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last edited 16 years ago by Bill Page |
Edit detail for SandBoxMyReduceInOpenAxiom revision 3 of 4
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Editor: Bill Page
Time: 2008/04/08 17:28:10 GMT-7 |
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| Note: using = from Mapping | ||
added:
Here is another version of the same thing using the '=' from the 'Mapping' domain.
\begin{spad}
)abbrev package MYRED2 MyReduce2
MyReduce(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"
\end{spad}
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.
\begin{axiom}
myred2(+,[1,2,3,4])
myred2(+,[]$List Integer)
myred2(*,[1,2,3,4])
myred2(*,[]$List Integer)
\end{axiom}
axiom)version Value = "Tuesday January 29, 2008 at 18:03:22 "
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$S error "reducing over an empty list needs the 3 argument form"
spad
Compiling OpenAxiom source code from file
/var/zope2/var/LatexWiki/6114676696124184375-25px002.spad using
old system compiler.
MYRED abbreviates package MyReduce
------------------------------------------------------------------------
initializing NRLIB MYRED for MyReduce
compiling into NRLIB MYRED
compiling local = : ((S,S) -> S,(S,S) -> S) -> Boolean
Time: 0 SEC.
importing NonNegativeInteger
compiling exported myred : ((S,S) -> S,List S) -> S
****** Domain: S already in scope
augmenting S: (AbelianMonoid)
****** Domain: S already in scope
augmenting S: (Monoid)
Time: 0.10 SEC.
(time taken in buildFunctor: 0)
;;; *** |MyReduce| REDEFINED
;;; *** |MyReduce| REDEFINED
Time: 0.05 SEC.
Cumulative Statistics for Constructor MyReduce
Time: 0.15 seconds
finalizing NRLIB MYRED
Processing MyReduce for Browser database:
--->-->MyReduce((myred (S (Mapping S S S) (List S)))): Not documented!!!!
--->-->MyReduce(constructor): Not documented!!!!
--->-->MyReduce(): Missing Description
------------------------------------------------------------------------
MyReduce is now explicitly exposed in frame initial
MyReduce will be automatically loaded when needed from
/var/zope2/var/LatexWiki/MYRED.NRLIB/codeaxiommyred(+,[1,2,3,4])
 | (1) |
Type: PositiveInteger?
axiommyred(+,[]$List Integer) theMap(INT;+;3$;37,536) theMap(newGoGet) theMap(INT;+;3$;37,536) 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 MyReduce(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 OpenAxiom source code from file
/var/zope2/var/LatexWiki/8074394904773086877-25px004.spad using
old system compiler.
MYRED2 abbreviates package MyReduce2
------------------------------------------------------------------------
initializing NRLIB MYRED for MyReduce
compiling into NRLIB MYRED
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: 0.01 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:
--->/var/zope2/var/LatexWiki/6114676696124184375-25px002.spad-->MyReduce((myred2 (S (Mapping S S S) (List S)))): Not documented!!!!
--->/var/zope2/var/LatexWiki/6114676696124184375-25px002.spad-->MyReduce(constructor): Not documented!!!!
--->/var/zope2/var/LatexWiki/6114676696124184375-25px002.spad-->MyReduce(): Missing Description
------------------------------------------------------------------------
MyReduce is already explicitly exposed in frame initial
MyReduce will be automatically loaded when needed from
/var/zope2/var/LatexWiki/MYRED.NRLIB/codeNotice 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.
axiommyred2(+,[1,2,3,4])
 | (2) |
Type: PositiveInteger?
axiommyred2(+,[]$List Integer) >> Error detected within library code: reducing over an empty list needs the 3 argument form