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SandBoxMorphism

Edit detail for SandBoxMorphism revision 1 of 15

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Editor: Bill Page Time: 2008/06/17 18:40:27 GMT-7
Note:

changed:
-
\begin{spad}
)abbrev domain MORPH Morphism
T ==> SetCategory
Morphism(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{spad}

\begin{axiom}
)show Morphism(Float,Integer)
f:Morphism(Float,Integer)
f:=(x:Float):Integer +->wholePart(x)
f(1.1)
(f::(Float->Integer))(1.1)
domain f
codomain f
(f::(domain(f)->codomain(f)))(1.1)

\end{axiom}

spad)abbrev domain MORPH Morphism
T ==> SetCategory
Morphism(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

spad

   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/7023236588135790421-25px001.spad using 
      Spad compiler.
   MORPH abbreviates domain Morphism 
   processing macro definition T$ ==> SetCategory 
------------------------------------------------------------------------
   initializing NRLIB MORPH for Morphism 
   compiling into NRLIB MORPH 
   Adding $ modemaps
   Adding source modemaps
   Adding target modemaps
   Parameters of  rep  are of wrong type:
    G1393 must have type source not $
   compiling local rep : source -> source -> target
      MORPH;rep is replaced by G1393 
Time: 0.01 SEC.
   compiling local per : source -> target -> %
      MORPH;per is replaced by G1393 
Time: 0 SEC.
   compiling exported domain : % -> SetCategory
Time: 0 SEC.
   compiling exported codomain : % -> SetCategory
Time: 0 SEC.
   compiling exported coerce : source -> target -> %
Time: 0 SEC.
   compiling exported coerce : % -> source -> target
      MORPH;coerce;$M;6 is replaced by p 
Time: 0 SEC.
   Adding OutputForm modemaps
   compiling exported coerce : % -> OutputForm
      MORPH;coerce;$Of;7 is replaced by p 
Time: 0.01 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |Morphism| REDEFINED
;;;     ***       |Morphism| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor Morphism
      Time: 0.02 seconds
--------------non extending category----------------------
   Morphism(#1,#2) of category CATEGORY(domain,domain: % -> 
      SetCategory,codomain: % -> SetCategory,coerce: (#1 -> #2) -> %,
      coerce: % -> (#1 -> #2),coerce: % -> OutputForm)
    has no NIL
   finalizing NRLIB MORPH 
   Processing Morphism for Browser database:
--->-->Morphism((domain (T$ %))): Not documented!!!!
--->-->Morphism((codomain (T$ %))): Not documented!!!!
--->-->Morphism((coerce (% (Mapping target source)))): Not documented!!!!
--->-->Morphism((coerce ((Mapping target source) %))): Not documented!!!!
--->-->Morphism((coerce ((OutputForm) %))): Not documented!!!!
--->-->Morphism(constructor): Not documented!!!!
--->-->Morphism(): Missing Description
------------------------------------------------------------------------
   Morphism is now explicitly exposed in frame initial 
   Morphism will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MORPH.NRLIB/code.o

axiom)show Morphism(Float,Integer)
 Morphism(Float,Integer) is a domain constructor.
 Abbreviation for Morphism is MORPH
 This constructor is exposed in this frame.
 Issue )edit /var/zope2/var/LatexWiki/7023236588135790421-25px001.spad to see algebra source
code for MORPH
------------------------------- Operations --------------------------------
 codomain : % -> SetCategory           coerce : % -> (Float -> Integer)
 coerce : % -> OutputForm              coerce : (Float -> Integer) -> %
 domain : % -> SetCategory
f:Morphism(Float,Integer)

Type: Void

axiomf:=(x:Float):Integer +->wholePart(x)
; (DEFUN |*1;anonymousFunction;0;initial;internal| ...) is being compiled.
;; The variable |*1;anonymousFunction;0;initial;internal;MV| is undefined.
;; The compiler will assume this variable is a global.

(1)

Type: Morphism(Float,Integer)

axiomf(1.1)
   There are no library operations named f
      Use HyperDoc Browse or issue
                                 )what op f
      to learn if there is any operation containing " f " in its name.
   Cannot find a definition or applicable library operation named f
      with argument type(s)
                                    Float
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
(f::(Float->Integer))(1.1)

(2)

Type: PositiveInteger?

axiom
domain f

(3)

Type: SetCategory?

axiom
codomain f

(4)

Type: SetCategory?

axiom
(f::(domain(f)->codomain(f)))(1.1)

(5)

Type: PositiveInteger?