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+\documentclass{article}
+\usepackage{axiom}
+
+\title{\File{src/interp/iterator.boot} Pamphlet}
+\author{The Axiom Team}
+
+\begin{document}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+
+\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
+-- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+-- 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>>
+
+--% ITERATORS
+
+compReduce(form,m,e) ==
+ compReduce1(form,m,e,$formalArgList)
+
+compReduce1(form is ["REDUCE",op,.,collectForm],m,e,$formalArgList) ==
+ [collectOp,:itl,body]:= collectForm
+ if STRINGP op then op:= INTERN op
+ ^MEMQ(collectOp,'(COLLECT COLLECTV COLLECTVEC)) =>
+ systemError ["illegal reduction form:",form]
+ $sideEffectsList: local
+ $until: local
+ $initList: local
+ $endTestList: local
+ $e:= e
+ itl:= [([.,$e]:= compIterator(x,$e) or return "failed").(0) for x in itl]
+ itl="failed" => return nil
+ e:= $e
+ acc:= GENSYM()
+ afterFirst:= GENSYM()
+ bodyVal:= GENSYM()
+ [part1,m,e]:= comp(["LET",bodyVal,body],m,e) or return nil
+ [part2,.,e]:= comp(["LET",acc,bodyVal],m,e) or return nil
+ [part3,.,e]:= comp(["LET",acc,parseTran [op,acc,bodyVal]],m,e) or return nil
+ identityCode:=
+ id:= getIdentity(op,e) => u.expr where u() == comp(id,m,e) or return nil
+ ["IdentityError",MKQ op]
+ finalCode:=
+ ["PROGN",
+ ["LET",afterFirst,nil],
+ ["REPEAT",:itl,
+ ["PROGN",part1,
+ ["IF", afterFirst,part3,
+ ["PROGN",part2,["LET",afterFirst,MKQ true]]]]],
+ ["IF",afterFirst,acc,identityCode]]
+ if $until then
+ [untilCode,.,e]:= comp($until,$Boolean,e)
+ finalCode:= substitute(["UNTIL",untilCode],'$until,finalCode)
+ [finalCode,m,e]
+
+getIdentity(x,e) ==
+ GETL(x,"THETA") is [y] => y
+
+numberize x ==
+ x=$Zero => 0
+ x=$One => 1
+ atom x => x
+ [numberize first x,:numberize rest x]
+
+compRepeatOrCollect(form,m,e) ==
+ fn(form,[m,:$exitModeStack],[#$exitModeStack,:$leaveLevelStack],$formalArgList
+ ,e) where
+ fn(form,$exitModeStack,$leaveLevelStack,$formalArgList,e) ==
+ $until: local
+ [repeatOrCollect,:itl,body]:= form
+ itl':=
+ [([x',e]:= compIterator(x,e) or return "failed"; x') for x in itl]
+ itl'="failed" => nil
+ targetMode:= first $exitModeStack
+ bodyMode:=
+ repeatOrCollect="COLLECT" =>
+ targetMode = '$EmptyMode => '$EmptyMode
+ (u:=modeIsAggregateOf('List,targetMode,e)) =>
+ CADR u
+ (u:=modeIsAggregateOf('PrimitiveArray,targetMode,e)) =>
+ repeatOrCollect:='COLLECTV
+ CADR u
+ (u:=modeIsAggregateOf('Vector,targetMode,e)) =>
+ repeatOrCollect:='COLLECTVEC
+ CADR u
+ stackMessage('"Invalid collect bodytype")
+ return nil
+ -- If we're doing a collect, and the type isn't conformable
+ -- then we've boobed. JHD 26.July.1990
+ $NoValueMode
+ [body',m',e']:=
+ -- (m1:= listOrVectorElementMode targetMode) and comp(body,m1,e) or
+ compOrCroak(body,bodyMode,e) or return nil
+ if $until then
+ [untilCode,.,e']:= comp($until,$Boolean,e')
+ itl':= substitute(["UNTIL",untilCode],'$until,itl')
+ form':= [repeatOrCollect,:itl',body']
+ m'':=
+ repeatOrCollect="COLLECT" =>
+ (u:=modeIsAggregateOf('List,targetMode,e)) => CAR u
+ ["List",m']
+ repeatOrCollect="COLLECTV" =>
+ (u:=modeIsAggregateOf('PrimitiveArray,targetMode,e)) => CAR u
+ ["PrimitiveArray",m']
+ repeatOrCollect="COLLECTVEC" =>
+ (u:=modeIsAggregateOf('Vector,targetMode,e)) => CAR u
+ ["Vector",m']
+ m'
+ coerceExit([form',m'',e'],targetMode)
+
+--constructByModemap([x,source,e],target) ==
+-- u:=
+-- [cexpr
+-- for (modemap:= [map,cexpr]) in getModemapList("construct",1,e) | map is [
+-- .,t,s] and modeEqual(t,target) and modeEqual(s,source)] or return nil
+-- fn:= (or/[selfn for [cond,selfn] in u | cond=true]) or return nil
+-- [["call",fn,x],target,e]
+
+listOrVectorElementMode x ==
+ x is [a,b,:.] and member(a,'(PrimitiveArray Vector List)) => b
+
+compIterator(it,e) ==
+ it is ["IN",x,y] =>
+ --these two lines must be in this order, to get "for f in list f"
+ --to give an error message if f is undefined
+ [y',m,e]:= comp(y,$EmptyMode,e) or return nil
+ $formalArgList:= [x,:$formalArgList]
+ [mOver,mUnder]:=
+ modeIsAggregateOf("List",m,e) or return
+ stackMessage ["mode: ",m," must be a list of some mode"]
+ if null get(x,"mode",e) then [.,.,e]:=
+ compMakeDeclaration([":",x,mUnder],$EmptyMode,e) or return nil
+ e:= put(x,"value",[genSomeVariable(),mUnder,e],e)
+ [y'',m'',e] := coerce([y',m,e], mOver) or return nil
+ [["IN",x,y''],e]
+ it is ["ON",x,y] =>
+ $formalArgList:= [x,:$formalArgList]
+ [y',m,e]:= comp(y,$EmptyMode,e) or return nil
+ [mOver,mUnder]:=
+ modeIsAggregateOf("List",m,e) or return
+ stackMessage ["mode: ",m," must be a list of other modes"]
+ if null get(x,"mode",e) then [.,.,e]:=
+ compMakeDeclaration([":",x,m],$EmptyMode,e) or return nil
+ e:= put(x,"value",[genSomeVariable(),m,e],e)
+ [y'',m'',e] := coerce([y',m,e], mOver) or return nil
+ [["ON",x,y''],e]
+ it is ["STEP",index,start,inc,:optFinal] =>
+ $formalArgList:= [index,:$formalArgList]
+ --if all start/inc/end compile as small integers, then loop
+ --is compiled as a small integer loop
+ final':= nil
+ (start':= comp(start,$SmallInteger,e)) and
+ (inc':= comp(inc,$NonNegativeInteger,start'.env)) and
+ (not (optFinal is [final]) or
+ (final':= comp(final,$SmallInteger,inc'.env))) =>
+ indexmode:=
+ comp(start,$NonNegativeInteger,e) =>
+ $NonNegativeInteger
+ $SmallInteger
+ if null get(index,"mode",e) then [.,.,e]:=
+ compMakeDeclaration([":",index,indexmode],$EmptyMode,
+ (final' => final'.env; inc'.env)) or return nil
+ e:= put(index,"value",[genSomeVariable(),indexmode,e],e)
+ if final' then optFinal:= [final'.expr]
+ [["ISTEP",index,start'.expr,inc'.expr,:optFinal],e]
+ [start,.,e]:=
+ comp(start,$Integer,e) or return
+ stackMessage ["start value of index: ",start," must be an integer"]
+ [inc,.,e]:=
+ comp(inc,$Integer,e) or return
+ stackMessage ["index increment:",inc," must be an integer"]
+ if optFinal is [final] then
+ [final,.,e]:=
+ comp(final,$Integer,e) or return
+ stackMessage ["final value of index: ",final," must be an integer"]
+ optFinal:= [final]
+ indexmode:=
+ comp(CADDR it,$NonNegativeInteger,e) => $NonNegativeInteger
+ $Integer
+ if null get(index,"mode",e) then [.,.,e]:=
+ compMakeDeclaration([":",index,indexmode],$EmptyMode,e) or return nil
+ e:= put(index,"value",[genSomeVariable(),indexmode,e],e)
+ [["STEP",index,start,inc,:optFinal],e]
+ it is ["WHILE",p] =>
+ [p',m,e]:=
+ comp(p,$Boolean,e) or return
+ stackMessage ["WHILE operand: ",p," is not Boolean valued"]
+ [["WHILE",p'],e]
+ it is ["UNTIL",p] => ($until:= p; ['$until,e])
+ it is ["|",x] =>
+ u:=
+ comp(x,$Boolean,e) or return
+ stackMessage ["SUCHTHAT operand: ",x," is not Boolean value"]
+ [["|",u.expr],u.env]
+ nil
+
+--isAggregateMode(m,e) ==
+-- m is [c,R] and MEMQ(c,'(Vector List)) => R
+-- name:=
+-- m is [fn,:.] => fn
+-- m="$" => "Rep"
+-- m
+-- get(name,"value",e) is [c,R] and MEMQ(c,'(Vector List)) => R
+
+modeIsAggregateOf(ListOrVector,m,e) ==
+ m is [ =ListOrVector,R] => [m,R]
+--m = '$EmptyMode => [m,m] I don't think this is correct, breaks POLY +
+ m is ["Union",:l] =>
+ mList:= [pair for m' in l | (pair:= modeIsAggregateOf(ListOrVector,m',e))]
+ 1=#mList => first mList
+ name:=
+ m is [fn,:.] => fn
+ m="$" => "Rep"
+ m
+ get(name,"value",e) is [[ =ListOrVector,R],:.] => [m,R]
+
+--% VECTOR ITERATORS
+
+--the following 4 functions are not currently used
+
+--compCollectV(form,m,e) ==
+-- fn(form,[m,:$exitModeStack],[#$exitModeStack,:$leaveLevelStack],e) where
+-- fn(form,$exitModeStack,$leaveLevelStack,e) ==
+-- [repeatOrCollect,it,body]:= form
+-- [it',e]:= compIteratorV(it,e) or return nil
+-- m:= first $exitModeStack
+-- [mOver,mUnder]:= modeIsAggregateOf("Vector",m,e) or $EmptyMode
+-- [body',m',e']:= compOrCroak(body,mUnder,e) or return nil
+-- form':= ["COLLECTV",it',body']
+-- {n:=
+-- it' is ("STEP",.,s,i,f) or it' is ("ISTEP",.,s,i,f) =>
+-- computeMaxIndex(s,f,i);
+-- return nil}
+-- coerce([form',mOver,e'],m)
+--
+--compIteratorV(it,e) ==
+-- it is ["STEP",index,start,inc,final] =>
+-- (start':= comp(start,$Integer,e)) and
+-- (inc':= comp(inc,$NonNegativeInteger,start'.env)) and
+-- (final':= comp(final,$Integer,inc'.env)) =>
+-- indexmode:=
+-- comp(start,$NonNegativeInteger,e) => $NonNegativeInteger
+-- $Integer
+-- if null get(index,"mode",e) then [.,.,e]:=
+-- compMakeDeclaration([":",index,indexmode],$EmptyMode,final'.env) or
+-- return nil
+-- e:= put(index,"value",[genSomeVariable(),indexmode,e],e)
+-- [["ISTEP",index,start'.expr,inc'.expr,final'.expr],e]
+-- [start,.,e]:=
+-- comp(start,$Integer,e) or return
+-- stackMessage ["start value of index: ",start," is not an integer"]
+-- [inc,.,e]:=
+-- comp(inc,$NonNegativeInteger,e) or return
+-- stackMessage ["index increment: ",inc," must be a non-negative integer"]
+-- [final,.,e]:=
+-- comp(final,$Integer,e) or return
+-- stackMessage ["final value of index: ",final," is not an integer"]
+-- indexmode:=
+-- comp(CADDR it,$NonNegativeInteger,e) => $NonNegativeInteger
+-- $Integer
+-- if null get(index,"mode",e) then [.,.,e]:=
+-- compMakeDeclaration([":",index,indexmode],$EmptyMode,e) or return nil
+-- e:= put(index,"value",[genSomeVariable(),indexmode,e],e)
+-- [["STEP",index,start,inc,final],e]
+-- nil
+--
+--computeMaxIndex(s,f,i) ==
+-- i^=1 => cannotDo()
+-- s=1 => f
+-- exprDifference(f,exprDifference(s,1))
+--
+--exprDifference(x,y) ==
+-- y=0 => x
+-- FIXP x and FIXP y => DIFFERENCE(x,y)
+-- ["DIFFERENCE",x,y]
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}