Edit detail for InputForm revision 2 of 4

Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.

)show InputForm

 InputForm  is a domain constructor
 Abbreviation for InputForm is INFORM
 This constructor is not exposed in this frame.
 Issue )edit /usr/local/lib/axiom/target/x86_64-unknown-linux/../../src/algebra/INFORM.spad
to see algebra source code for INFORM 

------------------------------- Operations --------------------------------
 #? : % -> Integer                     ?*? : (%,%) -> %
 ?**? : (%,Integer) -> %               ?+? : (%,%) -> %
 ?/? : (%,%) -> %                      ?=? : (%,%) -> Boolean
 1 : () -> %                           0 : () -> %
 atom? : % -> Boolean                  binary : (%,List %) -> %
 car : % -> %                          cdr : % -> %
 coerce : % -> OutputForm              convert : SExpression -> %
 convert : % -> SExpression            convert : OutputForm -> %
 convert : DoubleFloat -> %            convert : Integer -> %
 convert : Symbol -> %                 convert : String -> %
 convert : List % -> %                 declare : List % -> Symbol
 destruct : % -> List %                ?.? : (%,List Integer) -> %
 ?.? : (%,Integer) -> %                eq : (%,%) -> Boolean
 expr : % -> OutputForm                flatten : % -> %
 float : % -> DoubleFloat              float? : % -> Boolean
 hash : % -> SingleInteger             integer : % -> Integer
 integer? : % -> Boolean               interpret : % -> Any
 lambda : (%,List Symbol) -> %         latex : % -> String
 list? : % -> Boolean                  null? : % -> Boolean
 pair? : % -> Boolean                  string : % -> String
 string? : % -> Boolean                symbol : % -> Symbol
 symbol? : % -> Boolean                unparse : % -> String
 ?~=? : (%,%) -> Boolean
 ?**? : (%,NonNegativeInteger) -> %
 compile : (Symbol,List %) -> Symbol
 function : (%,List Symbol,Symbol) -> %

Add a new export for parse.

)abbrev domain INFORM InputForm
++ Parser forms
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 19 April 1991
++ Description:
++   Domain of parsed forms which can be passed to the interpreter.
++   This is also the interface between algebra code and facilities
++   in the interpreter.

--)boot $noSubsumption := true

InputForm():
  Join(SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm),
       ConvertibleTo SExpression) with
    interpret: % -> Any
      ++ interpret(f) passes f to the interpreter.
    convert  : SExpression -> %
      ++ convert(s) makes s into an input form.
    binary   : (%, List %) -> %
      ++ \spad{binary(op, [a1,...,an])} returns the input form
      ++ corresponding to  \spad{a1 op a2 op ... op an}.
    function : (%, List Symbol, Symbol) -> %
      ++ \spad{function(code, [x1,...,xn], f)} returns the input form
      ++ corresponding to \spad{f(x1,...,xn) == code}.
    lambda   : (%, List Symbol) -> %
      ++ \spad{lambda(code, [x1,...,xn])} returns the input form
      ++ corresponding to \spad{(x1,...,xn) +-> code} if \spad{n > 1},
      ++ or to \spad{x1 +-> code} if \spad{n = 1}.
    "+"      : (%, %) -> %
      ++ \spad{a + b} returns the input form corresponding to \spad{a + b}.
    "*"      : (%, %) -> %
      ++ \spad{a * b} returns the input form corresponding to \spad{a * b}.
    "/"      : (%, %) -> %
      ++ \spad{a / b} returns the input form corresponding to \spad{a / b}.
    "**"     : (%, NonNegativeInteger) -> %
      ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}.
    "**"     : (%, Integer) -> %
      ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}.
    0        : constant -> %
      ++ \spad{0} returns the input form corresponding to 0.
    1        : constant -> %
      ++ \spad{1} returns the input form corresponding to 1.
    flatten  : % -> %
      ++ flatten(s) returns an input form corresponding to s with
      ++ all the nested operations flattened to triples using new
      ++ local variables.
      ++ If s is a piece of code, this speeds up
      ++ the compilation tremendously later on.
    unparse  : % -> String
      ++ unparse(f) returns a string s such that the parser
      ++ would transform s to f.
      ++ Error: if f is not the parsed form of a string.
    parse    : String -> %
      ++ parse(s) is the inverse of unparse. It parses a
      ++ string to InputForm
    declare  : List %   -> Symbol
      ++ declare(t) returns a name f such that f has been
      ++ declared to the interpreter to be of type t, but has
      ++ not been assigned a value yet.
      ++ Note: t should be created as \spad{devaluate(T)$Lisp} where T is the
      ++ actual type of f (this hack is required for the case where
      ++ T is a mapping type).
    compile  : (Symbol, List %) -> Symbol
      ++ \spad{compile(f, [t1,...,tn])} forces the interpreter to compile
      ++ the function f with signature \spad{(t1,...,tn) -> ?}.
      ++ returns the symbol f if successful.
      ++ Error: if f was not defined beforehand in the interpreter,
      ++ or if the ti's are not valid types, or if the compiler fails.
 == SExpression add
    Rep := SExpression

    mkProperOp: Symbol -> %
    strsym    : % -> String
    tuplify   : List Symbol -> %
    flatten0  : (%, Symbol, NonNegativeInteger) ->
                                             Record(lst: List %, symb:%)

    0                        == convert(0::Integer)
    1                        == convert(1::Integer)
    convert(x:%):SExpression == x pretend SExpression
    convert(x:SExpression):% == x

    conv(ll : List %): % ==
      convert(ll pretend List SExpression)$SExpression pretend %

    lambda(f,l) == conv([convert("+->"::Symbol),tuplify l,f]$List(%))

    interpret x ==
      v := interpret(x)$Lisp
      mkObj(unwrap(objVal(v)$Lisp)$Lisp, objMode(v)$Lisp)$Lisp

    convert(x:DoubleFloat):% ==
      zero? x => 0
--      one? x => 1
      (x = 1) => 1
      convert(x)$Rep

    flatten s ==
      -- will not compile if I use 'or'
      atom? s => s
      every?(atom?,destruct s)$List(%) => s
      sy := new()$Symbol
      n:NonNegativeInteger := 0
      l2 := [flatten0(x, sy, n := n + 1) for x in rest(l := destruct s)]
      conv(concat(convert("SEQ"::Symbol)@%,
        concat(concat [u.lst for u in l2], conv(
           [convert("exit"::Symbol)@%, 1$%, conv(concat(first l,
               [u.symb for u in l2]))@%]$List(%))@%)))@%

    flatten0(s, sy, n) ==
      atom? s => [nil(), s]
      a := convert(concat(string sy, convert(n)@String)::Symbol)@%
      l2 := [flatten0(x, sy, n := n+1) for x in rest(l := destruct s)]
      [concat(concat [u.lst for u in l2], conv([convert(
        "LET"::Symbol)@%, a, conv(concat(first l,
             [u.symb for u in l2]))@%]$List(%))@%), a]

    strsym s ==
      string? s => string s
      symbol? s => string symbol s
      error "strsym: form is neither a string or symbol"

    unparse x ==
      atom?(s:% := form2String(x)$Lisp) => strsym s
      concat [strsym a for a in destruct s]

    parse(s:String):% ==
      ncParseFromString(s)$Lisp

    declare signature ==
      declare(name := new()$Symbol, signature)$Lisp
      name

    compile(name, types) ==
      symbol car cdr car
        selectLocalMms(mkProperOp name, convert(name)@%,
          types, nil$List(%))$Lisp

    mkProperOp name ==
      op := mkAtree(nme := convert(name)@%)$Lisp
      transferPropsToNode(nme, op)$Lisp
      convert op

    binary(op, args) ==
      (n := #args) < 2 => error "Need at least 2 arguments"
      n = 2 => convert([op, first args, last args]$List(%))
      convert([op, first args, binary(op, rest args)]$List(%))

    tuplify l ==
      empty? rest l => convert first l
      conv
        concat(convert("Tuple"::Symbol), [convert x for x in l]$List(%))

    function(f, l, name) ==
      nn := convert(new(1 + #l, convert(nil()$List(%)))$List(%))@%
      conv([convert("DEF"::Symbol), conv(cons(convert(name)@%,
                        [convert(x)@% for x in l])), nn, nn, f]$List(%))

    s1 + s2 ==
      s1 = 0 => s2
      s2 = 0 => s1
      conv [convert("+"::Symbol), s1, s2]$List(%)

    s1 * s2 ==
      s1 = 0 or s2 = 0 => 0
      s1 = 1 => s2
      s2 = 1 => s1
      conv [convert("*"::Symbol), s1, s2]$List(%)

    s1:% ** n:Integer ==
      s1 = 0 and n > 0 => 0
      s1 = 1 or zero? n => 1
--      one? n => s1
      (n = 1) => s1
      conv [convert("**"::Symbol), s1, convert n]$List(%)

    s1:% ** n:NonNegativeInteger == s1 ** (n::Integer)

    s1 / s2 ==
      s2 = 1 => s1
      conv [convert("/"::Symbol), s1, s2]$List(%)

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/6679376400046902071-25px002.spad using 
      old system compiler.
   INFORM abbreviates domain InputForm 
------------------------------------------------------------------------
   initializing NRLIB INFORM for InputForm 
   compiling into NRLIB INFORM 
   compiling exported Zero : () -> $
Time: 0.10 SEC.

   compiling exported One : () -> $
Time: 0.01 SEC.

   compiling exported convert : $ -> SExpression
      INFORM;convert;$Se;3 is replaced by x 
Time: 0 SEC.

   compiling exported convert : SExpression -> $
      INFORM;convert;Se$;4 is replaced by x 
Time: 0 SEC.

   compiling local conv : List $ -> $
Time: 0.05 SEC.

   compiling exported lambda : ($,List Symbol) -> $
Time: 0.10 SEC.

   compiling exported interpret : $ -> Any
Time: 0 SEC.

   compiling exported convert : DoubleFloat -> $
Time: 0 SEC.

   compiling exported flatten : $ -> $
Time: 0.17 SEC.

   compiling local flatten0 : ($,Symbol,NonNegativeInteger) -> Record(lst: List $,symb: $)
Time: 0.08 SEC.

   compiling local strsym : $ -> String
Time: 0.01 SEC.

   compiling exported unparse : $ -> String
Time: 0.09 SEC.

   compiling exported parse : String -> $
      INFORM;parse;S$;13 is replaced by ncParseFromString 
Time: 0 SEC.

   compiling exported declare : List $ -> Symbol
Time: 0 SEC.

   compiling exported compile : (Symbol,List $) -> Symbol
Time: 0.01 SEC.

   compiling local mkProperOp : Symbol -> $
Time: 0 SEC.

   compiling exported binary : ($,List $) -> $
Time: 0.01 SEC.

   compiling local tuplify : List Symbol -> $
Time: 0.02 SEC.

   compiling exported function : ($,List Symbol,Symbol) -> $
Time: 0.10 SEC.

   compiling exported + : ($,$) -> $
Time: 0.01 SEC.

   compiling exported * : ($,$) -> $
Time: 0.01 SEC.

   compiling exported ** : ($,Integer) -> $
Time: 0.01 SEC.

   compiling exported ** : ($,NonNegativeInteger) -> $
Time: 0 SEC.

   compiling exported / : ($,$) -> $
Time: 0.01 SEC.

(time taken in buildFunctor:  1)

;;;     ***       |InputForm| REDEFINED

;;;     ***       |InputForm| REDEFINED
Time: 0.01 SEC.

   Warnings: 
      [1] conv: pretend$ -- should replace by @

   Cumulative Statistics for Constructor InputForm
      Time: 0.80 seconds

   finalizing NRLIB INFORM 
   Processing InputForm for Browser database:
--------(interpret ((Any) %))---------
--------(convert (% (SExpression)))---------
--------(binary (% % (List %)))---------
--------(function (% % (List (Symbol)) (Symbol)))---------
--------(lambda (% % (List (Symbol))))---------
--------(+ (% % %))---------
--------(* (% % %))---------
--------(/ (% % %))---------
--------(** (% % (NonNegativeInteger)))---------
--------(** (% % (Integer)))---------
--------((Zero) (%) constant)---------
--------((One) (%) constant)---------
--------(flatten (% %))---------
--------(unparse ((String) %))---------
--------(parse (% (String)))---------
--------(declare ((Symbol) (List %)))---------
--------(compile ((Symbol) (Symbol) (List %)))---------
--------constructor---------
------------------------------------------------------------------------
   InputForm is now explicitly exposed in frame initial 
   InputForm will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/INFORM.NRLIB/code

Test

parse("sin x + 1")

(1)