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This domain provides a function-like type that can be queried
for domain and co-domain.
aldor #include "axiom.as"
T ==> SetCategory;
Signature(source:T, target:T): with {
domain:%->T;
codomain:%->T;
coerce:(source->target) -> %;
coerce:%->(source->target);
coerce:%->OutputForm;
} == (source->target) add {
Rep == (source->target);
domain(p:%):T == source;
codomain(p:%):T == target;
coerce(r:(source->target)):% == per(r);
coerce(p:%):(source->target) == p pretend (source->target);
coerce(p:%):OutputForm == p pretend OutputForm;
};
aldor Compiling FriCAS source code from file
/var/zope2/var/LatexWiki/sig.as using AXIOM-XL compiler and
options
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/algebra
Use the system command )set compiler args to change these
options.
"/var/zope2/var/LatexWiki/sig.as", line 13:
domain(p:%):T == source;
.........^
[L13 C10] #1 (Warning) Function returns a domain that might not be constant (which may cause problems if it is used in a dependent type).
"/var/zope2/var/LatexWiki/sig.as", line 14:
codomain(p:%):T == target;
...........^
[L14 C12] #2 (Warning) Function returns a domain that might not be constant (which may cause problems if it is used in a dependent type).
Compiling Lisp source code from file ./sig.lsp
Issuing )library command for sig
Reading /var/zope2/var/LatexWiki/sig.asy
Signature is now explicitly exposed in frame initial
Signature will be automatically loaded when needed from
/var/zope2/var/LatexWiki/sigaldor #include "axiom.as"
T ==> SetCategory;
Signature2(source1:T, source2:T, target:T): with {
domain:%->T;
codomain:%->T;
coerce:((source1,source2)->target) -> %;
coerce:%->((source1,source2)->target);
coerce:%->OutputForm;
} == ((source1,source2)->target) add {
Rep == ((source1,source2)->target);
domain(p:%):T == Product(source1,source2);
codomain(p:%):T == target;
coerce(r:(source1,source2)->target):% == per(r);
coerce(p:%):((source1,source2)->target) == p pretend ((source1,source2)->target);
coerce(p:%):OutputForm == p pretend OutputForm;
}
aldor Compiling FriCAS source code from file
/var/zope2/var/LatexWiki/sig2.as using AXIOM-XL compiler and
options
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/algebra
Use the system command )set compiler args to change these
options.
"/var/zope2/var/LatexWiki/sig2.as", line 13:
domain(p:%):T == Product(source1,source2);
.........^
[L13 C10] #1 (Warning) Function returns a domain that might not be constant (which may cause problems if it is used in a dependent type).
"/var/zope2/var/LatexWiki/sig2.as", line 14:
codomain(p:%):T == target;
...........^
[L14 C12] #2 (Warning) Function returns a domain that might not be constant (which may cause problems if it is used in a dependent type).
Compiling Lisp source code from file ./sig2.lsp
Issuing )library command for sig2
Reading /var/zope2/var/LatexWiki/sig2.asy
Signature2 is now explicitly exposed in frame initial
Signature2 will be automatically loaded when needed from
/var/zope2/var/LatexWiki/sig2axiom f:Signature(Float, Integer)
axiom f:=(x:Float):Integer +-> floor(x)
\begin{equation}
\label{eq1}# < \hbox{\axiomType{FUNCTION}\ } | 1 ; anonymousFunction ; 0 ; initial ; internal | > ()\end{equation*}
Type: Signature(Float,Integer) axiom domain f
\begin{equation}
\label{eq2}\hbox{\axiomType{Float}\ }\end{equation}
axiom codomain f
\begin{equation}
\label{eq3}\hbox{\axiomType{Integer}\ }\end{equation}
axiom (f::(Float->Integer))
\begin{equation}
\label{eq4}\mbox{theMap (...)}\end{equation}
axiom (f::(Float->Integer)) 2.2
\begin{equation}
\label{eq5}2\end{equation}
axiom f2:Signature2(Float,Float, Float)
axiom f2:=(x:Float,y:Float):Float +-> x+y
\begin{equation}
\label{eq6}# < \hbox{\axiomType{FUNCTION}\ } | 2 ; anonymousFunction ; 1 ; initial ; internal | > ()\end{equation*}
Type: Signature2(Float,Float,Float) axiom domain f2
\begin{equation}
\label{eq7}\hbox{\axiomType{Product}\ } (\hbox{\axiomType{Float}\ } , \hbox{\axiomType{Float}\ })\end{equation}
axiom codomain f2
\begin{equation}
\label{eq8}\hbox{\axiomType{Float}\ }\end{equation}
axiom f2::((Float,Float)->Float)
\begin{equation}
\label{eq9}\mbox{theMap (...)}\end{equation}
Type: ((Float,Float) -> Float) axiom (f2::((Float,Float)->Float))(1.2,2.1)
\begin{equation}
\label{eq10}3.3\end{equation}
Try this is Axiom SandBoxMorphism
Some or all expressions may not have rendered properly,
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LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
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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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Xy-pic is free software: see the User's Guide for details.
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You can't use `macro parameter character #' in display math mode.
l.63 \label{eq1}#
< \hbox{\axiomType{FUNCTION}\ } | * 1 ; anonymousFunction ...
[1] [2] [3] [4] [5]
You can't use `macro parameter character #' in display math mode.
l.78 \label{eq6}#
< \hbox{\axiomType{FUNCTION}\ } | * 2 ; anonymousFunction ...
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(see the transcript file for additional information)
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