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last edited 15 years ago by Bill Page |
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Editor: Bill Page
Time: 2008/07/27 03:05:59 GMT-7 |
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Note: 0 and 1 obsolete |
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From BillPage Sun Jul 27 03:05:59 -0700 2008
From: Bill Page
Date: Sun, 27 Jul 2008 03:05:59 -0700
Subject: 0 and 1 obsolete
Message-ID: <20080727030559-0700@axiom-wiki.newsynthesis.org>
If SPAD and the Axiom interpreter created values from the
domain 'Literal' then it would be unnecessary to treat
constants like '0' and '1' in a special manner, i.e. as
unary functions. The coercions from 'Literal' would do
that job.
Literals and Symbols in Axiom
I think Axiom needs a Literal
domain that works in a
manner similar to the Aldor language. SPAD and the Axiom
interpreter should not automatically treat a constant like
2
is a PositiveInteger
.
\begin{axiom}
2
\end{axiom}
There are many situations when I might want it to mean
something else, e.g. the mathematical category 2 or the
some Boolean-like lattice domain, but I do not want to
or cannot provide an artificial means of coercing
PositiveInteger
to things of the kind I want 2 to
represent. Instead we should see:
2 Type: Literal
Then if I use 2
in a context that requires, for example
a PositiveInteger
the interpreter should use it's normal
function selection mechanism to choose coercions for 2
and 3
and and a suitable operation for +
. So the end
result for
\begin{axiom}
2+3
\end{axiom}
would be the same.
If SPAD and the Axiom interpreter where changed to deal with literals in this way, then some Axiom domains would need to be extended to provide the needed coercions. Because Aldor already does this, the code required would be similar to that used in the Aldor-Axiom interface.
Here is the code from the Aldor interface for Axiom that deals
with coercions from the domain Literal
that is created by
the Aldor compiler. (Some code is commented out to enable it
to compile from within Axiom.) The point is that it must be
possible to convert literals like 2
appearing in the Aldor
source to something that Axiom can also understand, like
Integer
or however else it might be used.
\begin{aldor}
#include "axiom"
-----------------------------------------------------------------------------
----
---- axlit.as: Function definitions needed by the Axiom library.
----
-----------------------------------------------------------------------------
---- Copyright (c) 1990-2007 Aldor Software Organization Ltd (Aldor.org).
-----------------------------------------------------------------------------
--import from AxiomLib?; --inline from AxiomLib?;
Bit == Boolean; Str == String; SI == SingleInteger?; I == Integer; NNI == NonNegativeInteger?; PI == PositiveInteger?; BVal? == BuiltinValue?; BArr? == BuiltinArray?; SEG == Segment; UNISEG == UniversalSegment?; }
import { AXL_-error: String -> Exit; } from Foreign Lisp;
--error (s: String) : Exit == AXL_-error s; integer (l: Literal) : Literal == l;
--- Builtin value type. Used to store data values which fit in a single word. --BuiltinValue? : with == add;
--- Builtin array type. 0-based indexing. --BuiltinArray? : with { -- new: SI -> %; -- #: % -> SI; -- apply: (%, SI) -> BVal?; -- set!: (%, SI, BVal?) -> (); --} --== add { -- import { -- AXL_-arrayNew: SI -> %; -- AXL_-arraySize: % -> SI; -- AXL_-arrayRef: (%, SI) -> BVal?; -- AXL_-arraySet: (%, SI, BVal?) -> (); -- } from Foreign Lisp; -- -- new (n: SI) : % == AXL_-arrayNew n; -- # (x: %) : SI == AXL_-arraySize x; -- -- apply (x: %, n: SI) : BVal? == -- AXL_-arrayRef(x, n); -- -- set! (x: %, n: SI, v: BVal?) : () == -- - AXL_-arraySet(x, n, v); --}
extend String : with { string: Literal -> %; } == add { import { AXL_-LiteralToString?: Literal -> %; } from Foreign Lisp;
string (l: Literal) : % == AXL_-LiteralToString? l; }
extend Symbol : with { string: Literal -> %; } == add { string (l: Literal) : % == string(l)$String::%; }
extend SingleInteger? : with { integer: Literal -> %; coerce: I -> %;
zero: () -> %; one: () -> %; inc: % -> %; dec: % -> %; leq: (%, %) -> Bit; spit: % -> (); } == add { Rep ==> Integer;
import { AXL_-LiteralToSingleInteger?: Literal -> %; AXL_-zerofnSingleInteger: () -> %; AXL_-onefnSingleInteger: () -> %; AXL_-incSingleInteger: % -> %; AXL_-decSingleInteger: % -> %; AXL_-leSingleInteger: (%, %) -> Bit; AXL_-spitSInt: % -> (); } from Foreign Lisp;
integer (l: Literal) : % == AXL_-LiteralToSingleInteger? l; coerce (n: I) : % == per n;
zero () : % == AXL_-zerofnSingleInteger(); one () : % == AXL_-onefnSingleInteger(); inc (n: %) : % == AXL_-incSingleInteger n; dec (n: %) : % == AXL_-decSingleInteger n; leq (x: %, y: %) : Bit == AXL_-leSingleInteger(x, y); spit (x: %) : () == AXL_-spitSInt x; }
extend Integer : with { integer: Literal -> %; } == add { import { AXL_-LiteralToInteger?: Literal -> %; } from Foreign Lisp;
integer (l: Literal) : % == AXL_-LiteralToInteger? l; }
extend NonNegativeInteger? : with { integer: Literal -> %; coerce: Integer -> %; } == add { import { AXL_-IntegerIsNonNegative?: Integer -> Bit; } from Foreign Lisp; Rep ==> Integer; import from Rep, String;
integer (l: Literal) : % == integer(l)$Integer::%;
coerce (i: Integer) : % == { if AXL_-IntegerIsNonNegative? i then per i else error "Need a non-negative integer" } }
extend PositiveInteger? : with { integer: Literal -> %; coerce: Integer -> %; } == add { import { AXL_-IntegerIsPositive?: Integer -> Bit; } from Foreign Lisp; Rep ==> Integer; import from Rep, String; integer (l: Literal) : % == integer(l)$Integer::%; coerce (i: Integer) : % == { if AXL_-IntegerIsPositive? i then per i else error "Need a positive integer" }
}
extend DoubleFloat?: with { float: Literal -> %; } == add { import { AXL_-LiteralToDoubleFloat?: Literal -> %; } from Foreign Lisp;
float (l: Literal) : % == AXL_-LiteralToDoubleFloat? l; }
extend Float: with { float: Literal -> %; } == add { import { AXL_-StringToFloat?: String -> %; } from Foreign Lisp;
import from String; float (l: Literal) : % == AXL_-StringToFloat? string l; }
extend List (S: Type) : with { bracket: Tuple S -> %;
nil: %; first: % -> S; rest: % -> %; cons: (S, %) -> %;
empty: () -> %; empty?: % -> Bit; test: % -> Bit;
setfirst!: (%, S) -> S; setrest!: (%, %) -> %; } == add { import { AXL_-nilfn: () -> %; AXL_-car: % -> S; AXL_-cdr: % -> %; AXL_-cons: (S, %) -> %; AXL_-rplaca: (%, S) -> S; AXL_-rplacd: (%, %) -> %; AXL_-null?: % -> Bit; } from Foreign Lisp;
[t: Tuple S]?: % == { import { one: () -> %; dec: % -> %; leq: (%, %) -> Bit; } from SI;
--!! Remove the local when we can use the export. local nil: % := empty();
l := nil; i := length t; while leq(one(), i) repeat { l := cons(element(t, i), l); i := dec i; } l; }
-- Redefine a selection of List operations for efficiency.
nil : % == AXL_-nilfn(); first (x: %): S == AXL_-car x; rest (x: %): % == AXL_-cdr x; cons (x: S, y: %): % == AXL_-cons(x, y); setfirst!(x: %, y: S): S == AXL_-rplaca(x, y); setrest! (x: %, y: %): % == AXL_-rplacd(x, y);
empty (): % == AXL_-nilfn(); empty? (x: %): Bit == AXL_-null? x; test (x: %): Bit == not empty? x; }
\end{aldor}
Literal
then it would be unnecessary to treat
constants like 0
and 1
in a special manner, i.e. as
unary functions. The coercions from Literal
would do
that job.
Error: export FRICAS=/usr/local/lib/axiom/target/x86_64-unknown-linux; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/axiom/target/x86_64-unknown-linux/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7176996356010151088-25px.axm /bin/sh: /usr/local/lib/axiom/target/x86_64-unknown-linux/bin/FRICASsys: not found
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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 3893344738967034407-16.0px.sage (./3893344738967034407-16.0px.sout)) (/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)) (./3893344738967034407-16.0px.aux) (/usr/share/texmf-texlive/tex/latex/ucs/ucsencs.def) (/usr/share/texmf-texlive/tex/latex/base/t1cmtt.fd)
LaTeX Warning: Characters dropped after `\end{axiom}' on input line 123.
LaTeX Warning: Characters dropped after `\end{axiom}' on input line 126.
You can't use `macro parameter character #' in vertical mode. l.128 # include "axiom" Missing $ inserted. <inserted text> $ l.160 AXL_ -error: String -> Exit; (/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) Extra }, or forgotten $. l.161 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.162
Missing $ inserted. <inserted text> $ l.163 --error (s: String) : Exit == AXL_ -error s; Missing $ inserted. <inserted text> $ l.165
You can't use `macro parameter character #' in horizontal mode. l.172 -- # : % -> SI; Missing $ inserted. <inserted text> $ l.178 -- AXL_ -arrayNew: SI -> %; Extra }, or forgotten $. l.182 -- } from Foreign Lisp; You can't use `macro parameter character #' in math mode. l.185 -- # (x: %) : SI == AXL_-arraySize x; Extra }, or forgotten $. l.192 --}
Missing $ inserted. <inserted text> $ l.193
Missing $ inserted. <inserted text> $ l.199 AXL_ -LiteralToString: Literal -> %; Extra }, or forgotten $. l.200 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.201
Missing $ inserted. <inserted text> $ l.227 AXL_ -LiteralToSingleInteger: Literal -> %; Extra }, or forgotten $. l.234 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.235
Overfull \hbox (71.42375pt too wide) in paragraph at lines 226--235 []\T1/cmr/m/n/12 import AXL$[]\OML/cmm/m/it/12 LiteralToSingleInteger \OT1/cmr /m/n/12 : \OML/cmm/m/it/12 Literal\OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 > AXL[] zerofnSingleInteger \OT1/cmr/m/n/12 : ()\OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 > AXL[]onefnSingleInteger \OT1/cmr/m/n/12 : ()\OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it /12 > AXL[]incSingleInteger \OT1/cmr/m/n/12 : Missing $ inserted. <inserted text> $ l.252 AXL_ -LiteralToInteger: Literal -> %; Extra }, or forgotten $. l.253 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.254
Missing $ inserted. <inserted text> $ l.264 AXL_ -IntegerIsNonNegative: Integer -> Bit; Extra }, or forgotten $. l.265 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.268
Missing $ inserted. <inserted text> $ l.272 if AXL_ -IntegerIsNonNegative i then Extra }, or forgotten $. l.276 }
Extra }, or forgotten $. l.277 }
Missing $ inserted. <inserted text> $ l.278
Missing $ inserted. <inserted text> $ l.285 AXL_ -IntegerIsPositive: Integer -> Bit; Extra }, or forgotten $. l.286 } from Foreign Lisp; Extra }, or forgotten $. l.295 }
Missing $ inserted. <inserted text> $ l.296
Overfull \hbox (205.97543pt too wide) in paragraph at lines 279--296 \OML/cmm/m/it/12 Bit\OT1/cmr/m/n/12 ; \OML/cmm/m/it/12 fromForeignLisp\OT1/cmr/ m/n/12 ; \OML/cmm/m/it/12 Rep \OT1/cmr/m/n/12 ==\OML/cmm/m/it/12 > Integer\OT1/ cmr/m/n/12 ; \OML/cmm/m/it/12 importfromRep; String\OT1/cmr/m/n/12 ; \OML/cmm/m /it/12 integer\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 l \OT1/cmr/m/n/12 : \OML/cmm/m/ it/12 Literal\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 coerce\OT1/cmr/m/n/12 (\OML/c mm/m/it/12 i \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 Integer\OT1/cmr/m/n/12 ) : \OML /cmm/m/it/12 ifAXL[]IntegerIsPositiveithenperielseerror\OT1/cmr/m/n/12 "\OML/cm m/m/it/12 Needapositiveinteger\OT1/cmr/m/n/12 "$ Missing $ inserted. <inserted text> $ l.304 AXL_ -LiteralToDoubleFloat: Literal -> %; Extra }, or forgotten $. l.305 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.306
Missing $ inserted. <inserted text> $ l.315 AXL_ -StringToFloat: String -> %; Extra }, or forgotten $. l.316 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.317
[1] Missing $ inserted. <inserted text> $ l.353 AXL_ -nilfn: () -> %; Extra }, or forgotten $. l.360 } from Foreign Lisp; Missing $ inserted. <inserted text> $ l.361
Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage Missing } inserted. <inserted text> } l.395 \end{aldor} \newpage [2] [3] (./3893344738967034407-16.0px.aux) ) (see the transcript file for additional information) Output written on 3893344738967034407-16.0px.dvi (3 pages, 7120 bytes). Transcript written on 3893344738967034407-16.0px.log.