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SandBoxMyReduceInOpenAxiom

Edit detail for SandBoxMyReduceInOpenAxiom revision 1 of 4

	1 2 3 4
Editor: Bill Page Time: 2008/04/08 15:27:50 GMT-7
Note: test

changed:
-
\begin{spad}
)abbrev package MYRED MyReduce
MyReduce(S:Type): with
    myred: ((S,S)->S,List S) -> S
 == add
   -- Waldek's local helper function
   ((f:(S,S)->S) = (g:(S,S)->S)):Boolean ==
      print(coerceMap2E(f)$Lisp::OutputForm)
      print(coerceMap2E(g)$Lisp::OutputForm)
      EQ(f,g)$Lisp
   --
   import NonNegativeInteger
   myred(f:(S,S)->S, x:List S):S ==
     if #x>1 then
       f(first x, myred(f,rest x))
     else if #x=1 then
       first x
     else
       if S has AbelianMonoid then
         -- Must force "newGoGet" by applying operations before comparison!
         -- f(0,0)=(0+0)$S and (f = _+$S) => return 0$S
         (f = _+$S) => return 0$S
       if S has Monoid then
         -- f(1,1)=(1*1)$S and (f = _*$S) => return 1$S
         (f = _*$S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"
\end{spad}

\begin{axiom}
myred(+,[1,2,3,4])
myred(+,[]$List Integer)
myred(*,[1,2,3,4])
myred(*,[]$List Integer)

\end{axiom}

spad)abbrev package MYRED MyReduce
MyReduce(S:Type): with
    myred: ((S,S)->S,List S) -> S
 == add
   -- Waldek's local helper function
   ((f:(S,S)->S) = (g:(S,S)->S)):Boolean ==
      print(coerceMap2E(f)$Lisp::OutputForm)
      print(coerceMap2E(g)$Lisp::OutputForm)
      EQ(f,g)$Lisp
   --
   import NonNegativeInteger
   myred(f:(S,S)->S, x:List S):S ==
     if #x>1 then
       f(first x, myred(f,rest x))
     else if #x=1 then
       first x
     else
       if S has AbelianMonoid then
         -- Must force "newGoGet" by applying operations before comparison!
         -- f(0,0)=(0+0)$S and (f = _+$S) => return 0$S
         (f = _+$S) => return 0$S
       if S has Monoid then
         -- f(1,1)=(1*1)$S and (f = _*$S) => return 1$S
         (f = _*$S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"

spad

   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/6114676696124184375-25px001.spad using 
      old system compiler.
   MYRED abbreviates package MyReduce 
------------------------------------------------------------------------
   initializing NRLIB MYRED for MyReduce 
   compiling into NRLIB MYRED 
   compiling local = : ((S,S) -> S,(S,S) -> S) -> Boolean
Time: 0 SEC.
   importing NonNegativeInteger
   compiling exported myred : ((S,S) -> S,List S) -> S
****** Domain: S already in scope
augmenting S: (AbelianMonoid)
****** Domain: S already in scope
augmenting S: (Monoid)
Time: 0.10 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |MyReduce| REDEFINED
;;;     ***       |MyReduce| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor MyReduce
      Time: 0.10 seconds
   finalizing NRLIB MYRED 
   Processing MyReduce for Browser database:
--->-->MyReduce((myred (S (Mapping S S S) (List S)))): Not documented!!!!
--->-->MyReduce(constructor): Not documented!!!!
--->-->MyReduce(): Missing Description
------------------------------------------------------------------------
   MyReduce is now explicitly exposed in frame initial 
   MyReduce will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MYRED.NRLIB/code

axiom
myred(+,[1,2,3,4])

(1)

Type: PositiveInteger?

axiommyred(+,[]$List Integer)
   theMap(INT;+;3$;37,416)
   theMap(newGoGet)
   theMap(INT;+;3$;37,416)
   theMap(newGoGet)
   >> Error detected within library code:
   reducing over an empty list needs the 3 argument form