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SandBox Manipulating Domains ←	↑	→ SandBox Matrix

SandBox Mapping

Edit detail for SandBox Mapping revision 1 of 3

	1 2 3
Editor: Time: 2007/11/18 18:07:56 GMT-8
Note:

changed:
-
This domain provides a function-like type that can be queried
for domain and co-domain.
\begin{aldor}[sig]
#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;
};
\end{aldor}

\begin{aldor}[sig2]
#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;
}

\end{aldor}

\begin{axiom}
f:Signature(Float, Integer)
f:=(x:Float):Integer +-> floor(x)
domain f
codomain f
(f::(Float->Integer))
(f::(Float->Integer)) 2.2
\end{axiom}

\begin{axiom}
f2:Signature2(Float,Float, Float)
f2:=(x:Float,y:Float):Float +-> x+y
domain f2
codomain f2
f2::((Float,Float)->Float)
(f2::((Float,Float)->Float))(1.2,2.1)
\end{axiom}

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-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
"/var/zope2/var/LatexWiki/sig.as", line 13: 
  domain(p:%):T == source;
.........^
[L13 C10] #2 (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] #3 (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/sig

aldor#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-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
"/var/zope2/var/LatexWiki/sig2.as", line 13: 
  domain(p:%):T == Product(source1,source2);
.........^
[L13 C10] #2 (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] #3 (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/sig2

axiom
f:Signature(Float, Integer)

Type: Void

axiom
f:=(x:Float):Integer +-> floor(x)

(1)

Type: Signature(Float,Integer)

axiom
domain f

(2)

Type: SetCategory?

axiom
codomain f

(3)

Type: SetCategory?

axiom
(f::(Float->Integer))

(4)

Type: (Float -> Integer)

axiom
(f::(Float->Integer)) 2.2

(5)

Type: PositiveInteger?

axiom
f2:Signature2(Float,Float, Float)

Type: Void

axiom
f2:=(x:Float,y:Float):Float +-> x+y

(6)

Type: Signature2(Float,Float,Float)

axiom
domain f2

(7)

Type: SetCategory?

axiom
codomain f2

(8)

Type: SetCategory?

axiom
f2::((Float,Float)->Float)

(9)

Type: ((Float,Float) -> Float)

axiom
(f2::((Float,Float)->Float))(1.2,2.1)

(10)

Type: Float