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SandBoxMyReduce

Edit detail for SandBoxMyReduce revision 9 of 14

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Editor: Bill Page Time: 2008/04/07 20:37:34 GMT-7
Note: Waldek's function

changed:
-      print(coerceMap2E(f)$Lisp::OutputForm)
-      print(coerceMap2E(g)$Lisp::OutputForm)
-      EQ(coerceMap2E(f)$Lisp,coerceMap2E(g)$Lisp)$Lisp
      --print(coerceMap2E(f)$Lisp::OutputForm)
      --print(coerceMap2E(g)$Lisp::OutputForm)
      EQ(f,g)$Lisp

changed:
-         (f = _+$S) => return 0$S
         -- Must force "newGoGet" by applying operations before comparison!
         f(0,0)=(0+0)$S and (f = _+$S) => return 0$S

changed:
-         (f = _*$S) => return 1$S
         f(1,1)=(1*1)$S and (f = _*$S) => return 1$S

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
   ((f:F)=(g:F)):Boolean ==
      --print(coerceMap2E(f)$Lisp::OutputForm)
      --print(coerceMap2E(g)$Lisp::OutputForm)
      EQ(f,g)$Lisp
   --
   myred(f:(S,S)->S, x:List S):S ==
     if empty? x then
       if S has AbelianMonoid then
         -- Must force "newGoGet" by applying operations before comparison!
         f(0,0)=(0+0)$S and (f = _+$S) => return 0$S
       if S has Monoid then
         f(1,1)=(1*1)$S and (f = _*$S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"
     reduce(f, rest x, first x)

spad

   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/5320925977799285168-25px001.spad using 
      old system compiler.
   MYRED abbreviates package MyReduce 
------------------------------------------------------------------------
   initializing NRLIB MYRED for MyReduce 
   compiling into NRLIB MYRED 
   processing macro definition F ==> (S,S) -> S 
   compiling local = : ((S,S) -> S,(S,S) -> S) -> Boolean
      MYRED;= is replaced by EQ 
Time: 0.01 SEC.
   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: 0.08 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |MyReduce| REDEFINED
;;;     ***       |MyReduce| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor MyReduce
      Time: 0.09 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])

(1)

Type: PositiveInteger?

axiom
myred(+,[])$MyReduce(Integer)

(2)

Type: Integer

axiom
myred(*,[1,2,3])

(3)

Type: PositiveInteger?

axiom
myred(*,[])$MyReduce(Integer)

(4)

Type: Integer