path: root/src/algebra/fortran.spad.pamphlet

\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{src/algebra fortran.spad}
\author{Didier Pinchon, Mike Dewar, William Naylor}
\maketitle

\begin{abstract}
\end{abstract}
\tableofcontents
\eject

\section{domain RESULT Result}

<<domain RESULT Result>>=
import Boolean
import Symbol
import OutputForm
import Any
import TableAggregate
)abbrev domain RESULT Result
++ Author: Didier Pinchon and Mike Dewar
++ Date Created:  8 April 1994
++ Date Last Updated: 28 June 1994 
++ Basic Operations:
++ Related Domains:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ Examples:
++ References:
++ Description: A domain used to return the results from a call to the NAG
++ Library.  It prints as a list of names and types, though the user may 
++ choose to display values automatically if he or she wishes.
Result():Exports==Implementation where

  O  ==> OutputForm

  Exports ==> TableAggregate(Symbol,Any) with
    showScalarValues : Boolean -> Boolean
      ++ showScalarValues(true) forces the values of scalar components to be
      ++  displayed rather than just their types.
    showArrayValues : Boolean -> Boolean
      ++ showArrayValues(true) forces the values of array components to be
      ++  displayed rather than just their types.
    finiteAggregate

  Implementation ==> Table(Symbol,Any) add
    import SExpression

    -- Constant
    colon := ": "::Symbol::O
    elide := "..."::Symbol::O

    -- Flags
    showScalarValuesFlag : Boolean := false
    showArrayValuesFlag  : Boolean := false

    cleanUpDomainForm(d:SExpression):O ==
      not list? d => d::O
      #d=1 => (car d)::O
      -- If the car is an atom then we have a domain constructor, if not
      -- then we have some kind of value.  Since we often can't print these
      -- ****ers we just elide them.
      not atom? car d => elide
      prefix((car d)::O,[cleanUpDomainForm(u) for u in destruct cdr(d)]$List(O))

    display(v:Any,d:SExpression):O ==
      not list? d => error "Domain form is non-list"
      #d=1 =>
       showScalarValuesFlag => objectOf v
       cleanUpDomainForm d
      car(d) = convert("Complex"::Symbol)@SExpression =>
       showScalarValuesFlag => objectOf v
       cleanUpDomainForm d
      showArrayValuesFlag => objectOf v
      cleanUpDomainForm d
       
    makeEntry(k:Symbol,v:Any):O ==
      hconcat [k::O,colon,display(v,dom v)]

    coerce(r:%):O == 
      bracket [makeEntry(key,r.key) for key in reverse! keys(r)]

    showArrayValues(b:Boolean):Boolean  == showArrayValuesFlag := b
    showScalarValues(b:Boolean):Boolean == showScalarValuesFlag := b

@

\section{domain FC FortranCode}

<<domain FC FortranCode>>=
import Void
import List
import Fraction
)abbrev domain FC FortranCode 
-- The FortranCode domain is used to represent operations which are to be
-- translated into FORTRAN.
++ Author: Mike Dewar
++ Date Created: April 1991
++ Date Last Updated: 22 March 1994
++                    26 May 1994 Added common, MCD
++                    21 June 1994 Changed print to printStatement, MCD
++                    30 June 1994 Added stop, MCD
++                    12 July 1994 Added assign for String, MCD
++                     9 January 1995 Added fortran2Lines to getCall, MCD
++ Basic Operations:
++ Related Constructors: FortranProgram, Switch, FortranType
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ This domain builds representations of program code segments for use with
++ the FortranProgram domain.
FortranCode(): public == private where
  L ==> List
  PI ==> PositiveInteger
  PIN ==> Polynomial Integer
  SEX ==> SExpression
  O ==> OutputForm
  OP ==> Union(Null:"null",
               Assignment:"assignment",
               Conditional:"conditional",
               Return:"return",
               Block:"block",
               Comment:"comment",
               Call:"call",
               For:"for",
               While:"while",
               Repeat:"repeat",
               Goto:"goto",
               Continue:"continue",
	       ArrayAssignment:"arrayAssignment",
               Save:"save",
               Stop:"stop",
               Common:"common",
               Print:"print")
  ARRAYASS ==> Record(var:Symbol, rand:O, ints2Floats?:Boolean)
  EXPRESSION ==> Record(ints2Floats?:Boolean,expr:O)
  ASS ==> Record(var:Symbol,
                 arrayIndex:L PIN,
                 rand:EXPRESSION
                )
  COND ==> Record(switch: Switch(),
                  thenClause: $,
                  elseClause: $
                 )
  RETURN ==> Record(empty?:Boolean,value:EXPRESSION)
  BLOCK ==> List $
  COMMENT ==> List String
  COMMON ==> Record(name:Symbol,contents:List Symbol)
  CALL ==> String
  FOR ==> Record(range:SegmentBinding PIN, span:PIN,  body:$)
  LABEL ==> SingleInteger
  LOOP ==> Record(switch:Switch(),body:$)
  PRINTLIST ==> List O
  OPREC ==> Union(nullBranch:"null", assignmentBranch:ASS,
                  arrayAssignmentBranch:ARRAYASS,
                  conditionalBranch:COND, returnBranch:RETURN,
                  blockBranch:BLOCK, commentBranch:COMMENT, callBranch:CALL,
                  forBranch:FOR, labelBranch:LABEL, loopBranch:LOOP,
                  commonBranch:COMMON, printBranch:PRINTLIST)

  public == SetCategory with
    forLoop: (SegmentBinding PIN,$) -> $
     ++ forLoop(i=1..10,c) creates a representation of a FORTRAN DO loop with
     ++ \spad{i} ranging over the values 1 to 10.
    forLoop: (SegmentBinding PIN,PIN,$) -> $
     ++ forLoop(i=1..10,n,c) creates a representation of a FORTRAN DO loop with
     ++ \spad{i} ranging over the values 1 to 10 by n.
    whileLoop: (Switch,$) -> $
     ++ whileLoop(s,c) creates a while loop in FORTRAN.
    repeatUntilLoop: (Switch,$) -> $
     ++ repeatUntilLoop(s,c) creates a repeat ... until loop in FORTRAN.
    goto: SingleInteger -> $
      ++ goto(l) creates a representation of a FORTRAN GOTO statement
    continue: SingleInteger -> $
      ++ continue(l) creates a representation of a FORTRAN CONTINUE labelled 
      ++ with l
    comment: String -> $
      ++ comment(s) creates a representation of the String s as a single FORTRAN
      ++ comment.  
    comment: List String -> $
      ++ comment(s) creates a representation of the Strings s as a multi-line
      ++ FORTRAN comment.  
    call: String -> $
      ++ call(s) creates a representation of a FORTRAN CALL statement
    returns: () -> $
      ++ returns() creates a representation of a FORTRAN RETURN statement.
    returns: Expression MachineFloat -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    returns: Expression MachineInteger -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    returns: Expression MachineComplex -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    returns: Expression Float -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    returns: Expression Integer -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    returns: Expression Complex Float -> $
      ++ returns(e) creates a representation of a FORTRAN RETURN statement
      ++ with a returned value.
    cond: (Switch,$) -> $
      ++ cond(s,e) creates a representation of the FORTRAN expression
      ++ IF (s) THEN e.
    cond: (Switch,$,$) -> $
      ++ cond(s,e,f) creates a representation of the FORTRAN expression
      ++ IF (s) THEN e ELSE f.
    assign: (Symbol,String) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Expression MachineInteger) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Expression MachineFloat) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Expression MachineComplex) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix MachineInteger) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix MachineFloat) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix MachineComplex) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector MachineInteger) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector MachineFloat) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector MachineComplex) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression MachineInteger) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression MachineFloat) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression MachineComplex) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression MachineInteger) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression MachineFloat) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression MachineComplex) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,L PIN,Expression MachineInteger) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    assign: (Symbol,L PIN,Expression MachineFloat) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    assign: (Symbol,L PIN,Expression MachineComplex) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    assign: (Symbol,Expression Integer) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Expression Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Expression Complex Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression Integer) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Matrix Expression Complex Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression Integer) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,Vector Expression Complex Float) -> $
      ++ assign(x,y) creates a representation of the FORTRAN expression
      ++ x=y.
    assign: (Symbol,L PIN,Expression Integer) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    assign: (Symbol,L PIN,Expression Float) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    assign: (Symbol,L PIN,Expression Complex Float) -> $
      ++ assign(x,l,y) creates a representation of the assignment of \spad{y}
      ++ to the \spad{l}'th element of array \spad{x} (\spad{l} is a list of
      ++ indices).
    block: List($) -> $
      ++ block(l) creates a representation of the statements in l as a block.
    stop: () -> $
      ++ stop() creates a representation of a STOP statement.
    save: () -> $
      ++ save() creates a representation of a SAVE statement.
    printStatement: List O -> $
      ++ printStatement(l) creates a representation of a PRINT statement.
    common: (Symbol,List Symbol) -> $
      ++ common(name,contents) creates a representation a named common block.
    operation: $ -> OP
      ++ operation(f) returns the name of the operation represented by \spad{f}.
    code: $ -> OPREC
      ++ code(f) returns the internal representation of the object represented
      ++ by \spad{f}.
    printCode: $ -> Void
      ++ printCode(f) prints out \spad{f} in FORTRAN notation.
    getCode: $ -> SEX
      ++ getCode(f) returns a Lisp list of strings representing \spad{f}
      ++ in Fortran notation.  This is used by the FortranProgram domain.
    setLabelValue:SingleInteger -> SingleInteger
      ++ setLabelValue(i) resets the counter which produces labels to i

  private == add
    import Void
    import ASS
    import COND
    import RETURN
    import L PIN
    import O
    import SEX
    import FortranType
    import TheSymbolTable

    Rep := Record(op: OP, data: OPREC)

    -- We need to be able to generate unique labels
    labelValue:SingleInteger := 25000::SingleInteger
    setLabelValue(u:SingleInteger):SingleInteger == labelValue := u
    newLabel():SingleInteger ==
      labelValue := labelValue + 1$SingleInteger
      labelValue

    commaSep(l:List String):List(String) ==
      [(l.1),:[:[",",u] for u in rest(l)]]

    getReturn(rec:RETURN):SEX ==
      returnToken : SEX := convert("RETURN"::Symbol::O)$SEX
      elt(rec,empty?)$RETURN =>
        getStatement(returnToken,NIL$Lisp)$Lisp
      rt : EXPRESSION := elt(rec,value)$RETURN
      rv : O := elt(rt,expr)$EXPRESSION
      getStatement([returnToken,convert(rv)$SEX]$Lisp,
                   elt(rt,ints2Floats?)$EXPRESSION )$Lisp

    getStop():SEX ==
      fortran2Lines(LIST("STOP")$Lisp)$Lisp

    getSave():SEX ==
      fortran2Lines(LIST("SAVE")$Lisp)$Lisp

    getCommon(u:COMMON):SEX ==
      fortran2Lines(APPEND(LIST("COMMON"," /",string (u.name),"/ ")$Lisp,_
                    addCommas(u.contents)$Lisp)$Lisp)$Lisp
 
    getPrint(l:PRINTLIST):SEX ==
      ll : SEX := LIST("PRINT*")$Lisp
      for i in l repeat 
        ll := APPEND(ll,CONS(",",expression2Fortran(i)$Lisp)$Lisp)$Lisp
      fortran2Lines(ll)$Lisp

    getBlock(rec:BLOCK):SEX ==
      indentFortLevel(convert(1@Integer)$SEX)$Lisp
      expr : SEX := LIST()$Lisp
      for u in rec repeat
        expr := APPEND(expr,getCode(u))$Lisp
      indentFortLevel(convert(-1@Integer)$SEX)$Lisp
      expr

    getBody(f:$):SEX ==
      operation(f) case Block => getCode f
      indentFortLevel(convert(1@Integer)$SEX)$Lisp
      expr := getCode f
      indentFortLevel(convert(-1@Integer)$SEX)$Lisp
      expr

    getElseIf(f:$):SEX ==
      rec := code f
      expr :=
       fortFormatElseIf(elt(rec.conditionalBranch,switch)$COND::O)$Lisp
      expr := 
       APPEND(expr,getBody elt(rec.conditionalBranch,thenClause)$COND)$Lisp
      elseBranch := elt(rec.conditionalBranch,elseClause)$COND
      not(operation(elseBranch) case Null) =>
        operation(elseBranch) case Conditional => 
          APPEND(expr,getElseIf elseBranch)$Lisp
        expr := APPEND(expr, getStatement(ELSE::O,NIL$Lisp)$Lisp)$Lisp
        expr := APPEND(expr, getBody elseBranch)$Lisp
      expr

    getContinue(label:SingleInteger):SEX ==
      lab : O := label::O
      if (width(lab) > 6) then error "Label too big"
      cnt : O := "CONTINUE"::O
      --sp  : O := hspace(6-width lab)
      sp  : O := hspace(_$fortIndent$Lisp -width lab)
      LIST(STRCONC(STRINGIMAGE(lab)$Lisp,sp,cnt)$Lisp)$Lisp

    getGoto(label:SingleInteger):SEX ==
     fortran2Lines(
      LIST(STRCONC("GOTO ",STRINGIMAGE(label::O)$Lisp)$Lisp)$Lisp)$Lisp

    getRepeat(repRec:LOOP):SEX ==
      sw : Switch := NOT elt(repRec,switch)$LOOP
      lab := newLabel()
      bod := elt(repRec,body)$LOOP
      APPEND(getContinue lab,getBody bod,
           fortFormatIfGoto(sw::O,lab)$Lisp)$Lisp

    getWhile(whileRec:LOOP):SEX ==
      sw := NOT elt(whileRec,switch)$LOOP
      lab1 := newLabel()
      lab2 := newLabel()
      bod := elt(whileRec,body)$LOOP
      APPEND(fortFormatLabelledIfGoto(sw::O,lab1,lab2)$Lisp,
           getBody bod, getBody goto(lab1), getContinue lab2)$Lisp

    getArrayAssign(rec:ARRAYASS):SEX ==
      getfortarrayexp((rec.var)::O,rec.rand,rec.ints2Floats?)$Lisp

    getAssign(rec:ASS):SEX ==
      indices : L PIN := elt(rec,arrayIndex)$ASS
      if indices = []::(L PIN) then
        lhs := elt(rec,var)$ASS::O
      else
        lhs := cons(elt(rec,var)$ASS::PIN,indices)::O
        -- Must get the index brackets correct:
        lhs := (cdr car cdr convert(lhs)$SEX::SEX)::O -- Yuck!
      elt(elt(rec,rand)$ASS,ints2Floats?)$EXPRESSION =>
        assignment2Fortran1(lhs,elt(elt(rec,rand)$ASS,expr)$EXPRESSION)$Lisp
      integerAssignment2Fortran1(lhs,elt(elt(rec,rand)$ASS,expr)$EXPRESSION)$Lisp

    getCond(rec:COND):SEX ==
      expr := APPEND(fortFormatIf(elt(rec,switch)$COND::O)$Lisp,
                     getBody elt(rec,thenClause)$COND)$Lisp
      elseBranch := elt(rec,elseClause)$COND
      if not(operation(elseBranch) case Null) then
        operation(elseBranch) case Conditional =>
          expr := APPEND(expr,getElseIf elseBranch)$Lisp
        expr := APPEND(expr,getStatement(ELSE::O,NIL$Lisp)$Lisp,
                       getBody elseBranch)$Lisp
      APPEND(expr,getStatement(ENDIF::O,NIL$Lisp)$Lisp)$Lisp

    getComment(rec:COMMENT):SEX ==
      convert([convert(concat("C     ",c)$String)@SEX for c in rec])@SEX

    getCall(rec:CALL):SEX ==
      expr := concat("CALL ",rec)$String
      #expr > 1320 => error "Fortran CALL too large"
      fortran2Lines(convert([convert(expr)@SEX ])@SEX)$Lisp

    getFor(rec:FOR):SEX ==
      rnge : SegmentBinding PIN := elt(rec,range)$FOR
      increment : PIN := elt(rec,span)$FOR
      lab : SingleInteger := newLabel()
      declare!(variable rnge,fortranInteger())
      expr := fortFormatDo(variable rnge, (lo segment rnge)::O,_
        (hi segment rnge)::O,increment::O,lab)$Lisp
      APPEND(expr, getBody elt(rec,body)$FOR, getContinue(lab))$Lisp
 
    getCode(f:$):SEX ==
      opp:OP := operation f
      rec:OPREC:= code f
      opp case Assignment => getAssign(rec.assignmentBranch)
      opp case ArrayAssignment => getArrayAssign(rec.arrayAssignmentBranch)
      opp case Conditional => getCond(rec.conditionalBranch)
      opp case Return => getReturn(rec.returnBranch)
      opp case Block => getBlock(rec.blockBranch)
      opp case Comment => getComment(rec.commentBranch)
      opp case Call => getCall(rec.callBranch)
      opp case For => getFor(rec.forBranch)
      opp case Continue => getContinue(rec.labelBranch)
      opp case Goto => getGoto(rec.labelBranch)
      opp case Repeat => getRepeat(rec.loopBranch)
      opp case While => getWhile(rec.loopBranch)
      opp case Save => getSave()
      opp case Stop => getStop()
      opp case Print => getPrint(rec.printBranch)
      opp case Common => getCommon(rec.commonBranch)
      error "Unsupported program construct."
      convert(0)@SEX

    printCode(f:$):Void ==
      displayLines1$Lisp getCode f
      void()$Void

    code (f:$):OPREC ==
      elt(f,data)$Rep

    operation (f:$):OP ==
      elt(f,op)$Rep

    common(name':Symbol,contents':List Symbol):$ ==
      [["common"]$OP,[[name',contents']$COMMON]$OPREC]$Rep

    stop():$ ==
      [["stop"]$OP,["null"]$OPREC]$Rep

    save():$ ==
      [["save"]$OP,["null"]$OPREC]$Rep

    printStatement(l:List O):$ ==
      [["print"]$OP,[l]$OPREC]$Rep

    comment(s:List String):$ ==
      [["comment"]$OP,[s]$OPREC]$Rep

    comment(s:String):$ ==
      [["comment"]$OP,[list s]$OPREC]$Rep

    forLoop(r:SegmentBinding PIN,body':$):$ ==
      [["for"]$OP,[[r,(incr segment r)::PIN,body']$FOR]$OPREC]$Rep

    forLoop(r:SegmentBinding PIN,increment:PIN,body':$):$ ==
      [["for"]$OP,[[r,increment,body']$FOR]$OPREC]$Rep

    goto(l:SingleInteger):$ ==
      [["goto"]$OP,[l]$OPREC]$Rep

    continue(l:SingleInteger):$ ==
      [["continue"]$OP,[l]$OPREC]$Rep

    whileLoop(sw:Switch,b:$):$ ==
      [["while"]$OP,[[sw,b]$LOOP]$OPREC]$Rep

    repeatUntilLoop(sw:Switch,b:$):$ ==
      [["repeat"]$OP,[[sw,b]$LOOP]$OPREC]$Rep

    returns():$ ==
      v := [false,0::O]$EXPRESSION
      [["return"]$OP,[[true,v]$RETURN]$OPREC]$Rep

    returns(v:Expression MachineInteger):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    returns(v:Expression MachineFloat):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    returns(v:Expression MachineComplex):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    returns(v:Expression Integer):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    returns(v:Expression Float):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    returns(v:Expression Complex Float):$ ==
      [["return"]$OP,[[false,[false,v::O]$EXPRESSION]$RETURN]$OPREC]$Rep

    block(l:List $):$ ==
      [["block"]$OP,[l]$OPREC]$Rep
      
    cond(sw:Switch,thenC:$):$ ==
      [["conditional"]$OP,
       [[sw,thenC,[["null"]$OP,["null"]$OPREC]$Rep]$COND]$OPREC]$Rep

    cond(sw:Switch,thenC:$,elseC:$):$ ==
      [["conditional"]$OP,[[sw,thenC,elseC]$COND]$OPREC]$Rep

    coerce(f : $):O ==
      (f.op)::O

    assign(v:Symbol,rhs:String):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix MachineInteger):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix MachineFloat):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix MachineComplex):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector MachineInteger):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector MachineFloat):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector MachineComplex):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression MachineInteger):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression MachineFloat):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression MachineComplex):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression MachineInteger):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression MachineFloat):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression MachineComplex):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression MachineInteger):$ ==
      [["assignment"]$OP,[[v,index,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression MachineFloat):$ ==
      [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression MachineComplex):$ ==
      [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression MachineInteger):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression MachineFloat):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression MachineComplex):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression Integer):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression Float):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Matrix Expression Complex Float):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression Integer):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,false]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression Float):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Vector Expression Complex Float):$ ==
      [["arrayAssignment"]$OP,[[v,rhs::O,true]$ARRAYASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression Integer):$ ==
      [["assignment"]$OP,[[v,index,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression Float):$ ==
      [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,index:L PIN,rhs:Expression Complex Float):$ ==
      [["assignment"]$OP,[[v,index,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression Integer):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[false,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression Float):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    assign(v:Symbol,rhs:Expression Complex Float):$ ==
      [["assignment"]$OP,[[v,nil()::L PIN,[true,rhs::O]$EXPRESSION]$ASS]$OPREC]$Rep

    call(s:String):$ ==
      [["call"]$OP,[s]$OPREC]$Rep

@
\section{domain FORTRAN FortranProgram}
<<domain FORTRAN FortranProgram>>=
)abbrev domain FORTRAN FortranProgram
++ Author: Mike Dewar
++ Date Created: October 1992
++ Date Last Updated: 13 January 1994
++                    23 January 1995 Added support for intrinsic functions
++ Basic Operations:
++ Related Constructors: FortranType, FortranCode, Switch
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description: \axiomType{FortranProgram} allows the user to build and manipulate simple 
++ models of FORTRAN subprograms.  These can then be transformed into actual FORTRAN
++ notation.
FortranProgram(name,returnType,arguments,symbols): Exports == Implement where
  name       : Symbol
  returnType : Union(fst:FortranScalarType,void:"void")
  arguments  : List Symbol
  symbols    : SymbolTable

  FC     ==> FortranCode
  EXPR   ==> Expression
  INT    ==> Integer
  CMPX   ==> Complex
  MINT   ==> MachineInteger
  MFLOAT ==> MachineFloat
  MCMPLX ==> MachineComplex
  REP    ==> Record(localSymbols : SymbolTable, code : List FortranCode)

  Exports ==> FortranProgramCategory with
    coerce	: FortranCode -> $
	++ coerce(fc) \undocumented{}
    coerce	: List FortranCode -> $
	++ coerce(lfc) \undocumented{}
    coerce	: REP -> $
	++ coerce(r) \undocumented{}
    coerce      : EXPR MINT -> $
	++ coerce(e) \undocumented{}
    coerce      : EXPR MFLOAT -> $
	++ coerce(e) \undocumented{}
    coerce      : EXPR MCMPLX -> $
	++ coerce(e) \undocumented{}
    coerce      : Equation EXPR MINT -> $
	++ coerce(eq) \undocumented{}
    coerce      : Equation EXPR MFLOAT -> $
	++ coerce(eq) \undocumented{}
    coerce      : Equation EXPR MCMPLX -> $
	++ coerce(eq) \undocumented{}
    coerce      : EXPR INT -> $
	++ coerce(e) \undocumented{}
    coerce      : EXPR Float -> $
	++ coerce(e) \undocumented{}
    coerce      : EXPR CMPX Float -> $
	++ coerce(e) \undocumented{}
    coerce      : Equation EXPR INT -> $
	++ coerce(eq) \undocumented{}
    coerce      : Equation EXPR Float -> $
	++ coerce(eq) \undocumented{}
    coerce      : Equation EXPR CMPX Float -> $
	++ coerce(eq) \undocumented{}

  Implement ==> add

    Rep := REP

    import SExpression
    import TheSymbolTable
    import FortranCode

    makeRep(b:List FortranCode):$ ==
      construct(empty()$SymbolTable,b)$REP

    codeFrom(u:$):List FortranCode ==
      elt(u::Rep,code)$REP

    outputAsFortran(p:$):Void ==
      setLabelValue(25000::SingleInteger)$FC
      -- Do this first to catch any extra type declarations:
      tempName := "FPTEMP"::Symbol
      newSubProgram(tempName)
      initialiseIntrinsicList()$Lisp
      body : List SExpression := [getCode(l)$FortranCode for l in codeFrom(p)]
      intrinsics : SExpression := getIntrinsicList()$Lisp
      endSubProgram()
      fortFormatHead(returnType::OutputForm, name::OutputForm, _
                     arguments::OutputForm)$Lisp
      printTypes(symbols)$SymbolTable
      printTypes((p::Rep).localSymbols)$SymbolTable
      printTypes(tempName)$TheSymbolTable
      fortFormatIntrinsics(intrinsics)$Lisp
      clearTheSymbolTable(tempName)
      for expr in body repeat displayLines1(expr)$Lisp
      dispStatement(END::OutputForm)$Lisp
      void()$Void

    mkString(l:List Symbol):String ==
      unparse(convert(l::OutputForm)@InputForm)$InputForm

    checkVariables(user:List Symbol,target:List Symbol):Void ==
      -- We don't worry about whether the user has subscripted the
      -- variables or not.
      setDifference(map(name$Symbol,user),target) ~= empty()$List(Symbol) =>
        s1 : String := mkString(user)
        s2 : String := mkString(target)
        error ["Incompatible variable lists:", s1, s2]
      void()$Void

    coerce(u:EXPR MINT) : $ ==
      checkVariables(variables(u)$EXPR(MINT),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l

    coerce(u:Equation EXPR MINT) : $ ==
      retractIfCan(lhs u)@Union(Kernel(EXPR MINT),"failed") case "failed" =>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR MINT := [w::EXPR(MINT) for w in vList]
      aeList : List EXPR MINT := [w::EXPR(MINT) for w in arguments]
      eList : List Equation EXPR MINT := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$

    coerce(u:EXPR MFLOAT) : $ ==
      checkVariables(variables(u)$EXPR(MFLOAT),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l 

    coerce(u:Equation EXPR MFLOAT) : $ ==
      retractIfCan(lhs u)@Union(Kernel(EXPR MFLOAT),"failed") case "failed" =>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in vList]
      aeList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in arguments]
      eList : List Equation EXPR MFLOAT := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$

    coerce(u:EXPR MCMPLX) : $ ==
      checkVariables(variables(u)$EXPR(MCMPLX),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l

    coerce(u:Equation EXPR MCMPLX) : $ ==
      retractIfCan(lhs u)@Union(Kernel EXPR MCMPLX,"failed") case "failed"=>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in vList]
      aeList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in arguments]
      eList : List Equation EXPR MCMPLX := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$


    coerce(u:REP):$ ==
      u@Rep

    coerce(u:$):OutputForm ==
      coerce(name)$Symbol

    coerce(c:List FortranCode):$ ==
      makeRep c

    coerce(c:FortranCode):$ ==
      makeRep [c]

    coerce(u:EXPR INT) : $ ==
      checkVariables(variables(u)$EXPR(INT),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l

    coerce(u:Equation EXPR INT) : $ ==
      retractIfCan(lhs u)@Union(Kernel(EXPR INT),"failed") case "failed" =>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR INT := [w::EXPR(INT) for w in vList]
      aeList : List EXPR INT := [w::EXPR(INT) for w in arguments]
      eList : List Equation EXPR INT := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$

    coerce(u:EXPR Float) : $ ==
      checkVariables(variables(u)$EXPR(Float),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l 

    coerce(u:Equation EXPR Float) : $ ==
      retractIfCan(lhs u)@Union(Kernel(EXPR Float),"failed") case "failed" =>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR Float := [w::EXPR(Float) for w in vList]
      aeList : List EXPR Float := [w::EXPR(Float) for w in arguments]
      eList : List Equation EXPR Float := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$

    coerce(u:EXPR Complex Float) : $ ==
      checkVariables(variables(u)$EXPR(Complex Float),arguments)
      l : List(FC) := [assign(name,u)$FC,returns()$FC]
      makeRep l

    coerce(u:Equation EXPR CMPX Float) : $ ==
      retractIfCan(lhs u)@Union(Kernel EXPR CMPX Float,"failed") case "failed"=>
        error "left hand side is not a kernel"
      vList : List Symbol := variables lhs u
      #vList ~= #arguments =>
        error "Incorrect number of arguments"
      veList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in vList]
      aeList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in arguments]
      eList : List Equation EXPR CMPX Float := 
        [equation(w,v) for w in veList for v in aeList]
      (subst(rhs u,eList))::$

@
\section{domain M3D ThreeDimensionalMatrix}
<<domain M3D ThreeDimensionalMatrix>>=
)abbrev domain M3D ThreeDimensionalMatrix
++ Author: William Naylor
++ Date Created: 20 October 1993
++ Date Last Updated: 20 May 1994
++ BasicFunctions:
++ Related Constructors: Matrix
++ Also See: PrimitiveArray
++ AMS Classification:
++ Keywords:
++ References:
++ Description:
++ This domain represents three dimensional matrices over a general object type
ThreeDimensionalMatrix(R) : Exports == Implementation where

  R : SetCategory
  L ==> List
  NNI ==> NonNegativeInteger
  A1AGG ==> OneDimensionalArrayAggregate
  ARRAY1 ==> OneDimensionalArray
  PA ==> PrimitiveArray
  INT ==> Integer
  PI ==> PositiveInteger

  Exports ==> HomogeneousAggregate(R) with

    if R has Ring then
      zeroMatrix : (NNI,NNI,NNI) -> $
         ++ zeroMatrix(i,j,k) create a matrix with all zero terms
      identityMatrix : (NNI) -> $
         ++ identityMatrix(n) create an identity matrix
         ++ we note that this must be square
      plus : ($,$) -> $
         ++ plus(x,y) adds two matrices, term by term
         ++ we note that they must be the same size
    construct : (L L L R) -> $
       ++ construct(lll) creates a 3-D matrix from a List List List R lll
    elt : ($,NNI,NNI,NNI) -> R
       ++ elt(x,i,j,k) extract an element from the matrix x
    setelt! :($,NNI,NNI,NNI,R) -> R
       ++ setelt!(x,i,j,k,s) (or x.i.j.k:=s) sets a specific element of the array to some value of type R
    coerce : (PA PA PA R) -> $
       ++ coerce(p) moves from the representation type
       ++ (PrimitiveArray  PrimitiveArray  PrimitiveArray R)
       ++ to the domain
    coerce : $ -> (PA PA PA R)
    	++ coerce(x) moves from the domain to the representation type
    matrixConcat3D : (Symbol,$,$) -> $
         ++ matrixConcat3D(s,x,y) concatenates two 3-D matrices along a specified axis
    matrixDimensions : $ -> Vector NNI
         ++ matrixDimensions(x) returns the dimensions of a matrix

  Implementation ==>  (PA PA PA R) add

    import (PA PA PA R)
    import (PA PA R)
    import (PA R)
    import R

    matrix1,matrix2,resultMatrix : $

    -- function to concatenate two matrices
    -- the first argument must be a symbol, which is either i,j or k
    -- to specify the direction in which the concatenation is to take place
    matrixConcat3D(dir : Symbol,mat1 : $,mat2 : $) : $ ==
      not ((dir = (i::Symbol)) or (dir = (j::Symbol)) or (dir = (k::Symbol)))_
       => error "the axis of concatenation must be i,j or k"
      mat1Dim := matrixDimensions(mat1)
      mat2Dim := matrixDimensions(mat2)
      iDim1 := mat1Dim.1
      jDim1 := mat1Dim.2
      kDim1 := mat1Dim.3
      iDim2 := mat2Dim.1
      jDim2 := mat2Dim.2
      kDim2 := mat2Dim.3
      matRep1 : (PA PA PA R) := copy(mat1 :: (PA PA PA R))$(PA PA PA R)
      matRep2 : (PA PA PA R) := copy(mat2 :: (PA PA PA R))$(PA PA PA R)
      retVal : $

      if (dir = (i::Symbol)) then
        -- j,k dimensions must agree
        if (not ((jDim1 = jDim2) and (kDim1=kDim2)))
        then
          error "jxk do not agree"
        else
          retVal := (coerce(concat(matRep1,matRep2)$(PA PA PA R))$$)@$

      if (dir = (j::Symbol)) then
        -- i,k dimensions must agree
        if (not ((iDim1 = iDim2) and (kDim1=kDim2)))
        then
          error "ixk do not agree"
        else
          for i in 0..(iDim1-1) repeat
            setelt(matRep1,i,(concat(elt(matRep1,i)$(PA PA PA R)_
             ,elt(matRep2,i)$(PA PA PA R))$(PA PA R))@(PA PA R))$(PA PA PA R)
          retVal := (coerce(matRep1)$$)@$

      if (dir = (k::Symbol)) then
        temp : (PA PA R)
        -- i,j dimensions must agree
        if (not ((iDim1 = iDim2) and (jDim1=jDim2)))
        then
          error "ixj do not agree"
        else
          for i in 0..(iDim1-1) repeat
            temp := copy(elt(matRep1,i)$(PA PA PA R))$(PA PA R)
            for j in 0..(jDim1-1) repeat
              setelt(temp,j,concat(elt(elt(matRep1,i)$(PA PA PA R)_
              ,j)$(PA PA R),elt(elt(matRep2,i)$(PA PA PA R),j)$(PA PA R)_
              )$(PA R))$(PA PA R)
            setelt(matRep1,i,temp)$(PA PA PA R)
          retVal := (coerce(matRep1)$$)@$

      retVal

    matrixDimensions(mat : $) : Vector NNI ==
      matRep : (PA PA PA R) := mat :: (PA PA PA R)
      iDim : NNI := (#matRep)$(PA PA PA R)
      matRep2 : PA PA R := elt(matRep,0)$(PA PA PA R)
      jDim : NNI := (#matRep2)$(PA PA R)
      matRep3 : (PA R) := elt(matRep2,0)$(PA PA R)
      kDim : NNI := (#matRep3)$(PA R)
      retVal : Vector NNI := new(3,0)$(Vector NNI)
      retVal.1 := iDim
      retVal.2 := jDim
      retVal.3 := kDim
      retVal

    coerce(matrixRep : (PA PA PA R)) : $ == matrixRep pretend $

    coerce(mat : $) : (PA PA PA R) == mat pretend (PA PA PA R)

    -- i,j,k must be with in the bounds of the matrix
    elt(mat : $,i : NNI,j : NNI,k : NNI) : R ==
      matDims := matrixDimensions(mat)
      iLength := matDims.1
      jLength := matDims.2
      kLength := matDims.3
      ((i > iLength) or (j > jLength) or (k > kLength) or (i=0) or (j=0) or_
(k=0)) => error "coordinates must be within the bounds of the matrix"
      matrixRep : PA PA PA R := mat :: (PA PA PA R)
      elt(elt(elt(matrixRep,i-1)$(PA PA PA R),j-1)$(PA PA R),k-1)$(PA R)

    setelt!(mat : $,i : NNI,j : NNI,k : NNI,val : R)_
       : R ==
      matDims := matrixDimensions(mat)
      iLength := matDims.1
      jLength := matDims.2
      kLength := matDims.3
      ((i > iLength) or (j > jLength) or (k > kLength) or (i=0) or (j=0) or_
(k=0)) => error "coordinates must be within the bounds of the matrix"
      matrixRep : PA PA PA R := mat :: (PA PA PA R)
      row2 : PA PA R := copy(elt(matrixRep,i-1)$(PA PA PA R))$(PA PA R)
      row1 : PA R := copy(elt(row2,j-1)$(PA PA R))$(PA R)
      setelt(row1,k-1,val)$(PA R)
      setelt(row2,j-1,row1)$(PA PA R)
      setelt(matrixRep,i-1,row2)$(PA PA PA R)
      val

    if R has Ring then
      zeroMatrix(iLength:NNI,jLength:NNI,kLength:NNI) : $ ==
        (new(iLength,new(jLength,new(kLength,(0$R))$(PA R))$(PA PA R))$(PA PA PA R)) :: $

      identityMatrix(iLength:NNI) : $ ==
        retValueRep : PA PA PA R := zeroMatrix(iLength,iLength,iLength)$$ :: (PA PA PA R)
        row1 : PA R
        row2 : PA PA R
        row1empty : PA R := new(iLength,0$R)$(PA R)
        row2empty : PA PA R := new(iLength,copy(row1empty)$(PA R))$(PA PA R)
        for count in 0..(iLength-1) repeat
          row1 := copy(row1empty)$(PA R)
          setelt(row1,count,1$R)$(PA R)
          row2 := copy(row2empty)$(PA PA R)
          setelt(row2,count,copy(row1)$(PA R))$(PA PA R)
          setelt(retValueRep,count,copy(row2)$(PA PA R))$(PA PA PA R)
        retValueRep :: $


      plus(mat1 : $,mat2 :$) : $ ==

        mat1Dims := matrixDimensions(mat1)
        iLength1 := mat1Dims.1
        jLength1 := mat1Dims.2
        kLength1 := mat1Dims.3

        mat2Dims := matrixDimensions(mat2)
        iLength2 := mat2Dims.1
        jLength2 := mat2Dims.2
        kLength2 := mat2Dims.3

        -- check that the dimensions are the same
        (not (iLength1 = iLength2) or not (jLength1 = jLength2) or not(kLength1 = kLength2))_
         => error "error the matrices are different sizes"

        sum : R
        row1 : (PA R) := new(kLength1,0$R)$(PA R)
        row2 : (PA PA R) := new(jLength1,copy(row1)$(PA R))$(PA PA R)
        row3 : (PA PA PA R) := new(iLength1,copy(row2)$(PA PA R))$(PA PA PA R)

        for i in 1..iLength1 repeat
          for j in 1..jLength1 repeat
            for k in 1..kLength1 repeat
              sum := (elt(mat1,i,j,k)::R +$R_
                      elt(mat2,i,j,k)::R)
              setelt(row1,k-1,sum)$(PA R)
            setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R)
          setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R)

        resultMatrix := (row3 pretend $)

        resultMatrix

    construct(listRep : L L L R) : $ ==

      (#listRep)$(L L L R) = 0 => error "empty list"
      (#(listRep.1))$(L L R) = 0 => error "empty list"
      (#((listRep.1).1))$(L R) = 0 => error "empty list"
      iLength := (#listRep)$(L L L R)
      jLength := (#(listRep.1))$(L L R)
      kLength := (#((listRep.1).1))$(L R)

      --first check that the matrix is in the correct form
      for subList in listRep repeat
        not((#subList)$(L L R) = jLength) => error_
 "can not have an irregular shaped matrix"
        for subSubList in subList repeat
          not((#(subSubList))$(L R) = kLength) => error_
 "can not have an irregular shaped matrix"

      row1 : (PA R) := new(kLength,((listRep.1).1).1)$(PA R)
      row2 : (PA PA R) := new(jLength,copy(row1)$(PA R))$(PA PA R)
      row3 : (PA PA PA R) := new(iLength,copy(row2)$(PA PA R))$(PA PA PA R)
         
      for i in 1..iLength repeat
        for j in 1..jLength repeat
          for k in 1..kLength repeat

            element := elt(elt(elt(listRep,i)$(L L L R),j)$(L L R),k)$(L R)
            setelt(row1,k-1,element)$(PA R)
          setelt(row2,j-1,copy(row1)$(PA R))$(PA PA R)
        setelt(row3,i-1,copy(row2)$(PA PA R))$(PA PA PA R)

      resultMatrix := (row3 pretend $)

      resultMatrix

@
\section{domain SFORT SimpleFortranProgram}
<<domain SFORT SimpleFortranProgram>>=
)abbrev domain SFORT SimpleFortranProgram
-- Because of a bug in the compiler:
)bo $noSubsumption:=true 

++ Author: Mike Dewar
++ Date Created: November 1992
++ Date Last Updated: 
++ Basic Operations:
++ Related Constructors: FortranType, FortranCode, Switch
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ \axiomType{SimpleFortranProgram(f,type)} provides a simple model of some
++ FORTRAN subprograms, making it possible to coerce objects of various
++ domains into a FORTRAN subprogram called \axiom{f}.
++ These can then be translated into legal FORTRAN code.
SimpleFortranProgram(R,FS): Exports == Implementation where
  R  : OrderedSet
  FS : FunctionSpace(R)

  FST ==> FortranScalarType

  Exports ==> FortranProgramCategory with
    fortran : (Symbol,FST,FS) -> $
    ++fortran(fname,ftype,body) builds an object of type 
    ++\axiomType{FortranProgramCategory}. The three arguments specify
    ++the name, the type and the body of the program.

  Implementation ==> add

    Rep := Record(name : Symbol, type : FST, body : FS )

    fortran(fname, ftype, res) ==
      construct(fname,ftype,res)$Rep

    nameOf(u:$):Symbol == u . name

    typeOf(u:$):Union(FST,"void") == u . type

    bodyOf(u:$):FS == u . body

    argumentsOf(u:$):List Symbol == variables(bodyOf u)$FS

    coerce(u:$):OutputForm ==
      coerce(nameOf u)$Symbol

    outputAsFortran(u:$):Void ==
      ftype := (checkType(typeOf(u)::OutputForm)$Lisp)::OutputForm
      fname := nameOf(u)::OutputForm
      args := argumentsOf(u)
      nargs:=args::OutputForm
      val  := bodyOf(u)::OutputForm
      fortFormatHead(ftype,fname,nargs)$Lisp
      fortFormatTypes(ftype,args)$Lisp
      dispfortexp1$Lisp ["="::OutputForm, fname, val]@List(OutputForm)
      dispfortexp1$Lisp "RETURN"::OutputForm
      dispfortexp1$Lisp "END"::OutputForm
      void()$Void

@
\section{domain SWITCH Switch}
<<domain SWITCH Switch>>=
)abbrev domain SWITCH Switch
-- Because of a bug in the compiler:
)bo $noSubsumption:=false

++ Author: Mike Dewar
++ Date Created: April 1991
++ Date Last Updated: March 1994
++                    30.6.94 Added coercion from Symbol MCD
++ Basic Operations:
++ Related Constructors: FortranProgram, FortranCode, FortranTypes
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description:
++ This domain builds representations of boolean expressions for use with
++ the \axiomType{FortranCode} domain.
Switch():public == private where
  EXPR ==> Union(I:Expression Integer,F:Expression Float,
                 CF:Expression Complex Float,switch:%)

  public ==  CoercibleTo OutputForm with
    coerce : Symbol -> $
	++ coerce(s) \undocumented{}
    LT : (EXPR,EXPR) -> $
      ++ LT(x,y) returns the \axiomType{Switch} expression representing \spad{x<y}.
    GT : (EXPR,EXPR) -> $
      ++ GT(x,y) returns the \axiomType{Switch} expression representing \spad{x>y}.
    LE : (EXPR,EXPR) -> $
      ++ LE(x,y) returns the \axiomType{Switch} expression representing \spad{x<=y}.
    GE : (EXPR,EXPR) -> $
      ++ GE(x,y) returns the \axiomType{Switch} expression representing \spad{x>=y}.
    OR : (EXPR,EXPR) -> $
      ++ OR(x,y) returns the \axiomType{Switch} expression representing \spad{x or y}.
    EQ : (EXPR,EXPR) -> $
      ++ EQ(x,y) returns the \axiomType{Switch} expression representing \spad{x = y}.
    AND : (EXPR,EXPR) -> $
      ++ AND(x,y) returns the \axiomType{Switch} expression representing \spad{x and y}.
    NOT : EXPR -> $
      ++ NOT(x) returns the \axiomType{Switch} expression representing \spad{\~~x}.
    NOT : $ -> $
      ++ NOT(x) returns the \axiomType{Switch} expression representing \spad{\~~x}.
    
  private == add
    Rep := Record(op:BasicOperator,rands:List EXPR)

    -- Public function definitions

    nullOp : BasicOperator := operator NULL

    coerce(s:%):OutputForm ==
      rat := (s . op)::OutputForm
      ran := [u::OutputForm for u in s.rands]
      (s . op) = nullOp => first ran
      #ran = 1 =>
        prefix(rat,ran)
      infix(rat,ran)

    coerce(s:Symbol):$ == [nullOp,[[s::Expression(Integer)]$EXPR]$List(EXPR)]$Rep

    NOT(r:EXPR):% ==
      [operator("~"::Symbol),[r]$List(EXPR)]$Rep

    NOT(r:%):% ==
      [operator("~"::Symbol),[[r]$EXPR]$List(EXPR)]$Rep

    LT(r1:EXPR,r2:EXPR):% ==
      [operator("<"::Symbol),[r1,r2]$List(EXPR)]$Rep

    GT(r1:EXPR,r2:EXPR):% ==
      [operator(">"::Symbol),[r1,r2]$List(EXPR)]$Rep

    LE(r1:EXPR,r2:EXPR):% ==
      [operator("<="::Symbol),[r1,r2]$List(EXPR)]$Rep

    GE(r1:EXPR,r2:EXPR):% ==
      [operator(">="::Symbol),[r1,r2]$List(EXPR)]$Rep

    AND(r1:EXPR,r2:EXPR):% ==
      [operator("and"::Symbol),[r1,r2]$List(EXPR)]$Rep

    OR(r1:EXPR,r2:EXPR):% ==
      [operator("or"::Symbol),[r1,r2]$List(EXPR)]$Rep

    EQ(r1:EXPR,r2:EXPR):% ==
      [operator("EQ"::Symbol),[r1,r2]$List(EXPR)]$Rep

@
\section{domain FTEM FortranTemplate}
<<domain FTEM FortranTemplate>>=
)abbrev domain FTEM FortranTemplate
++ Author: Mike Dewar
++ Date Created:  October 1992
++ Date Last Updated: 
++ Basic Operations:
++ Related Domains:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ Examples:
++ References:
++ Description: Code to manipulate Fortran templates
FortranTemplate() : specification == implementation where

  specification == FileCategory(FileName, String) with

    processTemplate : (FileName, FileName) -> FileName
      ++ processTemplate(tp,fn) processes the template tp, writing the
      ++ result out to fn.
    processTemplate : (FileName) -> FileName
      ++ processTemplate(tp) processes the template tp, writing the
      ++ result to the current FORTRAN output stream.
    fortranLiteralLine : String -> Void
      ++ fortranLiteralLine(s) writes s to the current Fortran output stream,
      ++ followed by a carriage return
    fortranLiteral : String -> Void
      ++ fortranLiteral(s) writes s to the current Fortran output stream
    fortranCarriageReturn : () -> Void
      ++ fortranCarriageReturn() produces a carriage return on the current
      ++ Fortran output stream

  implementation == TextFile add

    import TemplateUtilities
    import FortranOutputStackPackage

    Rep := TextFile

    fortranLiteralLine(s:String):Void ==
      PRINTEXP(s,_$fortranOutputStream$Lisp)$Lisp
      TERPRI(_$fortranOutputStream$Lisp)$Lisp 

    fortranLiteral(s:String):Void ==
      PRINTEXP(s,_$fortranOutputStream$Lisp)$Lisp

    fortranCarriageReturn():Void ==
      TERPRI(_$fortranOutputStream$Lisp)$Lisp

    writePassiveLine!(line:String):Void ==
    -- We might want to be a bit clever here and look for new SubPrograms etc.
      fortranLiteralLine line

    processTemplate(tp:FileName, fn:FileName):FileName == 
      pushFortranOutputStack(fn)
      processTemplate(tp)
      popFortranOutputStack()
      fn

    getLine(fp:TextFile):String ==
      line : String := stripCommentsAndBlanks readLine!(fp)
      while not empty?(line) and elt(line,maxIndex line) = char "__" repeat
        setelt(line,maxIndex line,char " ")
        line := concat(line, stripCommentsAndBlanks readLine!(fp))$String
      line

    processTemplate(tp:FileName):FileName == 
      fp : TextFile := open(tp,"input")
      active : Boolean := true
      line : String
      endInput : Boolean := false
      while not (endInput or endOfFile? fp) repeat
        if active then
          line := getLine fp
          line = "endInput" => endInput := true
          if line = "beginVerbatim" then
            active := false
          else
            not empty? line => interpretString line
        else
          line := readLine!(fp)
          if line = "endVerbatim" then
            active := true
          else
            writePassiveLine! line
      close!(fp)
      if not active then 
        error concat(["Missing `endVerbatim' line in ",tp::String])$String
      string(_$fortranOutputFile$Lisp)::FileName

@
\section{domain FEXPR FortranExpression}
<<domain FEXPR FortranExpression>>=
)abbrev domain FEXPR FortranExpression
++ Author: Mike Dewar
++ Date Created:  December 1993
++ Date Last Updated: 19 May 1994
++                     7 July 1994 added %power to f77Functions
++                    12 July 1994 added RetractableTo(R)
++ Basic Operations:
++ Related Domains:
++ Also See: FortranMachineTypeCategory, MachineInteger, MachineFloat,
++  MachineComplex
++ AMS Classifications:
++ Keywords:
++ Examples:
++ References:
++ Description: A domain of expressions involving functions which can be
++ translated into standard Fortran-77, with some extra extensions from
++ the NAG Fortran Library.  
FortranExpression(basicSymbols,subscriptedSymbols,R):
                                Exports==Implementation where
  basicSymbols : List Symbol
  subscriptedSymbols : List Symbol
  R : FortranMachineTypeCategory

  EXPR ==> Expression
  EXF2 ==> ExpressionFunctions2
  S    ==> Symbol
  L    ==> List
  BO   ==> BasicOperator
  FRAC ==> Fraction
  POLY ==> Polynomial

  Exports ==> Join(ExpressionSpace,Algebra(R),RetractableTo(R),
                   PartialDifferentialRing(Symbol)) with
    retract : EXPR R -> $
      ++ retract(e) takes e and transforms it into a 
      ++  FortranExpression checking that it contains no non-Fortran
      ++  functions, and that it only contains the given basic symbols
      ++  and subscripted symbols which correspond to scalar and array
      ++  parameters respectively.
    retractIfCan : EXPR R -> Union($,"failed")
      ++ retractIfCan(e) takes e and tries to transform it into a 
      ++  FortranExpression checking that it contains no non-Fortran
      ++  functions, and that it only contains the given basic symbols
      ++  and subscripted symbols which correspond to scalar and array
      ++  parameters respectively.
    retract : S -> $
      ++ retract(e) takes e and transforms it into a FortranExpression
      ++  checking that it is one of the given basic symbols
      ++  or subscripted symbols which correspond to scalar and array
      ++  parameters respectively.
    retractIfCan : S -> Union($,"failed")
      ++ retractIfCan(e) takes e and tries to transform it into a FortranExpression
      ++  checking that it is one of the given basic symbols
      ++  or subscripted symbols which correspond to scalar and array
      ++  parameters respectively.
    coerce : $ -> EXPR R
	++ coerce(x) \undocumented{}
    if (R has RetractableTo(Integer)) then
      retract : EXPR Integer -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : EXPR Integer -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retract : FRAC POLY  Integer -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : FRAC POLY  Integer -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retract : POLY  Integer -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : POLY  Integer -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
    if (R has RetractableTo(Float)) then
      retract : EXPR Float -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : EXPR Float -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retract : FRAC POLY  Float -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : FRAC POLY  Float -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retract : POLY  Float -> $
        ++ retract(e) takes e and transforms it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
      retractIfCan : POLY  Float -> Union($,"failed")
        ++ retractIfCan(e) takes e and tries to transform it into a 
        ++  FortranExpression checking that it contains no non-Fortran
        ++  functions, and that it only contains the given basic symbols
        ++  and subscripted symbols which correspond to scalar and array
        ++  parameters respectively.
    abs    : $ -> $
      ++ abs(x) represents the Fortran intrinsic function ABS
    sqrt   : $ -> $
      ++ sqrt(x) represents the Fortran intrinsic function SQRT
    exp    : $ -> $
      ++ exp(x) represents the Fortran intrinsic function EXP
    log    : $ -> $
      ++ log(x) represents the Fortran intrinsic function LOG
    log10  : $ -> $
      ++ log10(x) represents the Fortran intrinsic function LOG10
    sin    : $ -> $
      ++ sin(x) represents the Fortran intrinsic function SIN
    cos    : $ -> $
      ++ cos(x) represents the Fortran intrinsic function COS
    tan    : $ -> $
      ++ tan(x) represents the Fortran intrinsic function TAN
    asin   : $ -> $
      ++ asin(x) represents the Fortran intrinsic function ASIN
    acos   : $ -> $
      ++ acos(x) represents the Fortran intrinsic function ACOS
    atan   : $ -> $
      ++ atan(x) represents the Fortran intrinsic function ATAN
    sinh   : $ -> $
      ++ sinh(x) represents the Fortran intrinsic function SINH
    cosh   : $ -> $
      ++ cosh(x) represents the Fortran intrinsic function COSH
    tanh   : $ -> $
      ++ tanh(x) represents the Fortran intrinsic function TANH
    pi     : () -> $
      ++ pi(x) represents the NAG Library function X01AAF which returns 
      ++  an approximation to the value of pi
    variables : $ -> L S
      ++ variables(e) return a list of all the variables in \spad{e}.
    useNagFunctions : () -> Boolean
      ++ useNagFunctions() indicates whether NAG functions are being used
      ++  for mathematical and machine constants.
    useNagFunctions : Boolean -> Boolean
      ++ useNagFunctions(v) sets the flag which controls whether NAG functions 
      ++  are being used for mathematical and machine constants.  The previous
      ++  value is returned.

  Implementation ==> EXPR R add

    -- The standard FORTRAN-77 intrinsic functions, plus nthRoot which
    -- can be translated into an arithmetic expression:
    f77Functions : L S := [abs,sqrt,exp,log,log10,sin,cos,tan,asin,acos,
                           atan,sinh,cosh,tanh,nthRoot,%power]
    nagFunctions : L S := [pi, X01AAF]
    useNagFunctionsFlag : Boolean := true

    -- Local functions to check for "unassigned" symbols etc.

    mkEqn(s1:Symbol,s2:Symbol):Equation EXPR(R) ==
      equation(s2::EXPR(R),script(s1,scripts(s2))::EXPR(R))

    fixUpSymbols(u:EXPR R):Union(EXPR R,"failed") ==
      -- If its a univariate expression then just fix it up:
      syms   : L S := variables(u)
      one?(#basicSymbols) and zero?(#subscriptedSymbols) =>
        not one?(#syms) => "failed"
        subst(u,equation(first(syms)::EXPR(R),first(basicSymbols)::EXPR(R)))
      -- We have one variable but it is subscripted:
      zero?(#basicSymbols) and one?(#subscriptedSymbols) =>
        -- Make sure we don't have both X and X_i
        for s in syms repeat
          not scripted?(s) => return "failed"
        not one?(#(syms:=removeDuplicates! [name(s) for s in syms]))=> "failed"
        sym : Symbol := first subscriptedSymbols
        subst(u,[mkEqn(sym,i) for i in variables(u)]) 
      "failed"

    extraSymbols?(u:EXPR R):Boolean ==
      syms   : L S := [name(v) for v in variables(u)]
      extras : L S := setDifference(syms,
                                    setUnion(basicSymbols,subscriptedSymbols))
      not empty? extras

    checkSymbols(u:EXPR R):EXPR(R) ==
      syms   : L S := [name(v) for v in variables(u)]
      extras : L S := setDifference(syms,
                                    setUnion(basicSymbols,subscriptedSymbols))
      not empty? extras => 
        m := fixUpSymbols(u)
        m case EXPR(R) => m::EXPR(R)
        error ["Extra symbols detected:",[string(v) for v in extras]$L(String)]
      u

    notSymbol?(v:BO):Boolean ==
      s : S := name v
      member?(s,basicSymbols) or 
        scripted?(s) and member?(name s,subscriptedSymbols) => false
      true

    extraOperators?(u:EXPR R):Boolean ==
      ops    : L S := [name v for v in operators(u) | notSymbol?(v)]
      if useNagFunctionsFlag then
        fortranFunctions : L S := append(f77Functions,nagFunctions)
      else
        fortranFunctions : L S := f77Functions
      extras : L S := setDifference(ops,fortranFunctions)
      not empty? extras

    checkOperators(u:EXPR R):Void ==
      ops    : L S := [name v for v in operators(u) | notSymbol?(v)]
      if useNagFunctionsFlag then
        fortranFunctions : L S := append(f77Functions,nagFunctions)
      else
        fortranFunctions : L S := f77Functions
      extras : L S := setDifference(ops,fortranFunctions)
      not empty? extras => 
        error ["Non FORTRAN-77 functions detected:",[string(v) for v in extras]]
      void()

    checkForNagOperators(u:EXPR R):$ ==
      useNagFunctionsFlag =>
        import Pi
        import PiCoercions(R)
        piOp : BasicOperator := operator X01AAF
        piSub : Equation EXPR R :=
          equation(pi()$Pi::EXPR(R),kernel(piOp,0::EXPR(R))$EXPR(R))
        per subst(u,piSub)
      per u

    -- Conditional retractions:

    if R has RetractableTo(Integer) then 

      retractIfCan(u:POLY Integer):Union($,"failed") ==
        retractIfCan((u::EXPR Integer)$EXPR(Integer))@Union($,"failed")

      retract(u:POLY Integer):$ ==
        retract((u::EXPR Integer)$EXPR(Integer))@$

      retractIfCan(u:FRAC POLY Integer):Union($,"failed") ==
        retractIfCan((u::EXPR Integer)$EXPR(Integer))@Union($,"failed")

      retract(u:FRAC POLY  Integer):$ ==
        retract((u::EXPR Integer)$EXPR(Integer))@$

      int2R(u:Integer):R == u::R

      retractIfCan(u:EXPR Integer):Union($,"failed") ==
        retractIfCan(map(int2R,u)$EXF2(Integer,R))@Union($,"failed")

      retract(u:EXPR Integer):$ ==
        retract(map(int2R,u)$EXF2(Integer,R))@$

    if R has RetractableTo(Float) then 

      retractIfCan(u:POLY Float):Union($,"failed") ==
        retractIfCan((u::EXPR Float)$EXPR(Float))@Union($,"failed")

      retract(u:POLY Float):$ ==
        retract((u::EXPR Float)$EXPR(Float))@$

      retractIfCan(u:FRAC POLY Float):Union($,"failed") ==
        retractIfCan((u::EXPR Float)$EXPR(Float))@Union($,"failed")

      retract(u:FRAC POLY  Float):$ ==
        retract((u::EXPR Float)$EXPR(Float))@$

      float2R(u:Float):R == (u::R)

      retractIfCan(u:EXPR Float):Union($,"failed") ==
        retractIfCan(map(float2R,u)$EXF2(Float,R))@Union($,"failed")

      retract(u:EXPR Float):$ ==
        retract(map(float2R,u)$EXF2(Float,R))@$

    -- Exported Functions

    useNagFunctions():Boolean == useNagFunctionsFlag
    useNagFunctions(v:Boolean):Boolean == 
      old := useNagFunctionsFlag
      useNagFunctionsFlag := v
      old
 
    log10(x:$):$ ==
      kernel(operator log10,x)

    pi():$ == kernel(operator X01AAF,0)

    coerce(u:$):EXPR R == rep u

    retractIfCan(u:EXPR R):Union($,"failed") ==
      if (extraSymbols? u) then 
        m := fixUpSymbols(u)
        m case "failed" => return "failed"
        u := m::EXPR(R)
      extraOperators? u => "failed"
      checkForNagOperators(u)

    retract(u:EXPR R):$ ==
      u:=checkSymbols(u)
      checkOperators(u)
      checkForNagOperators(u)

    retractIfCan(u:Symbol):Union($,"failed") ==
      not (member?(u,basicSymbols) or
           scripted?(u) and member?(name u,subscriptedSymbols)) => "failed"
      per (u::EXPR(R))

    retract(u:Symbol):$ ==
      res : Union($,"failed") := retractIfCan(u)
      res case "failed" => error ["Illegal Symbol Detected:",u::String]
      res

@
\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>>

<<domain RESULT Result>>
<<domain FC FortranCode>>
<<domain FORTRAN FortranProgram>>
<<domain M3D ThreeDimensionalMatrix>>
<<domain SFORT SimpleFortranProgram>>
<<domain SWITCH Switch>>
<<domain FTEM FortranTemplate>>
<<domain FEXPR FortranExpression>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}