Return to tr-ja.oxt CVS log

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

Fixed a bug of oxgentexi;  { and } were not output in example:

Added a todo list to tr-ja.oxt.

/*&generate-prologue
*/
$Id: tr.oxt,v 1.17 2005/04/06 08:52:38 taka Exp $
$OpenXM: OpenXM/src/asir-contrib/testing/tr-ja.oxt,v 1.5 2005/04/06 09:26:28 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.

$B$3$N%U%!%$%k$+$i(B texi $B%U%!%$%k$r:n@.$9$k$K$O0J2<$N$h$&$KF~NO$7$F2<$5$$(B.
oxgentexi $B$O(B OpenXM/src/util $B$N2<$K$"$j$^$9(B.

nkf -e tr.oxt | oxgentexi --noSorting --title 'Term rewriting functions for Risa/Asir' --author 'Nobuki Takayama' >t.texi

begin: AAA01|

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


$BJQ?t%Q%?!<%s(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))

Todo; fn $B$OB?J,$$$i$J$$(B. qt_is_function(x) $B$G(B OK.
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               


$B%Q%?!<%s$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(x))))
$B$O(B x $B$,(B $B@0?t$G(B - $B$,@hF,$K$D$$$F$$$J$$>l9g%^%C%A$9$k(B.

end:

begin: AAA02|

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

end:


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:


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:


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.
 example: qt_child(quote(1+2*3),0)     quote(1) $B$rLa$9(B.
end:

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

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

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:

begin: qt_is_function(Q)
 quote $B%G!<%?(B {Q} $B$,4X?t$N$H$-(B 1, $B$=$&$G$J$$$H$-(B 0.
 example: qt_is_function(f(x,y));
end:

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

begin: qt_zero()
 quote 0 $B$rLa$9(B.
end:

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

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.
   description:
    $B2]Bj(B; x, y $B$OBgJ8;z$b5v$9$+(B? @var{Qobj} $B$b85!94^$^$l$F$$$kBgJ8;z$rI>2A$7$FCV$-49$($k(B
    $B4X?t$bI,MW$+(B?

   example: qt_replace(quote(sin(x*@pi)), [[x,quote( (2*t+3) )]])
end:

   qt_replace $B$O(B asir-contrib $B$N(B base_replace $B$H;w$?5!G=(B.
   quote $B$NFbIt$KBgJ8;z$G$O$8$^$kJQ?t(B($BI>2A$9$k(B)$B$,=q$1$J$$$?$a(B.

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(B asir $B$NJ8K!$G$N1i;;;R$N6/$5$r2>Dj$9$k(B.
  description:
  $B;29M(B;
   noro_simplify.rr  $B$N(B @code{remove_paren()} $B$,$9$G$K<B8=$E$_(B?
   @code{flatten()} $B$d(B @code{quote_to_funargs()} $B$rMxMQ$7$F$kLOMM(B.

end:

begin: qt_eval(Qobj,type)
   Qobj $B$r(B asir $B$NB>$N(B object $B$KJQ49(B.
  description:
   @code{eval_quote()} $B$,$9$G$K<B8=$E$_(B.

end:

begin: qt_(Obj)
   asir $B$N(B Obj $B$r(B quote $B7?$KJQ49(B.  
   description:
     @code{objtoquote()} $B$,$9$G$K<B8=$E$_(B.

end:


begin: tr|

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

end:

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)))        
                 x $B$K(B quote(1), y $B$K(B quote(2*3)           
          tr_match0(quote(1+2*3),quote(pn(x)+pn(y,qt_is_integer,y)))
                 qt_is_integer(2*3) $B$O(B 0 $B$J$N$G(B y $B$K$O%^%C%A$7$J$$(B.
end:

begin: pn(X)
  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.
description:
  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.
end:
                 
begin: tr_match0_act(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_match0_act(quote(1+2*3),quote(pn(x)+pn(y)),[myadd,x,y])                   
end:

begin: tr_or_match0_act(Qobj,Rules)
end:

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$$>l9g$O$=$N;R6!$K(B
  tr_apply_rule1 $B$rE,MQ$9$k(B ($B$3$3$,(B tr_match_act $B$H$O0[$J$k(B). 
 $B%^%C%A$7$J$$>l9g$O(B Qobj $B$r$=$N$^$^La$9(B ($B$3$l$,:F5"E*$KE,MQ$5$l$k(B).

description:
 $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,
 $B$=$&$G$J$$$H$-$O(B quote(sin(X*@@pi)) $B$rLa$9(B.
 $B?<$5M%@h$G=q$-49$($r$9$k$K$O(B $B4X?t(B sin_int $B$NCf$G$^$?(B tr_apply_rule1 $B$r8F$S=P$;$P(B
 $B$h$$(B.

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


begin: tr_apply_or_rules(Qobj,Rules)
end:

@subsection $BFbIt4X?t(B

begin: tr_apply_function0(Qobj,BindingTable)
end:

begin: tr_rp(Qobj,P,A)
end:

begin: tr_make_binding(Qobj,P)
end:


begin: zzz00|

@section $BNcBj(B

end:

begin: zzz01|
$BNcBj(B  sin($B@0?t(B*@@pi) $B$r(B 0 $B$K(B.
example:
   /* $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);
end:
   
@c ------------------------------------------------------
@section $BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.

begin: zzz02|
$BNcBj(B Mathematica $B$N(B N[ ] $BAjEv$N4X?t$r%f!<%6$,=q$1$k$h$&$K(B.
example:
    nn(sin(cos(@pi)+sqrt(2))) 
    --> nn(sin(nn(cos(nn(@pi)))+nn(sqrt(nn(2)))))
   Prog; test1-tr.rr $B$N(B test4().

  qt_map_arg $B4X?t$rMQ$$$k(B.
  def test4() {
    Rule=[quote(nn(pn(f))),[qt_map_arg,nn,f]];
    /* nn $B$G0O$^$l$?$b$N$,$"$l$P(B, nn $B$r$=$NFbIt$K:F5"E*$K(B apply $B$9$k(B */
    R0 = quote(nn(sin(1/2)*cos(1/3)));
    print(print_input_form(R0));
    R=tr_apply_rule1(R0,Rule[0],Rule[1]);
    return R;
  }

end:

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

begin: zzz03|
$BNcBj(B  $BITDj@QJ,(B
example:
   /* 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.
end:

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

begin: zzz04|sortKey: zzz04
description:

$BNcBj(B  $B4JC1$J9=J82r@O(B

example:
   $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)));
end:

begin: misc|

@section $B9M$(J}$K$D$$$F$N35@b(B

 $B%H%C%W%l%Y%k$N4X?tC#(B.  (stylesheet $B$N9M$($K;w$F$k(B.)

  iterator $B$N0l<o(B.

  yacc $B$K;w$F$k(B.

@section $B%G%P%C%,!<(B

  $BA*Br$9$Y$-%k!<%k$,Bt;3$"$k$H$-$O(B, $B7Y9p$9$k5!G=(B.

  $BL58B%k!<%W$N(B|$B8!=P(B.

end:

begin: exp|

@c ------------------------------------------------
@section $B<B83E*4X?t(B

end:

begin: qt_map_arg(F,Q)
 $B4X?t(B F $B$r(B quote $B%G!<%?(B {Q} $B$N(B $B$9$Y$F$N%N!<%I$K:F5"E*$K(B
 apply $B$7$?(B quote $B%G!<%?$rLa$9(B.
 example: qt_map_arg(nn,quote(sin(@pi)+2/3))
           nn(nn(sin(nn(@pi)))+nn(nn(2)/nn(3)))
end:

begin: todo|

@section  Todo

@subsection $B%f!<%6Dj5A$NCfCV1i;;;R(B

   tfb $B$N=q$-J}$rF3F~(B.

@subsection $B?t3X$h$j$NNcBj(B

$B?t3XE*$K$*$b$7$m$$NcBj$r$J$k$Y$/Bt;3MQ0U$9$k(B.
$B$3$l$i$NNcBj$KBP$7$F(B tr $B$,;n:nIJ$r:n$k$N$KM-8z$G$"$k$H$$$&$3$H$r$$$&(B.

 $BNc(B; gcd $B7W;;$NB?9`<0(B reduction $B$r(B tr $B$G<B8=(B.

 $BNc(B; $BQQ5i?t$N7W;;$r(B quote $B$G<B8=(B.
        sort $B$d(B expand $B$OAH$_9~$_$G(B.

 $BNc(B; Mathematica $B$N(B Expand[], Toghether[] $BAjEv$N$b$N(B.

 $BNc(B; D $B$N3]$1;;$r(B $B%Q%?!<%s%^%C%A$G<B8=(B.  
    holonomic $B4X?t$r78?t$H$9$kHyJ,:nMQAG4D$G$N7W;;(B.

 $BNc(B; (x^(1/n))^n --> x $BEy(B.

 $BNc(B; $B5-9fHyJ,$HHyJ,4D$G$N7W;;(B.
       y''+xy=0,  y''=y^2+x $BEy(B.  index $BIU$-$NJQ?t@8@.$,I,MW(B. idxtov

 $BNc(B; QE, $BO@M}<0(B.

 $BNc(B; $B30@QBe?t(B. 

 $BNc(B; $B4dGH(B, $B1~MQ?t3X(B, $B?@J]$N%=%j%H%s$NK\$K$"$k$h$&$J(B fermion $BEy$NNc(B.


 $BNc(B;
   Bergman, George M.
   The diamond lemma for ring theory.
   Advances in Math. 29 (1978), no. 2, 178--218.
   $B$K$"$k$h$&$JHs2D49Be?t$NNc(B.

end:

begin: new-functions|

@section   $B$^$@%9%1%C%A$N$_$N4X?t;EMM(B

  qt_ltor, qt_rtol ; $BLZ$N9=B$$NJQ49(B; $BNc(B (x*y)*z --> x*(y*z)


@subsection Index $B$D$-JQ?t(B

  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. 
                                    base_name $BB0@-$r(B  x $B$K(B.
  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. 
  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.

  idxtov $B4X?t$O(B $B4X?tL>$K$b;H$($k$h$&$K$9$k(B --> $BHyJ,4DBP1~(B.

  qt_function($BL>A0(B, $B0z?t(B) --> quote($BL>A0(B($B0z?t(B)) $B$r@8@.(B.  
   index $BIU$-4X?t$OHyJ,4D$N<h07$KI,MW(B.

@subsection $BQQ5i?t(B, dp $B$N(B pretty print.

  $B6R5i?t$N<h07(B, dp $B$N(B pretty print $B$N$?$a(B.
  qt_qttodp(Qobj | vlist,  order?)  quote $B$+$i(B dp $B$r:n$k(B. 
       exponent $B$,?t$G$J$$$H:n$l$:(B.
  qt_dptoqt(Qobj | vlist)  dp $B$+$i(B quote $B$r:n$k(B.  vlist $B$OB0@-$GBP1~(B?

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

end:

/*&generate-epilogue
*/