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SandBoxSEXPM

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Editor: pagani Time: 2018/07/16 20:56:26 GMT+0
Note:

changed:
-
\begin{spad}
)abbrev package SEXPM SExprPatternMatch
++ Author: Kurt Pagani
++ Date Created: Mon Feb 06 18:56:20 CET 2017
++ License: BSD
++ References:
++ Description: 
++
SExprPatternMatch(X) : Exports == Implementation where
  
  X: Join(ConvertibleTo InputForm, ExpressionSpace)
  IF ==> InputForm
  SEXP ==> SExpression
  
  Exports ==  with
  
    sexpr : X -> IF
      ++ Convert to InputForm
    occursIn : (IF,IF) -> Boolean
      ++ Return true if ELT occurs in EXP at any level
    cons : (IF,IF) -> IF 
      ++ Cons
    subst1 : (IF,IF,IF) -> IF
      ++ Substitute A for each occurrence of B in LST.
    doSubst : (IF,IF) -> IF
      ++ Perform all substitutions in L on EXP in reverse order.
    unify : (IF,IF) -> IF
    
  Implementation == IF add
  
    notuf:String := "not-unifiable"
  
    sexpr(x:X):IF == convert(x)@IF
    
    occursIn(elt,exp) ==
      elt=exp => true
      atom? exp => false
      occursIn(elt,car exp) or occursIn(elt,cdr exp)
      
    cons(a:IF,b:IF):IF == 
      s:SExpression:=CONS(a,b)$Lisp
      convert(s)$IF
      
    subst1(a:IF,b:IF,lst:IF):IF ==
      null? lst => lst
      lst=b => a
      atom? lst => lst
      b=car lst => cons(a,subst1(a,b,cdr lst))
      atom? car lst => cons(car lst, subst1(a,b,cdr lst))
      cons(subst1(a,b,car lst),subst1(a,b,cdr lst))
      

    doSubst(exp:IF,l:IF):IF ==
      null? l => exp
      a:=car l
      subst1(car a, car cdr a, doSubst(exp,cdr l))

    variable?(x:IF):Boolean ==
      not atom? x => false
      symbol? x => true
      false

    addPair(term:IF,variable:IF,u:IF):IF ==
      occursIn(variable,term) => error notuf
      cons(convert [term,variable],subst1(term,variable,u))
      

    unify1(termlist1:IF,termlist2:IF,u:IF):IF ==
      termlist1=termlist2 => u
      null? termlist1 or null? termlist2 => error notuf
      variable? termlist1 => addPair(termlist2,termlist1,u)
      variable? termlist2 => addPair(termlist1,termlist2,u)
      atom? termlist1 or atom? termlist2 => error notuf
      u:=unify1(doSubst(car termlist1,u),doSubst(car termlist2,u),u)
      unify1(cdr termlist1,cdr termlist2,u)
      
    
    unify(literal1:IF,literal2:IF):IF ==
      u:=convert([])$IF
      if car literal1 = car literal2 then
        unify1(cdr literal1,cdr literal2,u)
      else
        error notuf
    
-- s:=convert(s)$InputForm
-- t:=convert(t)$InputForm
-- st:=cons(s,t)$SEXPM(EXPR INT)
\end{spad}

Test flavours

\begin{axiom}
--)co sexpm
)set break resume

X ==> Expression Integer
IF ==> InputForm
SPM ==> SEXPM(X)

p:=convert(p)$InputForm
x:=x::IF
f:=f::IF
g:=g::IF
h:=h::IF
a:=a::IF
b:=b::IF
y:=y::IF
z:=z::IF

l1:=convert([p,x,convert [f,a]])$IF
l2:=convert([p,b,y])$IF
l3:=convert([p,convert [f,x],convert [g,a,y]])$IF
l4:=convert([p,convert [f,convert [h,b]],convert [g,x,y]])$IF
l5:=convert([p,x])$IF
l6:=convert([p,convert [f,x]])$IF
l7:=convert([p,x,convert [f,y],x])$IF 
l8:=convert([p,z,convert [f,z],a])$IF 

r1:=unify(l1,l2)$SPM  -- (((f a) y) (b x))
r2:=unify(l3,l4)$SPM  -- (((h b) a) ((h b) x)) , only if variable? a
r3:=unify(l5,l6)$SPM  -- not-unifiable
r4:=unify(l7,l8)$SPM  --  ((a z) (a y) (a x))

s11:=doSubst(l1,r1)$SPM
s21:=doSubst(l2,r1)$SPM
s74:=doSubst(l7,r4)$SPM
s84:=doSubst(l8,r4)$SPM


L1:=exp(-r^2+s)::IF
L2:=exp(-r^2+q)::IF
unify(L1,L2)$SPM  -- oweeh


unify(x+y,y+x)$SPM

\end{axiom}

What's the matter with TeX for InputForm ???

spad
)abbrev package SEXPM SExprPatternMatch
++ Author: Kurt Pagani
++ Date Created: Mon Feb 06 18:56:20 CET 2017
++ License: BSD
++ References:
++ Description: 
++
SExprPatternMatch(X) : Exports == Implementation where

  X: Join(ConvertibleTo InputForm, ExpressionSpace)
  IF ==> InputForm
  SEXP ==> SExpression

  Exports ==  with

    sexpr : X -> IF
      ++ Convert to InputForm
    occursIn : (IF,IF) -> Boolean
      ++ Return true if ELT occurs in EXP at any level
    cons : (IF,IF) -> IF 
      ++ Cons
    subst1 : (IF,IF,IF) -> IF
      ++ Substitute A for each occurrence of B in LST.
    doSubst : (IF,IF) -> IF
      ++ Perform all substitutions in L on EXP in reverse order.
    unify : (IF,IF) -> IF

  Implementation == IF add

    notuf:String := "not-unifiable"

    sexpr(x:X):IF == convert(x)@IF

    occursIn(elt,exp) ==
      elt=exp => true
      atom? exp => false
      occursIn(elt,car exp) or occursIn(elt,cdr exp)

    cons(a:IF,b:IF):IF == 
      s:SExpression:=CONS(a,b)$Lisp
      convert(s)$IF

    subst1(a:IF,b:IF,lst:IF):IF ==
      null? lst => lst
      lst=b => a
      atom? lst => lst
      b=car lst => cons(a,subst1(a,b,cdr lst))
      atom? car lst => cons(car lst, subst1(a,b,cdr lst))
      cons(subst1(a,b,car lst),subst1(a,b,cdr lst))

    doSubst(exp:IF,l:IF):IF ==
      null? l => exp
      a:=car l
      subst1(car a, car cdr a, doSubst(exp,cdr l))

    variable?(x:IF):Boolean ==
      not atom? x => false
      symbol? x => true
      false

    addPair(term:IF,variable:IF,u:IF):IF ==
      occursIn(variable,term) => error notuf
      cons(convert [term,variable],subst1(term,variable,u))

    unify1(termlist1:IF,termlist2:IF,u:IF):IF ==
      termlist1=termlist2 => u
      null? termlist1 or null? termlist2 => error notuf
      variable? termlist1 => addPair(termlist2,termlist1,u)
      variable? termlist2 => addPair(termlist1,termlist2,u)
      atom? termlist1 or atom? termlist2 => error notuf
      u:=unify1(doSubst(car termlist1,u),doSubst(car termlist2,u),u)
      unify1(cdr termlist1,cdr termlist2,u)

    unify(literal1:IF,literal2:IF):IF ==
      u:=convert([])$IF
      if car literal1 = car literal2 then
        unify1(cdr literal1,cdr literal2,u)
      else
        error notuf

-- s:=convert(s)$InputForm
-- t:=convert(t)$InputForm
-- st:=cons(s,t)$SEXPM(EXPR INT)
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6012102641383544618-25px001.spad
      using old system compiler.
   SEXPM abbreviates package SExprPatternMatch 
------------------------------------------------------------------------
   initializing NRLIB SEXPM for SExprPatternMatch 
   compiling into NRLIB SEXPM 
****** Domain: X already in scope
   compiling exported sexpr : X -> InputForm
Time: 0 SEC.

   compiling exported occursIn : (InputForm,InputForm) -> Boolean
Time: 0 SEC.

   compiling exported cons : (InputForm,InputForm) -> InputForm
Time: 0 SEC.

   compiling exported subst1 : (InputForm,InputForm,InputForm) -> InputForm
Time: 0 SEC.

   compiling exported doSubst : (InputForm,InputForm) -> InputForm
Time: 0 SEC.

   compiling local variable? : InputForm -> Boolean
Time: 0 SEC.

   compiling local addPair : (InputForm,InputForm,InputForm) -> InputForm
Time: 0.02 SEC.

   compiling local unify1 : (InputForm,InputForm,InputForm) -> InputForm
Time: 0 SEC.

   compiling exported unify : (InputForm,InputForm) -> InputForm
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |SExprPatternMatch| REDEFINED

;;;     ***       |SExprPatternMatch| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor SExprPatternMatch
      Time: 0.02 seconds

--------------non extending category----------------------
.. SExprPatternMatch(#1) of cat 
(CATEGORY |package| (SIGNATURE |sexpr| ((|InputForm|) |#1|))
 (SIGNATURE |occursIn| ((|Boolean|) (|InputForm|) (|InputForm|)))
 (SIGNATURE |cons| ((|InputForm|) (|InputForm|) (|InputForm|)))
 (SIGNATURE |subst1| ((|InputForm|) (|InputForm|) (|InputForm|) (|InputForm|)))
 (SIGNATURE |doSubst| ((|InputForm|) (|InputForm|) (|InputForm|)))
 (SIGNATURE |unify| ((|InputForm|) (|InputForm|) (|InputForm|))))   has no 
(|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|))    finalizing NRLIB SEXPM 
   Processing SExprPatternMatch for Browser database:
--------constructor---------
--------(sexpr ((InputForm) X))---------
--->-->SExprPatternMatch((sexpr ((InputForm) X))): Improper first word in comments: Convert
"Convert to InputForm"
--------(occursIn ((Boolean) (InputForm) (InputForm)))---------
--->-->SExprPatternMatch((occursIn ((Boolean) (InputForm) (InputForm)))): Improper first word in comments: Return
"Return \\spad{true} if ELT occurs in EXP at any level"
--------(cons ((InputForm) (InputForm) (InputForm)))---------
--------(subst1 ((InputForm) (InputForm) (InputForm) (InputForm)))---------
--->-->SExprPatternMatch((subst1 ((InputForm) (InputForm) (InputForm) (InputForm)))): Improper first word in comments: Substitute
"Substitute A for each occurrence of \\spad{B} in \\spad{LST}."
--------(doSubst ((InputForm) (InputForm) (InputForm)))---------
--->-->SExprPatternMatch((doSubst ((InputForm) (InputForm) (InputForm)))): Improper first word in comments: Perform
"Perform all substitutions in \\spad{L} on EXP in reverse order."
--->-->SExprPatternMatch((unify ((InputForm) (InputForm) (InputForm)))): Not documented!!!!
; compiling file "/var/aw/var/LatexWiki/SEXPM.NRLIB/SEXPM.lsp" (written 16 JUL 2018 08:56:26 PM):

; /var/aw/var/LatexWiki/SEXPM.NRLIB/SEXPM.fasl written
; compilation finished in 0:00:00.049
------------------------------------------------------------------------
   SExprPatternMatch is now explicitly exposed in frame initial 
   SExprPatternMatch will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SEXPM.NRLIB/SEXPM

Test flavours
fricas
--)co sexpm
fricas
)set break resume

X ==> Expression Integer
Type: Void
fricas
IF ==> InputForm
Type: Void
fricas
SPM ==> SEXPM(X)
Type: Void
fricas
p:=convert(p)$InputForm
\begin{equation}
\label{eq1}p\end{equation}
Type: InputForm?
fricas
x:=x::IF
\begin{equation}
\label{eq2}x\end{equation}
Type: InputForm?
fricas
f:=f::IF
\begin{equation}
\label{eq3}f\end{equation}
Type: InputForm?
fricas
g:=g::IF
\begin{equation}
\label{eq4}g\end{equation}
Type: InputForm?
fricas
h:=h::IF
\begin{equation}
\label{eq5}h\end{equation}
Type: InputForm?
fricas
a:=a::IF
\begin{equation}
\label{eq6}a\end{equation}
Type: InputForm?
fricas
b:=b::IF
\begin{equation}
\label{eq7}b\end{equation}
Type: InputForm?
fricas
y:=y::IF
\begin{equation}
\label{eq8}y\end{equation}
Type: InputForm?
fricas
z:=z::IF
\begin{equation}
\label{eq9}z\end{equation}
Type: InputForm?
fricas
l1:=convert([p,x,convert [f,a]])$IF
\begin{equation}
\label{eq10}\left(p \  x \ {\left(f \  a \right)}\right)\end{equation}
Type: InputForm?
fricas
l2:=convert([p,b,y])$IF
\begin{equation}
\label{eq11}\left(p \  b \  y \right)\end{equation}
Type: InputForm?
fricas
l3:=convert([p,convert [f,x],convert [g,a,y]])$IF
\begin{equation}
\label{eq12}\left(p \ {\left(f \  x \right)}\ {\left(g \  a \  y \right)}\right)\end{equation}
Type: InputForm?
fricas
l4:=convert([p,convert [f,convert [h,b]],convert [g,x,y]])$IF
\begin{equation}
\label{eq13}\left(p \ {\left(f \ {\left(h \  b \right)}\right)}\ {\left(g \  x \  y \right)}\right)\end{equation}
Type: InputForm?
fricas
l5:=convert([p,x])$IF
\begin{equation}
\label{eq14}\left(p \  x \right)\end{equation}
Type: InputForm?
fricas
l6:=convert([p,convert [f,x]])$IF
\begin{equation}
\label{eq15}\left(p \ {\left(f \  x \right)}\right)\end{equation}
Type: InputForm?
fricas
l7:=convert([p,x,convert [f,y],x])$IF
\begin{equation}
\label{eq16}\left(p \  x \ {\left(f \  y \right)}\  x \right)\end{equation}
Type: InputForm?
fricas
l8:=convert([p,z,convert [f,z],a])$IF
\begin{equation}
\label{eq17}\left(p \  z \ {\left(f \  z \right)}\  a \right)\end{equation}
Type: InputForm?
fricas
r1:=unify(l1,l2)$SPM  -- (((f a) y) (b x))
\begin{equation}
\label{eq18}\left({\left({\left(f \  a \right)}\  y \right)}\ {\left(b \  x \right)}\right)\end{equation}
Type: InputForm?
fricas
r2:=unify(l3,l4)$SPM  -- (((h b) a) ((h b) x)) , only if variable? a
\begin{equation}
\label{eq19}\left({\left({\left(h \  b \right)}\  a \right)}\ {\left({\left(h \  b \right)}\  x \right)}\right)\end{equation}
Type: InputForm?
fricas
r3:=unify(l5,l6)$SPM  -- not-unifiable

   >> Error detected within library code:
   not-unifiable

   Continuing to read the file...

r4:=unify(l7,l8)$SPM  --  ((a z) (a y) (a x))
\begin{equation}
\label{eq20}\left({\left(a \  z \right)}\ {\left(a \  y \right)}\ {\left(a \  x \right)}\right)\end{equation}
Type: InputForm?
fricas
s11:=doSubst(l1,r1)$SPM
\begin{equation}
\label{eq21}\left(p \  b \ {\left(f \  a \right)}\right)\end{equation}
Type: InputForm?
fricas
s21:=doSubst(l2,r1)$SPM
\begin{equation}
\label{eq22}\left(p \  b \ {\left(f \  a \right)}\right)\end{equation}
Type: InputForm?
fricas
s74:=doSubst(l7,r4)$SPM
\begin{equation}
\label{eq23}\left(p \  a \ {\left(f \  a \right)}\  a \right)\end{equation}
Type: InputForm?
fricas
s84:=doSubst(l8,r4)$SPM
\begin{equation}
\label{eq24}\left(p \  a \ {\left(f \  a \right)}\  a \right)\end{equation}
Type: InputForm?
fricas
L1:=exp(-r^2+s)::IF
\begin{equation}
\label{eq25}\left(exp \ {\left(+ \  s \ {\left( \  - 1 \ {\left(^\  r \  2 \right)}\right)}\right)}\right)\end{equation*}
Type: InputForm?
fricas
L2:=exp(-r^2+q)::IF
\begin{equation}
\label{eq26}\left(exp \ {\left(+ \ {\left( \  - 1 \ {\left(^\  r \  2 \right)}\right)}\  q \right)}\right)\end{equation*}
Type: InputForm?
fricas
unify(L1,L2)$SPM  -- oweeh
\begin{equation}
\label{eq27}\left({\left({\left( \  - 1 \ {\left(^\  r \  2 \right)}\right)}\  q \right)}\ {\left({\left( \  - 1 \ {\left(^\  r \  2 \right)}\right)}\  s \right)}\right)\end{equation}
Type: InputForm?
fricas
unify(x+y,y+x)$SPM
\begin{equation}
\label{eq28}\left({\left(y \  x \right)}\right)\end{equation}
Type: InputForm?

What's the matter with TeX? for InputForm? ???

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(see the transcript file for additional information)
Output written on 7941444861566870036-16.0px.dvi (28 pages, 6780 bytes).
Transcript written on 7941444861566870036-16.0px.log.