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SandBoxMyReduceInOpenAxiom
  
last edited 16 years ago by Bill Page

Edit detail for SandBoxMyReduceInOpenAxiom revision 4 of 4
1 2 3 4
Editor: Bill Page
Time: 2008/04/08 17:33:55 GMT-7
Note: using = from Mapping 
changed:
-MyReduce(S:Type): with
MyReduce2(S:Type): with

changed:
-Notice that it fails in the same way as above, but it would work if we used the original trick of applying the function before comparing it.
Notice that it fails in the same way as above:

added:

But it works if we used the original trick of applying the function to get rid of 'newGoGet' before comparing the functions.

\begin{spad}
)abbrev package MYRED3 MyReduce3
MyReduce3(S:Type): with
    myred3: ((S,S)->S,List S) -> S
 == add
   import NonNegativeInteger
   myred3(f:(S,S)->S, x:List S):S ==
     if #x>1 then
       f(first x, myred3(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)$Mapping(S,S,S) => return 0$S
       if S has Monoid then
         f(1,1)=(1*1)$S and (f = _*$S)$Mapping(S,S,S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"
\end{spad}

\begin{axiom}
myred3(+,[1,2,3,4])
myred3(+,[]$List Integer)
myred3(*,[1,2,3,4])
myred3(*,[]$List Integer)
\end{axiom}

fricas
(1) -> )version

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

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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6114676696124184375-25px002.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: 0.01 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MyReduce| REDEFINED

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

   Cumulative Statistics for Constructor MyReduce
      Time: 0.01 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 16 FEB 2025 09:21:57 AM):

; wrote /var/aw/var/LatexWiki/MYRED.NRLIB/MYRED.fasl
; compilation finished in 0:00:00.032
------------------------------------------------------------------------
   MyReduce is now explicitly exposed in frame initial 
   MyReduce will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYRED.NRLIB/MYRED

fricas
myred(+,[1,2,3,4])
\label{eq1}10(1)
Type: PositiveInteger?
fricas
myred(+,[]$List Integer)

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

   >> Error detected within library code:
   reducing over an empty list needs the 3 argument form

Here is another version of the same thing using the = from the Mapping domain.

spad
)abbrev package MYRED2 MyReduce2
MyReduce2(S:Type): with
    myred2: ((S,S)->S,List S) -> S
 == add
   import NonNegativeInteger
   myred2(f:(S,S)->S, x:List S):S ==
     if #x>1 then
       f(first x, myred2(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)$Mapping(S,S,S) => return 0$S
       if S has Monoid then
         -- f(1,1)=(1*1)$S and (f = _*$S) => return 1$S
         (f = _*$S)$Mapping(S,S,S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7640641182681721660-25px004.spad
      using old system compiler.
   MYRED2 abbreviates package MyReduce2 
------------------------------------------------------------------------
   initializing NRLIB MYRED2 for MyReduce2 
   compiling into NRLIB MYRED2 
   importing NonNegativeInteger
   compiling exported myred2 : ((S,S) -> S,List S) -> S
****** Domain: S already in scope
augmenting S: (AbelianMonoid)
****** Domain: S already in scope
augmenting S: (Monoid)
****** Domain: (Mapping S S S) already in scope
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MyReduce2| REDEFINED

;;;     ***       |MyReduce2| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MyReduce2
      Time: 0 seconds

   finalizing NRLIB MYRED2 
   Processing MyReduce2 for Browser database:
--->-->MyReduce2(constructor): Not documented!!!!
--->-->MyReduce2((myred2 (S (Mapping S S S) (List S)))): Not documented!!!!
--->-->MyReduce2(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYRED2.NRLIB/MYRED2.lsp" (written 16 FEB 2025 09:21:57 AM):

; wrote /var/aw/var/LatexWiki/MYRED2.NRLIB/MYRED2.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   MyReduce2 is now explicitly exposed in frame initial 
   MyReduce2 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYRED2.NRLIB/MYRED2

Notice that it fails in the same way as above:

fricas
myred2(+,[1,2,3,4])
\label{eq2}10(2)
Type: PositiveInteger?
fricas
myred2(+,[]$List Integer)

   >> Error detected within library code:
   reducing over an empty list needs the 3 argument form

But it works if we used the original trick of applying the function to get rid of newGoGet before comparing the functions.

spad
)abbrev package MYRED3 MyReduce3
MyReduce3(S:Type): with
    myred3: ((S,S)->S,List S) -> S
 == add
   import NonNegativeInteger
   myred3(f:(S,S)->S, x:List S):S ==
     if #x>1 then
       f(first x, myred3(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)$Mapping(S,S,S) => return 0$S
       if S has Monoid then
         f(1,1)=(1*1)$S and (f = _*$S)$Mapping(S,S,S) => return 1$S
       error "reducing over an empty list needs the 3 argument form"
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1899462816039391804-25px006.spad
      using old system compiler.
   MYRED3 abbreviates package MyReduce3 
------------------------------------------------------------------------
   initializing NRLIB MYRED3 for MyReduce3 
   compiling into NRLIB MYRED3 
   importing NonNegativeInteger
   compiling exported myred3 : ((S,S) -> S,List S) -> S
****** Domain: S already in scope
augmenting S: (AbelianMonoid)
****** Domain: S already in scope
augmenting S: (Monoid)
****** Domain: (Mapping S S S) already in scope
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MyReduce3| REDEFINED

;;;     ***       |MyReduce3| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MyReduce3
      Time: 0 seconds

   finalizing NRLIB MYRED3 
   Processing MyReduce3 for Browser database:
--->-->MyReduce3(constructor): Not documented!!!!
--->-->MyReduce3((myred3 (S (Mapping S S S) (List S)))): Not documented!!!!
--->-->MyReduce3(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYRED3.NRLIB/MYRED3.lsp" (written 16 FEB 2025 09:21:57 AM):

; wrote /var/aw/var/LatexWiki/MYRED3.NRLIB/MYRED3.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   MyReduce3 is now explicitly exposed in frame initial 
   MyReduce3 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYRED3.NRLIB/MYRED3

fricas
myred3(+,[1,2,3,4])
\label{eq3}10(3)
Type: PositiveInteger?
fricas
myred3(+,[]$List Integer)
\label{eq4}0(4)
Type: NonNegativeInteger?
fricas
myred3(*,[1,2,3,4])
\label{eq5}24(5)
Type: PositiveInteger?
fricas
myred3(*,[]$List Integer)
\label{eq6}1(6)
Type: PositiveInteger?