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+\documentclass{article}
+\usepackage{axiom}
+
+\title{\$SPAD/src/interp modemap.boot}
+\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>>
+
+--% EXTERNAL ROUTINES
+ 
+--These functions are called from outside this file to add a domain
+--   or to get the current domains in scope;
+ 
+addDomain(domain,e) ==
+  atom domain =>
+    EQ(domain,"$EmptyMode") => e
+    EQ(domain,"$NoValueMode") => e
+    not IDENTP domain or 2<#(s:= STRINGIMAGE domain) and
+      EQ(char "#",s.(0)) and EQ(char "#",s.(1)) => e
+    MEMQ(domain,getDomainsInScope e) => e
+    isLiteral(domain,e) => e
+    addNewDomain(domain,e)
+  (name:= first domain)='Category => e
+  domainMember(domain,getDomainsInScope e) => e
+  getmode(name,e) is ["Mapping",target,:.] and isCategoryForm(target,e)=>
+      addNewDomain(domain,e)
+    -- constructor? test needed for domains compiled with $bootStrapMode=true
+  isFunctor name or constructor? name => addNewDomain(domain,e)
+  if not isCategoryForm(domain,e) and
+    not member(name,'(Mapping CATEGORY)) then
+      unknownTypeError name
+  e        --is not a functor
+ 
+domainMember(dom,domList) == or/[modeEqual(dom,d) for d in domList]
+ 
+--% MODEMAP FUNCTIONS
+ 
+--getTargetMode(x is [op,:argl],e) ==
+--  CASES(#(mml:= getModemapList(op,#argl,e)),
+--    (1 =>
+--    ([[.,target,:.],:.]:= first mml; substituteForFormalArguments(argl,target))
+--      ; 0 => MOAN(x," has no modemap"); systemError [x," has duplicate modemaps"]))
+ 
+getModemap(x is [op,:.],e) ==
+  for modemap in get(op,'modemap,e) repeat
+    if u:= compApplyModemap(x,modemap,e,nil) then return
+      ([.,.,sl]:= u; SUBLIS(sl,modemap))
+ 
+getUniqueSignature(form,e) ==
+  [[.,:sig],:.]:= getUniqueModemap(first form,#rest form,e) or return nil
+  sig
+ 
+getUniqueModemap(op,numOfArgs,e) ==
+  1=#(mml:= getModemapList(op,numOfArgs,e)) => first mml
+  1<#mml =>
+    stackWarning [numOfArgs,'" argument form of: ",op,
+      '" has more than one modemap"]
+    first mml
+  nil
+ 
+getModemapList(op,numOfArgs,e) ==
+  op is ['elt,D,op'] => getModemapListFromDomain(op',numOfArgs,D,e)
+  [mm for
+    (mm:= [[.,.,:sigl],:.]) in get(op,'modemap,e) | numOfArgs=#sigl]
+ 
+getModemapListFromDomain(op,numOfArgs,D,e) ==
+  [mm
+    for (mm:= [[dc,:sig],:.]) in get(op,'modemap,e) | dc=D and #rest sig=
+      numOfArgs]
+ 
+addModemapKnown(op,mc,sig,pred,fn,$e) ==
+--  if knownInfo pred then pred:=true
+--  that line is handled elsewhere
+  $insideCapsuleFunctionIfTrue=true =>
+    $CapsuleModemapFrame :=
+      addModemap0(op,mc,sig,pred,fn,$CapsuleModemapFrame)
+    $e
+  addModemap0(op,mc,sig,pred,fn,$e)
+ 
+addModemap0(op,mc,sig,pred,fn,e) ==
+  --mc is the "mode of computation"; fn the "implementation"
+  $functorForm is ['CategoryDefaults,:.] and mc="$" => e
+    --don't put CD modemaps into environment
+  --fn is ['Subsumed,:.] => e  -- don't skip subsumed modemaps
+                               -- breaks -:($,$)->U($,failed) in DP
+  op='elt or op='setelt => addEltModemap(op,mc,sig,pred,fn,e)
+  addModemap1(op,mc,sig,pred,fn,e)
+ 
+addEltModemap(op,mc,sig,pred,fn,e) ==
+   --hack to change selectors from strings to identifiers; and to
+   --add flag identifiers as literals in the envir
+  op='elt and sig is [:lt,sel] =>
+    STRINGP sel =>
+      id:= INTERN sel
+      if $insideCapsuleFunctionIfTrue=true
+         then $e:= makeLiteral(id,$e)
+         else e:= makeLiteral(id,e)
+      addModemap1(op,mc,[:lt,id],pred,fn,e)
+    -- atom sel => systemErrorHere '"addEltModemap"
+    addModemap1(op,mc,sig,pred,fn,e)
+  op='setelt and sig is [:lt,sel,v] =>
+    STRINGP sel =>
+      id:= INTERN sel
+      if $insideCapsuleFunctionIfTrue=true
+         then $e:= makeLiteral(id,$e)
+         else e:= makeLiteral(id,e)
+      addModemap1(op,mc,[:lt,id,v],pred,fn,e)
+    -- atom sel => systemError '"addEltModemap"
+    addModemap1(op,mc,sig,pred,fn,e)
+  systemErrorHere '"addEltModemap"
+ 
+--------------------> NEW DEFINITION (override in xruncomp.boot.pamphlet)
+addModemap1(op,mc,sig,pred,fn,e) ==
+   --mc is the "mode of computation"; fn the "implementation"
+  if mc='Rep then
+     if fn is [kind,'Rep,.] and
+               -- save old sig for NRUNTIME
+       (kind = 'ELT or kind = 'CONST) then fn:=[kind,'Rep,sig]
+     sig:= substitute("$",'Rep,sig)
+  currentProplist:= getProplist(op,e) or nil
+  newModemapList:=
+    mkNewModemapList(mc,sig,pred,fn,LASSOC('modemap,currentProplist),e,nil)
+  newProplist:= augProplist(currentProplist,'modemap,newModemapList)
+  newProplist':= augProplist(newProplist,"FLUID",true)
+  unErrorRef op
+        --There may have been a warning about op having no value
+  addBinding(op,newProplist',e)
+ 
+mkNewModemapList(mc,sig,pred,fn,curModemapList,e,filenameOrNil) ==
+  entry:= [map:= [mc,:sig],[pred,fn],:filenameOrNil]
+  member(entry,curModemapList) => curModemapList
+  (oldMap:= ASSOC(map,curModemapList)) and oldMap is [.,[opred, =fn],:.] =>
+    $forceAdd => mergeModemap(entry,curModemapList,e)
+    opred=true => curModemapList
+    if pred^=true and pred^=opred then pred:= ["OR",pred,opred]
+    [if x=oldMap then [map,[pred,fn],:filenameOrNil] else x
+ 
+  --if new modemap less general, put at end; otherwise, at front
+      for x in curModemapList]
+  $InteractiveMode => insertModemap(entry,curModemapList)
+  mergeModemap(entry,curModemapList,e)
+ 
+mergeModemap(entry is [[mc,:sig],[pred,:.],:.],modemapList,e) ==
+  for (mmtail:= [[[mc',:sig'],[pred',:.],:.],:.]) in tails modemapList repeat
+    mc=mc' or isSuperDomain(mc',mc,e) =>
+      newmm:= nil
+      mm:= modemapList
+      while (not EQ(mm,mmtail)) repeat (newmm:= [first mm,:newmm]; mm:= rest mm)
+      if (mc=mc') and (sig=sig') then
+        --We only need one of these, unless the conditions are hairy
+        not $forceAdd and TruthP pred' =>
+          entry:=nil
+              --the new predicate buys us nothing
+          return modemapList
+        TruthP pred => mmtail:=rest mmtail
+          --the thing we matched against is useless, by comparison
+      modemapList:= NCONC(NREVERSE newmm,[entry,:mmtail])
+      entry:= nil
+      return modemapList
+  if entry then [:modemapList,entry] else modemapList
+ 
+-- next definition RPLACs, and hence causes problems.
+-- In ptic., SubResGcd in SparseUnivariatePolynomial is miscompiled
+--mergeModemap(entry:=((mc,:sig),:.),modemapList,e) ==
+--    for (mmtail:= (((mc',:sig'),:.),:.)) in tails modemapList do
+--       mc=mc' or isSuperDomain(mc',mc,e)  =>
+--         RPLACD(mmtail,(first mmtail,: rest mmtail))
+--         RPLACA(mmtail,entry)
+--         entry := nil
+--         return modemapList
+--     if entry then (:modemapList,entry) else modemapList
+ 
+isSuperDomain(domainForm,domainForm',e) ==
+  isSubset(domainForm',domainForm,e) => true
+  domainForm='Rep and domainForm'="$" => true --regard $ as a subdomain of Rep
+  LASSOC(opOf domainForm',get(domainForm,"SubDomain",e))
+ 
+--substituteForRep(entry is [[mc,:sig],:.],curModemapList) ==
+--  --change 'Rep to "$" unless the resulting signature is already in $
+--  member(entry':= substitute("$",'Rep,entry),curModemapList) =>
+--    [entry,:curModemapList]
+--  [entry,entry',:curModemapList]
+ 
+addNewDomain(domain,e) ==
+  augModemapsFromDomain(domain,domain,e)
+ 
+augModemapsFromDomain(name,functorForm,e) ==
+  member(KAR name or name,$DummyFunctorNames) => e
+  name=$Category or isCategoryForm(name,e) => e
+  member(name,curDomainsInScope:= getDomainsInScope e) => e
+  if u:= GETDATABASE(opOf functorForm,'SUPERDOMAIN) then
+    e:= addNewDomain(first u,e)
+    --need code to handle parameterized SuperDomains
+  if innerDom:= listOrVectorElementMode name then e:= addDomain(innerDom,e)
+  if name is ["Union",:dl] then for d in stripUnionTags dl
+                         repeat e:= addDomain(d,e)
+  augModemapsFromDomain1(name,functorForm,e)
+     --see LISPLIB BOOT
+ 
+substituteCategoryArguments(argl,catform) ==
+  argl:= substitute("$$","$",argl)
+  arglAssoc:= [[INTERNL("#",STRINGIMAGE i),:a] for i in 1.. for a in argl]
+  SUBLIS(arglAssoc,catform)
+ 
+         --Called, by compDefineFunctor, to add modemaps for $ that may
+         --be equivalent to those of Rep. We must check that these
+         --operations are not being redefined.
+augModemapsFromCategoryRep(domainName,repDefn,functorBody,categoryForm,e) ==
+  [fnAlist,e]:= evalAndSub(domainName,domainName,domainName,categoryForm,e)
+  [repFnAlist,e]:= evalAndSub('Rep,'Rep,repDefn,getmode(repDefn,e),e)
+  catform:= (isCategory categoryForm => categoryForm.(0); categoryForm)
+  compilerMessage ["Adding ",domainName," modemaps"]
+  e:= putDomainsInScope(domainName,e)
+  $base:= 4
+  for [lhs:=[op,sig,:.],cond,fnsel] in fnAlist repeat
+    u:=ASSOC(SUBST('Rep,domainName,lhs),repFnAlist)
+    u and not AMFCR_,redefinedList(op,functorBody) =>
+      fnsel':=CADDR u
+      e:= addModemap(op,domainName,sig,cond,fnsel',e)
+    e:= addModemap(op,domainName,sig,cond,fnsel,e)
+  e
+ 
+AMFCR_,redefinedList(op,l) == "OR"/[AMFCR_,redefined(op,u) for u in l]
+ 
+AMFCR_,redefined(opname,u) ==
+  not(u is [op,:l]) => nil
+  op = 'DEF => opname = CAAR l
+  MEMQ(op,'(PROGN SEQ)) => AMFCR_,redefinedList(opname,l)
+  op = 'COND => "OR"/[AMFCR_,redefinedList(opname,CDR u) for u in l]
+ 
+augModemapsFromCategory(domainName,domainView,functorForm,categoryForm,e) ==
+  [fnAlist,e]:= evalAndSub(domainName,domainView,functorForm,categoryForm,e)
+  --  catform:= (isCategory categoryForm => categoryForm.(0); categoryForm)
+  -- catform appears not to be used, so why set it?
+  --if ^$InteractiveMode then
+  compilerMessage ["Adding ",domainName," modemaps"]
+  e:= putDomainsInScope(domainName,e)
+  $base:= 4
+  condlist:=[]
+  for [[op,sig,:.],cond,fnsel] in fnAlist repeat
+--  e:= addModemap(op,domainName,sig,cond,fnsel,e)
+---------next 5 lines commented out to avoid wasting time checking knownInfo on
+---------conditions attached to each modemap being added, takes a very long time
+---------instead conditions will be checked when maps are actually used
+  --v:=ASSOC(cond,condlist) =>
+  --  e:= addModemapKnown(op,domainName,sig,CDR v,fnsel,e)
+  --$e:local := e  -- $e is used by knownInfo
+  --if knownInfo cond then cond1:=true else cond1:=cond
+  --condlist:=[[cond,:cond1],:condlist]
+    e:= addModemapKnown(op,domainName,sig,cond,fnsel,e) -- cond was cond1
+--  for u in sig | (not member(u,$DomainsInScope)) and
+--                   (not atom u) and
+--                     (not isCategoryForm(u,e)) do
+--     e:= addNewDomain(u,e)
+  e
+ 
+--subCatParametersInto(domainForm,catForm,e) ==
+--  -- JHD 08/08/84 perhaps we are fortunate that it is not used
+--  --this is particularly dirty and should be cleaned up, say, by wrapping
+--  -- an appropriate lambda expression around mapping forms
+--  domainForm is [op,:l] and l =>
+--    get(op,'modemap,e) is [[[mc,:.],:.]] => SUBLIS(PAIR(rest mc,l),catForm)
+--  catForm
+ 
+--------------------> NEW DEFINITION (override in xruncomp.boot.pamphlet)
+evalAndSub(domainName,viewName,functorForm,form,$e) ==
+  $lhsOfColon: local:= domainName
+  isCategory form => [substNames(domainName,viewName,functorForm,form.(1)),$e]
+  --next lines necessary-- see MPOLY for which $ is actual arg. --- RDJ 3/83
+  if CONTAINED("$$",form) then $e:= put("$$","mode",get("$","mode",$e),$e)
+  opAlist:= getOperationAlist(domainName,functorForm,form)
+  substAlist:= substNames(domainName,viewName,functorForm,opAlist)
+  [substitute("$","$$",substAlist),$e]
+ 
+getOperationAlist(name,functorForm,form) ==
+  if atom name and GETDATABASE(name,'NILADIC) then functorForm:= [functorForm]
+-- (null isConstructorForm functorForm) and (u:= isFunctor functorForm)
+  (u:= isFunctor functorForm) and not
+    ($insideFunctorIfTrue and first functorForm=first $functorForm) => u
+  $insideFunctorIfTrue and name="$" =>
+    ($domainShell => $domainShell.(1); systemError '"$ has no shell now")
+  T:= compMakeCategoryObject(form,$e) => ([.,.,$e]:= T; T.expr.(1))
+  stackMessage ["not a category form: ",form]
+ 
+--------------------> NEW DEFINITION (override in xruncomp.boot.pamphlet)
+substNames(domainName,viewName,functorForm,catForm) ==
+  EQSUBSTLIST(KDR functorForm,$FormalMapVariableList,
+ -- [[[op,if KAR fnsel="PAC" then sig else SUBSTQ(domainName,"$",sig),:x],pred,
+ --   SUBSTQ(viewName,"$",fnsel)] for [[op,sig,:x],pred,fnsel] in catForm])
+       -- following calls to SUBSTQ must copy to save RPLAC's in
+       -- putInLocalDomainReferences
+    [[:SUBSTQ(domainName,"$",modemapform),SUBSTQ(viewName,"$",fnsel)]
+      for [:modemapform,fnsel] in catForm])
+ 
+compCat(form is [functorName,:argl],m,e) ==
+  fn:= GETL(functorName,"makeFunctionList") or return nil
+  [funList,e]:= FUNCALL(fn,form,form,e)
+  catForm:=
+    ["Join",'(SetCategory),["CATEGORY","domain",:
+      [["SIGNATURE",op,sig] for [op,sig,.] in funList | op^="="]]]
+  --RDJ: for coercion purposes, it necessary to know it's a Set; I'm not
+  --sure if it uses any of the other signatures(see extendsCategoryForm)
+  [form,catForm,e]
+ 
+--------------------> NEW DEFINITION (override in xruncomp.boot.pamphlet)
+addConstructorModemaps(name,form is [functorName,:.],e) ==
+  $InteractiveMode: local:= nil
+  e:= putDomainsInScope(name,e) --frame
+  fn := GETL(functorName,"makeFunctionList")
+  [funList,e]:= FUNCALL(fn,name,form,e)
+  for [op,sig,opcode] in funList repeat
+    e:= addModemap(op,name,sig,true,opcode,e)
+  e
+ 
+ 
+--The way XLAMs work:
+--  ((XLAM ($1 $2 $3) (SETELT $1 0 $3)) X "c" V) ==> (SETELT X 0 V)
+ 
+getDomainsInScope e ==
+  $insideCapsuleFunctionIfTrue=true => $CapsuleDomainsInScope
+  get("$DomainsInScope","special",e)
+ 
+putDomainsInScope(x,e) ==
+  l:= getDomainsInScope e
+  if member(x,l) then SAY("****** Domain: ",x," already in scope")
+  newValue:= [x,:delete(x,l)]
+  $insideCapsuleFunctionIfTrue => ($CapsuleDomainsInScope:= newValue; e)
+  put("$DomainsInScope","special",newValue,e)
+ 
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}