\begin{axiom}
)version
\end{axiom}
\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)=(11)$S and (f = _$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(*,[]$List Integer)
\end{axiom}
Here is another version of the same thing using the = from the Mapping domain.
\begin{spad}
)abbrev package MYRED2 MyReduce2
MyReduce2(S:Type): with
myred2: ((S,S)->S,List S) -> S
== add
import NonNegativeInteger
myred2(f:(S,S)->S, x:List S):S ==
if #x>1 then
f(first x, myred2(f,rest x))
else if #x=1 then
first x
else
if S has AbelianMonoid then
-- Must force "newGoGet" by applying operations before comparison!
-- f(0,0)=(0+0)$S and (f = _+$S) => return 0$S
(f = _+$S)$Mapping(S,S,S) => return 0$S
if S has Monoid then
-- f(1,1)=(11)$S and (f = _$S) => return 1$S
(f = _*$S)$Mapping(S,S,S) => return 1$S
error "reducing over an empty list needs the 3 argument form"
\end{spad}
Notice that it fails in the same way as above:
\begin{axiom}
myred2(+,[1,2,3,4])
myred2(+,[]$List Integer)
myred2(*,[1,2,3,4])
myred2(*,[]$List Integer)
\end{axiom}
But it works if we used the original trick of applying the function to get rid of newGoGet before comparing the functions.
\begin{spad}
)abbrev package MYRED3 MyReduce3
MyReduce3(S:Type): with
myred3: ((S,S)->S,List S) -> S
== add
import NonNegativeInteger
myred3(f:(S,S)->S, x:List S):S ==
if #x>1 then
f(first x, myred3(f,rest x))
else if #x=1 then
first x
else
if S has AbelianMonoid then
-- Must force "newGoGet" by applying operations before comparison!
f(0,0)=(0+0)$S and (f = _+$S)$Mapping(S,S,S) => return 0$S
if S has Monoid then
f(1,1)=(11)$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(*,[]$List Integer)
\end{axiom}
Some or all expressions may not have rendered properly,
because Axiom returned the following error:
Error: export FRICAS=/usr/local/lib/open-axiom/x86_64-unknown-linux/1.1.0-2008-01-28; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/open-axiom/x86_64-unknown-linux/1.1.0-2008-01-28/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7234157229126066145-25px.axm
/bin/sh: /usr/local/lib/open-axiom/x86_64-unknown-linux/1.1.0-2008-01-28/bin/FRICASsys: not found
Some or all expressions may not have rendered properly,
because Latex returned the following error:
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ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i
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Xy-pic version 3.7 <1999/02/16>
Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr>
Xy-pic is free software: see the User's Guide for details.
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(./7990258885462259044-16.0px.sout))
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l.137 if #
x>1 then
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l.139 else if #
x=1 then
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<inserted text>
$
l.144 -- f(0,0)=(0+0)$S and (f = _
+$S) => return 0$S
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<inserted text>
$
l.147 -- f(1,1)=(11)$S and (f = _
$S) => return 1$S
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$
l.150 \end{spad}
\newpage
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\T1/cmr/m/n/12 ((f:(S,S)->S) = (g:(S,S)->S)):Boolean == print(coerceMap2E(f)$\O
ML/cmm/m/it/12 Lisp \OT1/cmr/m/n/12 :: \OML/cmm/m/it/12 OutputForm\OT1/cmr/m/n/
12 )\OML/cmm/m/it/12 print\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 coerceMap\OT1/cmr/m
/n/12 2\OML/cmm/m/it/12 E\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 )$\
T1/cmr/m/n/12 Lisp::OutputForm) EQ(f,g)$\OML/cmm/m/it/12 Lisp \OMS/cmsy/m/n/12
^^@
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\OMS/cmsy/m/n/12 ^^@\OML/cmm/m/it/12 importNonNegativeIntegermyred\OT1/cmr/m/n/
12 (\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 : (\OML/cmm/m/it/12 S; S\OT1/cmr/m/n/12
)\OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 > S; x \OT1/cmr/m/n/12 : \OML/cmm/m/it/1
2 ListS\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 S \OT1/cmr/m/n/12 == \OML/cmm/m/it/
12 ifx > \OT1/cmr/m/n/12 1\OML/cmm/m/it/12 thenf\OT1/cmr/m/n/12 (\OML/cmm/m/it/
12 firstx; myred\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 f; restx\OT1/cmr/m/n/12 ))\OM
L/cmm/m/it/12 elseifx \OT1/cmr/m/n/12 = 1\OML/cmm/m/it/12 thenfirstxelseifShasA
belianMonoidthen \OMS/cmsy/m/n/12 ^^@
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\T1/cmr/m/n/12 0$\OML/cmm/m/it/12 SifShasMonoidthen \OMS/cmsy/m/n/12 ^^@ ^^@\OM
L/cmm/m/it/12 f\OT1/cmr/m/n/12 (1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1) = (1 \OM
S/cmsy/m/n/12 ^^C \OT1/cmr/m/n/12 1)$\T1/cmr/m/n/12 S and (f = $[]$S) => re-tur
n 1$\OML/cmm/m/it/12 S\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 =[]$\
T1/cmr/m/n/12 S) => re-turn 1$\OML/cmm/m/it/12 Serror\OT1/cmr/m/n/12 "\OML/cmm/
m/it/12 reducingoveranemptylistneedsthe\OT1/cmr/m/n/12 3\OML/cmm/m/it/12 argume
ntform\OT1/cmr/m/n/12 "$
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(see the transcript file for additional information)
Output written on 7990258885462259044-16.0px.dvi (4 pages, 4444 bytes).
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