login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit
AxiomDocumentation SandBox Aldor
Axiom Volume 1  ← ↑  

SandBox Aldor Join and Meet
  
last edited 1 year ago by test1

Edit detail for SandBox Aldor Join and Meet revision 8 of 9
1 2 3 4 5 6 7 8 9
Editor: page
Time: 2008/08/06 20:49:29 GMT-7
Note: new version of FriCAS and Aldor interface 

        

        


Aldor-Meet


  On Date: Nov 19, 2007 10:58 AM Oleg Golubitsky wrote to aldor-l :


By analogy with Join, Meet(C1,C2) should return
a category which has the intersection of exports
of C1 and C2.


A simple test (see below) confirmed this semantics;
I also could not find a description of Meet in the guide.


\begin{aldor}
#include "aldor"
define C1:Category == with {
       f: Integer;
       g: Integer;
}
define C2:Category == with {
       f: Integer;
       h: Integer;
}
D: Meet(C1,C2) == add {
       f: Integer == 1;  -- OK; if this line is commented out, error:
                               -- The domain is missing some exports.
                               -- Missing f: AldorInteger
}
\end{aldor}


The Axiom library apparently does not define Meet.
\begin{aldor}
#include "axiom"
Meet(T: Tuple Category): Category == with;


define C1:Category == with {
       f: Integer;
       g: Integer;
}
D1: C1 == add {
  f: Integer == 1;
  g: Integer == 2;
}
define C2:Category == with {
       f: Integer;
       h: Integer;
}
D2: C2 == add {
  f: Integer == 1;
  h: Integer == 3;
}


define M12:Category == Meet(C1,C2);


DM12: M12 == add {
  f: Integer == 1;  -- if this line is commented out, error:
                    -- The domain is missing some exports.
  g: Integer == 2;
  h: Integer == 3;


}


define J12:Category == Join(C1,C2);


DJ12: J12 == add {
  f: Integer == 1;
  g: Integer == 2;
  h: Integer == 3;
}


main1():Record(D1hasM12:Boolean,D2hasM12:Boolean) ==
  [D1 has M12, D2 has M12];
main2():Record(M12hasC1:Boolean,DM12hasC2:Boolean) ==
  [DM12 has C1, DM12 has C2];
main3():Record(DJ12hasC1:Boolean, DJ12hasC2:Boolean) ==
  [DJ12 has C1, DJ12 has C2];


main4():Record(D1hasMeet:Boolean, D2hasMeet:Boolean, D1hasF:Boolean) ==
  [D1 has Meet(C1,C2), D2 has Meet(C1,C2), D1 has with {f:Integer}];


--Evaluating more complex Meet/Joint expressions causes seg fault:
--main5():Record(D1hasMeetJoin:Boolean, D1hasJoinMeet:Boolean) ==
--  [D1 has Meet(C1,Join(C1,C2)), D1 has Join(C1,Meet(C1,C2))];
\end{aldor}


\begin{axiom}
f()$DM12
-- expect not defined
g()$DM12
-- expect not defined
h()$DM12
f()$DJ12
g()$DJ12
h()$DJ12
\end{axiom}




\begin{axiom}


expect False, False
main1()
\end{axiom}




Comment of Ralf Hemmecke 20-Nov-2007: I would expect (false,false) for main2(), because, DM12 is not explicitly declared to be of type C1 or C2 even if its "add" domain has all the exports (except for the names C1 and C2).
\begin{axiom}
-- expect True, True
main2()
-- expect True, True
main3()
-- expect True, True, True
main4()
-- expect True, True
--main5()
\end{axiom}
Comment of Ralf Hemmecke 20-Nov-2007: That main4() returns (false, false, true) should be considered a bug.





    Some or all expressions may not have rendered properly,
    because Axiom returned the following error:
Error: export FRICAS=/usr/local/lib/fricas/target/x86_64-unknown-linux; 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/fricas/target/x86_64-unknown-linux/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5296335634530161560-25px.axm
/bin/sh: /usr/local/lib/fricas/target/x86_64-unknown-linux/bin/FRICASsys: not found





Some or all expressions may not have rendered properly,
because Latex returned the following error:
This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6)
 \write18 enabled.
 %&-line parsing enabled.
entering extended mode
(./4438143605901807536-16.0px.tex
LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov
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
eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia
n, swedish, ukenglish, pinyin, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/bbm/bbm.sty)
(/usr/share/texmf-texlive/tex/latex/jknapltx/mathrsfs.sty)
(/usr/share/texmf-texlive/tex/latex/base/fontenc.sty
(/usr/share/texmf-texlive/tex/latex/base/t1enc.def))
(/usr/share/texmf-texlive/tex/latex/pstricks/pstricks.sty
(/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.tex
`PSTricks' v1.15  <2006/12/22> (tvz)
(/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.con))
(/usr/share/texmf/tex/latex/xcolor/xcolor.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def)))
(/usr/share/texmf-texlive/tex/latex/graphics/epsfig.sty
(/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty
(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty)
(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty
(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty)
(/etc/texmf/tex/latex/config/graphics.cfg))))
(/usr/share/texmf-texlive/tex/latex/pst-grad/pst-grad.sty
(/usr/share/texmf-texlive/tex/generic/pst-grad/pst-grad.tex
(/usr/share/texmf-texlive/tex/latex/xkeyval/pst-xkey.tex
(/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.sty
(/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.tex)))
`pst-plot' v1.05, 2006/11/04 (tvz,dg,hv)))
(/usr/share/texmf-texlive/tex/latex/pstricks/pst-plot.sty
(/usr/share/texmf-texlive/tex/generic/pstricks/pst-plot.tex
 v97 patch 2, 1999/12/12
(/usr/share/texmf-texlive/tex/generic/multido/multido.tex
 v1.41, 2004/05/18 <tvz>)))
(/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty
(/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)


Package geometry Warning: `lmargin' and `rmargin' result in NEGATIVE (-108.405p
t).
    `width' should be shortened in length.


) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `? option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty)
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/setspace/setspace.sty
Package: `setspace 6.7 <2000/12/01>
) (/usr/share/texmf-texlive/tex/generic/xypic/xy.sty
(/usr/share/texmf-texlive/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes,
docmode, (/usr/share/texmf-texlive/tex/generic/xypic/xyrecat.tex)
(/usr/share/texmf-texlive/tex/generic/xypic/xyidioms.tex)
 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.




Loading kernel: messages; fonts; allocations: state, direction,
utility macros; pictures: \xy, positions, objects, decorations;
kernel objects: directionals, circles, text; options; algorithms: directions,
edges, connections;  Xy-pic loaded))
(/usr/share/texmf-texlive/tex/generic/xypic/xyall.tex
 Xy-pic option: All features v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xycurve.tex
 Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyframe.tex
 Xy-pic option: Frame and Bracket extension v.3.7 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xycmtip.tex
 Xy-pic option: Computer Modern tip extension v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xytips.tex
 Xy-pic option: More Tips extension v.3.3 loaded) loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyline.tex
 Xy-pic option: Line styles extension v.3.6 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyrotate.tex
 Xy-pic option: Rotate and Scale extension v.3.3 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xycolor.tex
 Xy-pic option: Colour extension v.3.3 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xymatrix.tex
 Xy-pic option: Matrix feature v.3.4 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyarrow.tex
 Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xygraph.tex
 Xy-pic option: Graph feature v.3.7 loaded) loaded)
(/usr/share/texmf-texlive/tex/latex/tools/verbatim.sty)
(/usr/share/texmf/tex/latex/graphviz/graphviz.sty
(/usr/share/texmf-texlive/tex/latex/psfrag/psfrag.sty))
(/usr/share/texmf/tex/latex/sagetex.sty
Writing sage input file 4438143605901807536-16.0px.sage
) (/usr/share/texmf-texlive/tex/latex/gnuplottex/gnuplottex.sty
(/usr/share/texmf-texlive/tex/latex/base/latexsym.sty)
(/usr/share/texmf-texlive/tex/latex/moreverb/moreverb.sty)
(/usr/share/texmf-texlive/tex/latex/base/ifthen.sty))
(./4438143605901807536-16.0px.aux)
(/usr/share/texmf-texlive/tex/latex/ucs/ucsencs.def)
 You can't use `macro parameter character #' in vertical mode.
l.122 #
       include "aldor"
[1]
 You can't use `macro parameter character #' in vertical mode.
l.138 #
       include "axiom"


Overfull \hbox (44.68077pt too wide) in paragraph at lines 176--182
[]\T1/cmr/m/n/12 main1():Record(D1hasM12:Boolean,D2hasM12:Boolean) == [D1 has M
12, D2 has M12]; main2():Record(M12hasC1:Boolean,DM12hasC2:Boolean)
[2] (/usr/share/texmf-texlive/tex/latex/base/t1cmtt.fd)


LaTeX Warning: Characters dropped after `\end{axiom}' on input line 199.


LaTeX Warning: Characters dropped after `\end{axiom}' on input line 203.


LaTeX Warning: Characters dropped after `\end{axiom}' on input line 213.


(/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) [3]
(./4438143605901807536-16.0px.aux) )
(see the transcript file for additional information)
Output written on 4438143605901807536-16.0px.dvi (3 pages, 3176 bytes).
Transcript written on 4438143605901807536-16.0px.log.