\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/interp termrw.boot}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\begin{verbatim}
Algorithms for Term Reduction
 
The following assumptions are made:

a term rewrite system is represented by a pair (varlist,varRules) where
  varlist is the list of rewrite variables (test by MEMQ) and varRules
  is an alist (no variables may occur in varRules)

the following rewrite functions are available:
  termRW looks for a fixpoint in applying varRules, where the outermost
    leftmost is reduced first by term1RW
  term1RW applies the first rule

subCopy uses an alist (calls of ASSQ) to substitute a list structure
  no left side of a pair of alist may appear on a righthand side
  this means, subCopy is an idempotent function

in both cases copying is only done if necessary to avoid destruction
this means, EQ can be used to check whether something was done
 
\end{verbatim}
\section{License}
<<license>>=
-- Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
-- All rights reserved.
--
-- Redistribution and use in source and binary forms, with or without
-- modification, are permitted provided that the following conditions are
-- met:
--
--     - Redistributions of source code must retain the above copyright
--       notice, this list of conditions and the following disclaimer.
--
--     - Redistributions in binary form must reproduce the above copyright
--       notice, this list of conditions and the following disclaimer in
--       the documentation and/or other materials provided with the
--       distribution.
--
--     - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--       names of its contributors may be used to endorse or promote products
--       derived from this software without specific prior written permission.
--
-- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
-- IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
-- TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
-- PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
-- OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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-- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
-- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

@
<<*>>=
<<license>>
 
termRW(t,R) ==
  -- reduce t by rewrite system R
  until b repeat
    t0:= termRW1(t,R)
    b:= EQ(t,t0)
    t:= t0
  t
 
termRW1(t,R) ==
  -- tries to do one reduction on the leftmost outermost subterm of t
  t0:= term1RW(t,R)
  not EQ(t0,t) or atom t => t0
  [t1,:t2]:= t
  tt1:= termRW1(t1,R)
  tt2:= t2 and termRW1(t2,R)
  EQ(t1,tt1) and EQ(t2,tt2) => t
  CONS(tt1,tt2)
 
term1RW(t,R) ==
  -- tries to reduce t at the top node
  [vars,:varRules]:= R
  for r in varRules until not (SL='failed) repeat
    SL:= termMatch(CAR r,t,NIL,vars)
    not (SL='failed) =>
      t:= subCopy(copy CDR r,SL)
  t
 
term1RWall(t,R) ==
  -- same as term1RW, but returns a list
  [vars,:varRules]:= R
  [not (SL='failed) and subCopy(copy CDR r,SL) for r in varRules |
    not EQ(SL:= termMatch(CAR r,t,NIL,vars),'failed)]
 
termMatch(tp,t,SL,vars) ==
  -- t is a term pattern, t a term
  -- then the result is the augmented substitution SL or 'failed
  tp=t => SL
  atom tp =>
    MEMQ(tp,vars) =>
      p:= ASSOC(tp,SL) => ( CDR p=t )
      CONS(CONS(tp,t),SL)
    'failed
  atom t => 'failed
  [tp1,:tp2]:= tp
  [t1,:t2]:= t
  SL:= termMatch(tp1,t1,SL,vars)
  SL='failed => 'failed
  tp2 and t2 => termMatch(tp2,t2,SL,vars)
  tp2 or t2 => 'failed
  SL
 
 
--% substitution handling
 
-- isContained(v,t) ==
--   -- tests (by EQ), whether v occurs in term t
--   -- v must not be NIL
--   EQ(v,t) => 'T
--   atom t => NIL
--   isContained(v,CAR t) or isContained(v,CDR t)
 
augmentSub(v,t,SL) ==
  -- destructively adds the pair (v,t) to the substitution list SL
  -- t doesn't contain any of the variables of SL
  q:= CONS(v,t)
  null SL => [q]
--  for p in SL repeat RPLACD(p,SUBSTQ(t,v,CDR p))
  CONS(q,SL)
 
mergeSubs(S1,S2) ==
  -- augments S2 by each pair of S1
  -- S1 doesn't contain any of the variables of S2
  null S1 => S2
  null S2 => S1
  S3 := [p for p in S2 | not ASSQ(CAR p, S1)]
--  for p in S1 repeat S3:= augmentSub(CAR p,CDR p,S3)
  APPEND(S1,S3)
 
subCopy(t,SL) ==
  -- t is any LISP structure, SL a substitution list for sharp variables
  -- then t is substituted and copied if necessary
  SL=NIL => t
  subCopy0(t,SL)
 
subCopy0(t, SL) ==
  p := subCopyOrNil(t, SL) => CDR p
  t
  
subCopyOrNil(t,SL) ==
  -- the same as subCopy, but the result is NIL if nothing was copied
  p:= ASSOC(t,SL) => p
  atom t => NIL
  [t1,:t2]:= t
  t0:= subCopyOrNil(t1,SL) =>
    t2 => CONS(t, CONS(CDR t0, subCopy0(t2,SL)))
    CONS(t,CONS(CDR t0,t2))
  t2 and ( t0:= subCopyOrNil(t2,SL) ) => CONS(t, CONS(t1,CDR t0))
  NIL
 
 
deepSubCopy(t,SL) ==
  -- t is any LISP structure, SL a substitution list for sharp variables
  -- then t is substituted and copied if necessary
  SL=NIL => t
  deepSubCopy0(t,SL)
 
deepSubCopy0(t, SL) ==
  p := deepSubCopyOrNil(t, SL) => CDR p
  t
  
deepSubCopyOrNil(t,SL) ==
  -- the same as subCopy, but the result is NIL if nothing was copied
  p:= ASSOC(t,SL) => CONS(t, deepSubCopy0(CDR p, SL))
  atom t => NIL
  [t1,:t2]:= t
  t0:= deepSubCopyOrNil(t1,SL) =>
    t2 => CONS(t, CONS(CDR t0, deepSubCopy0(t2,SL)))
    CONS(t,CONS(CDR t0,t2))
  t2 and ( t0:= deepSubCopyOrNil(t2,SL) ) => CONS(t, CONS(t1,CDR t0))
 
 
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}