    $BG$0U$N$b$N$K%^%C%A(B. $B%^%C%A$7$?$b$N$r(B x $B$K(B bind.
pn(x,qt_is_integer(x))
fn(f)                    $BG$0U$N4X?t$K%^%C%A(B. $B%^%C%A$7$?4X?tL>$r(B f $B$K(B bind.
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.
                         f $B$N0z?t$r(B x, y $B$K(B bind               

@c ---------------------------------------------------------
@section $B%Q%?!<%s(B

$B%Q%?!<%s$O(B quote $B$GM?$($k(B.
$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.
$B$?$H$($P(B
quote(tr_and(pn(x,qt_is_integer),pn(x,qt_is_non_negative)))
$B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.

@c ---------------------------------------------------------
@section $BNcBj(B  sin($B@0?t(B*@pi) $B$r(B 0 $B$K(B.

   /* $B=`Hw(B */
   extern P,A;
   P=quote(sin(pn(x)*@pi));  /* $B%Q%?!<%s(B */
   A=[sin_int,x]             /* action, action $B4X?t(B */ 
   def sin_int(X) {
     X = tr_apply_rule1(X,P,A); /* $B;R6!$K(B [P,A] $B$r:F5"E*$KE,MQ(B */  
     if (qt_is_integer(X)) return qt_zero();
     else qt_replace(sin(y*@pi),[[y,X]]);  /* sin(x*@pi) $B$r$=$N$^$^La$9(B.*/ 
   }

   /* $B7W;;(B */
   Qobj=quote(1+sin(sin(2*@pi)*@pi)*sin((1/2)*@pi));
   tr_apply_rule1(Qobj,P,A);
   

@c ---------------------------------------------------------
@section $BNcBj(B  $BITDj@QJ,(B

   /* integral(f+g) => integral(f)+integral(g) */
   S1=[quote(integral(pn(f)+pn(g))),
       [int_linear1,f,g]];
   def int_linear1(X,Y) {
      return qt_replace(quote(integral(f)+integral(g)),[[f,X],[g,Y]]);
   }

   /* integral(c*f) => c*integral(f) */
   def qt_independent(F,X) { return !qt_dependent(F,X); }
   S2=[quote(integral(pn(c,qt_independent(c,x))*f)),
       [int_linear2,c,f]];
   def int_linear2(X,Y) {
      return qt_replace(quote(c*integral(f)),[[c,X],[f,Y]]);
   }

   apply_or_rules(quote(integral(a*x^2+x+2/x)),[S1,S2]);
   $B$3$l$r$3$l0J>e=q$-49$($,5/$-$J$$$^$G7+$jJV$9(B.
   $B$3$N%k!<%k$N>l9gEz$($O(B
   a*integral(x^2)+integral(x)+integral(2/x);   

   quote(integral(x^pn(n))) --> x^(n+1)/(n+1) or log(x) $B$r=q$/(B.

@c ---------------------------------------------------------
@section $BNcBj(B  $B4JC1$J9=J82r@O(B

   $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

   extern R1,R2,R3,R4,S1,S2,S3,S4;
   /* $BJ8K!$rK~$?$9$+$I$&$+$N(B check $BMQ(B. Action $BIt$O(B 1 $B$+(B 0 */
   R1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), 1];
   R2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), 1];
   R3=[quote((pn(x,is_expression(x)))), 1];
   R4=[quote(pn(x,qt_is_integer(x))), 1];
   def is_expression(Qobj) {
     R = [R1,R2,R3,R4];
     A = apply_or_match0(Qobj,R);
     if (A == 0) return 0; else return 1;
   }

   /* $B7W;;MQ(B. R1,R2,R3,R4 $B$H:8$O6&DL(B. */
   S1=[quote(pn(x,is_expression(x))+pn(y,is_expression(y))), [myadd,x,y]];
   S2=[quote(pn(x,is_expression(x))*pn(y,is_expression(y))), [mymul,x,y]];
   S3=[quote((pn(x,is_expression(x)))), [qt_id,x]];
   S4=[quote(pn(x,qt_is_integer(x))), [qt_id,x]]; 

   def eval_expression(Qobj) {
     S = [S1,S2,S3,S4];
     return apply_or_rules(Qobj,S);
   }

   def myadd(X,Y) {
     return qt_(qt_eval(X,1)+qt_eval(Y,1));
   }

   def mymul(X,Y) {
     return qt_(qt_eval(X,1)*qt_eval(Y,1));
   }

   /* $B7W;;(B */
   tr_eval_expression(quote(1+2*(3+15)));

@c ---------------------------------------------------------
@section $BNcBj(B  $BHs2D494D$N4JC1$J9=J82r@O(B





/*&generate-epilogue
*/