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\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
if S has Monoid then
f(1,1)=(11)$S and (f = _$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(*,[]$List Integer)
\end{axiom}
SandBoxMyReduceInOpenAxiom
SandBoxMyReduceInFriCAS
Some or all expressions may not have rendered properly,
because Axiom returned the following error:
Error: export FRICAS=/usr/local/lib/open-axiom/x86_64-unknown-linux/1.1.0-2008-01-28; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$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/3373524299801295110-25px.axm
/bin/sh: /usr/local/lib/open-axiom/x86_64-unknown-linux/1.1.0-2008-01-28/bin/FRICASsys: not found
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because Latex returned the following error:
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ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon
ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i
nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp
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You can't use `macro parameter character #' in math mode.
l.134 if #
x>1 then
You can't use `macro parameter character #' in math mode.
l.136 else if #
x=1 then
Missing $ inserted.
<inserted text>
$
l.141 f(0,0)=(0+0)$S and (f = _
+$S) => return 0$S
Missing $ inserted.
<inserted text>
$
l.143 f(1,1)=(11)$S and (f = _
$S) => return 1$S
Missing $ inserted.
<inserted text>
$
l.145 \end{spad}
\newpage
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(see the transcript file for additional information)
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