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last edited 16 years ago by Bill Page |
Edit detail for SandBoxMyReduceInOpenAxiom revision 4 of 4
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Editor: Bill Page
Time: 2008/04/08 17:33:55 GMT-7 |
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| 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}
\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(*,[]$List Integer)
\end{axiom}
Here is another version of the same thing using the
=from theMappingdomain.\begin{spad} )abbrev package MYRED2 MyReduce2 MyReduce2(S:Type): with myred2: ((S,S)->S,List S) -> S == add import NonNegativeInteger myred2(f:(S,S)->S, x:List S):S == if #x>1 then f(first x, myred2(f,rest x)) else if #x=1 then first x else if S has AbelianMonoid then -- Must force "newGoGet" by applying operations before comparison! -- f(0,0)=(0+0)$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(*,[]$List Integer) \end{axiom}
But it works if we used the original trick of applying the function to get rid of
newGoGetbefore comparing the functions.\begin{spad} )abbrev package MYRED3 MyReduce3 MyReduce3(S:Type): with myred3: ((S,S)->S,List S) -> S == add import NonNegativeInteger myred3(f:(S,S)->S, x:List S):S == if #x>1 then f(first x, myred3(f,rest x)) else if #x=1 then first x else if S has AbelianMonoid then -- Must force "newGoGet" by applying operations before comparison! f(0,0)=(0+0)$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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LaTeX Warning: Characters dropped after `\end{axiom}' on input line 123.
(/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd) (/usr/share/texmf-texlive/tex/latex/base/ulasy.fd) You can't use `macro parameter character #' in math mode. l.137 if # x>1 then You can't use `macro parameter character #' in math mode. l.139 else if # x=1 then Missing $ inserted. <inserted text> $ l.144 -- f(0,0)=(0+0)$S and (f = _ +$S) => return 0$S Missing $ inserted. <inserted text> $ l.147 -- f(1,1)=(11)$S and (f = _ $S) => return 1$S Missing $ inserted. <inserted text> $ l.150 \end{spad} \newpage
Overfull \hbox (4.921pt too wide) in paragraph at lines 125--150 \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)$\OML/cmm/m/it/12 Lisp \OMS/cmsy/m/n/12 ^^@
Overfull \hbox (137.34442pt too wide) in paragraph at lines 125--150 \OMS/cmsy/m/n/12 ^^@\OML/cmm/m/it/12 importNonNegativeIntegermyred\OT1/cmr/m/n/ 12 (\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 : (\OML/cmm/m/it/12 S; S\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 > S; x \OT1/cmr/m/n/12 : \OML/cmm/m/it/1 2 ListS\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 S \OT1/cmr/m/n/12 == \OML/cmm/m/it/ 12 ifx > \OT1/cmr/m/n/12 1\OML/cmm/m/it/12 thenf\OT1/cmr/m/n/12 (\OML/cmm/m/it/ 12 firstx; myred\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 f; restx\OT1/cmr/m/n/12 ))\OM L/cmm/m/it/12 elseifx \OT1/cmr/m/n/12 = 1\OML/cmm/m/it/12 thenfirstxelseifShasA belianMonoidthen \OMS/cmsy/m/n/12 ^^@
Overfull \hbox (43.71477pt too wide) in paragraph at lines 125--150 \T1/cmr/m/n/12 0$\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$\OML/cmm/m/it/12 Serror\OT1/cmr/m/n/12 "\OML/cmm/ m/it/12 reducingoveranemptylistneedsthe\OT1/cmr/m/n/12 3\OML/cmm/m/it/12 argume ntform\OT1/cmr/m/n/12 "$ [1]
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[4] (./7990258885462259044-16.0px.aux) ) (see the transcript file for additional information) Output written on 7990258885462259044-16.0px.dvi (4 pages, 4444 bytes). Transcript written on 7990258885462259044-16.0px.log.