MathAction SandBoxMyReduceInFriCAS

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    - SandBoxMyReduceInFriCAS <-- You are here.

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(1) -> )version

"FriCAS 1.3.10 compiled at Wed 10 Jan 02:19:45 CET 2024"

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)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"

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   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3864115453202676649-25px002.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: 0.02 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MyReduce| REDEFINED

;;;     ***       |MyReduce| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MyReduce
      Time: 0.03 seconds

   finalizing NRLIB MYRED 
   Processing MyReduce for Browser database:
--->-->MyReduce(constructor): Not documented!!!!
--->-->MyReduce((myred (S (Mapping S S S) (List S)))): Not documented!!!!
--->-->MyReduce(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYRED.NRLIB/MYRED.lsp" (written 08 NOV 2024 11:34:43 PM):

; wrote /var/aw/var/LatexWiki/MYRED.NRLIB/MYRED.fasl
; compilation finished in 0:00:00.016
------------------------------------------------------------------------
   MyReduce is now explicitly exposed in frame initial 
   MyReduce will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYRED.NRLIB/MYRED

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

$\label{eq1}10$

(1)

Type: PositiveInteger?

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myred(+,[]$List Integer)

   theMap(INT;+;3%;37,655)
   theMap(INT;+;3%;37,655)

$\label{eq2}0$

(2)

Type: NonNegativeInteger?

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myred(*,[1,2,3,4])

$\label{eq3}24$

(3)

Type: PositiveInteger?

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myred(*,[]$List Integer)

   theMap(INT;*;3%;40,655)
   theMap(INT;+;3%;37,655)
   theMap(INT;*;3%;40,655)
   theMap(INT;*;3%;40,655)

$\label{eq4}1$

(4)

Type: PositiveInteger?

Waldek writes:

Problem with recompilation.

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eq((f:(INT,INT)->INT),(g:(INT,INT)->INT)):Boolean ==
      print(coerceMap2E(f)$Lisp::OutputForm)
      print(coerceMap2E(g)$Lisp::OutputForm)
      not null? EQ(f,g)$Lisp

   Function declaration eq : (((Integer, Integer) -> Integer), ((
      Integer, Integer) -> Integer)) -> Boolean has been added to 
      workspace.

Type: Void

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f1 := _+$Integer @ Mapping(Integer, Integer, Integer)

$\label{eq5}\mbox{theMap (...)}$

(5)

Type: ((Integer, Integer) -> Integer)

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f2 := _+$Integer @ Mapping(Integer, Integer, Integer)

$\label{eq6}\mbox{theMap (...)}$

(6)

Type: ((Integer, Integer) -> Integer)

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eq(f1,f2)

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Compiling function eq with type (((Integer, Integer) -> Integer), ((
      Integer, Integer) -> Integer)) -> Boolean 
   (theMap INT;+;3%;37 655)
   (theMap INT;+;3%;37 655)

$\label{eq7} \mbox{\rm true}$

(7)

Type: Boolean

FOO has nothing to do with Integer:

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)abbrev category FOO FOO
FOO(): Category == with ()

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   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4158498938098016222-25px005.spad
      using old system compiler.
   FOO abbreviates category FOO 
------------------------------------------------------------------------
   initializing NRLIB FOO for FOO 
   compiling into NRLIB FOO 

;;;     ***       FOO REDEFINED
Time: 0 SEC.

   finalizing NRLIB FOO 
   Processing FOO for Browser database:
--->-->FOO(): Missing Description
; compiling file "/var/aw/var/LatexWiki/FOO.NRLIB/FOO.lsp" (written 08 NOV 2024 11:34:43 PM):

; wrote /var/aw/var/LatexWiki/FOO.NRLIB/FOO.fasl
; compilation finished in 0:00:00.000
------------------------------------------------------------------------
   FOO is now explicitly exposed in frame initial 
   FOO will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/FOO.NRLIB/FOO

but mere fact that I compiled FOO invalidates all domain vectors...

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g := _+$Integer @ Mapping(Integer, Integer, Integer)

$\label{eq8}\mbox{theMap (...)}$

(8)

Type: ((Integer, Integer) -> Integer)

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eq(f1,g)

   (theMap INT;+;3%;37 655)
   (theMap INT;+;3%;37 655)

$\label{eq9} \mbox{\rm false}$

(9)

Type: Boolean

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f1(1,2)

$\label{eq10}3$

(10)

Type: PositiveInteger?

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g(1,2)

$\label{eq11}3$

(11)

Type: PositiveInteger?

Note: Both functions f1 and g point to the same function although the names have changed.

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