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SandBoxMorphism
  
last edited 14 years ago by Bill Page

Edit detail for SandBoxMorphism revision 13 of 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Editor: Bill Page
Time: 2008/06/18 19:31:51 GMT-7
Note: new Rep for Morphism 
changed:
-If we define 'elt' (commented out above), then 'f(1.1)' gives the following::
The naive represetation of 'Rep == (source->target)' gives the
following error.

changed:
-  Fast links are on: do (si::use-fast-links nil) for debugging
-  Error signalled by RETURN.
-  Broken at APPLY.  Type :H for Help.
-  BOOT>>
-  Error: The variable QUIT is unbound.
-  Fast links are on: do (si::use-fast-links nil) for debugging
  ...

changed:
-But the same coercion works in the interpreter.
But using 'SExpression' seems to work.

added:
g:Morphism(Integer,String):=(i:Integer):String +-> i::String
g(1985)


\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
  elt:(%,source)->target
 == (source->target) add
  -- Rep == (source->target)
  Rep == SExpression
  domain(p:%):T == source
  codomain(p:%):T == target
  coerce(r:(source->target)):% == per(r pretend SExpression)
  coerce(p:%):(source->target) == (rep(p) pretend (source->target))
  coerce(p:%):OutputForm == p pretend OutputForm
  elt(f,x) == (rep(f) pretend (source->target))(x)
\end{spad}


The naive represetation of Rep == (source->target) gives the
following error.
  Error: Caught fatal error [memory may be damaged]
  ...
  Error signalled by EVALHOOK.
  Backtrace: system:universal-error-handler > evalhook > lambda > lambda-closure > block > apply > APPLY




But using SExpression seems to work.
\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)
g:Morphism(Integer,String):=(i:Integer):String +-> i::String
g(1985)
\end{axiom}


Next let's study how this sort of thing is accomplished in a similar domain.
\begin{spad}
)abbrev domain HOM Hom
++ Based on Automorphism by: Manuel Bronstein
++ Description:
++       Hom(R,S) is the domain of homomorphisms - Mapping(S,R).
Hom(R:SetCategory,S:SetCategory): Join(SetCategory, Eltable(R, S)) with
      morphism: (R -> S) -> %
        ++ morphism(f) returns the non-invertible morphism given by f.
   == add
      -- Why doesn't the obvious representation just (R->S) work?
      Rep == SExpression
      morphism(f) == per(f pretend SExpression)
      elt(f, r)   == (rep(f) pretend (R->S))(r)
      --Rep == List(R -> S)
      --morphism(f) == per([f #1])
      --elt(f, r)   == (rep(f)(1))(r)


      --Rep := ((R, Integer) -> S)
      --morphism(f)                     == (#2; f(#1))
      --elt(f, r) == (g := f pretend ((R, Integer) -> S); g(r, 1))


      f = g                           == EQ(f, g)$Lisp
      coerce(f:%):OutputForm          == message("theMap ...")




\end{spad}


\begin{axiom}
p:=morphism((x:Integer):Float +-> x+1.0)$Hom(Integer,Float)
p(2)
p(-1)
\end{axiom}




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Overfull \hbox (19.45984pt too wide) in paragraph at lines 63--82
[]\OT1/cmr/m/n/12 )abbrev do-main MORPH Mor-phism T ==> Set-Cat-e-gory Mor-phis
m(source:T,


Overfull \hbox (21.96378pt too wide) in paragraph at lines 63--82
\OT1/cmr/m/n/12 tar-get:T): with domain:codomain:coerce:(source->target) -> co-
erce:coerce:elt:(==


Overfull \hbox (160.7693pt too wide) in paragraph at lines 63--82
\OT1/cmr/m/n/12 (source->target) add -- Rep == (source->target) Rep == SEx-pres
-sion domain(p:codomain(p:coerce(r:(source-
[1] [2]
Overfull \hbox (27.85265pt too wide) in paragraph at lines 97--109
\OT1/cmr/m/n/12 Map-ping(S,R). Hom(R:SetCategory,S:SetCategory): Join(SetCatego
ry, Eltable(R,
 You can't use `macro parameter character #' in horizontal mode.
l.111       --morphism(f) == per([f #
                                     1])


Overfull \hbox (13.3474pt too wide) in paragraph at lines 110--113
[]\OT1/cmr/m/n/12 --Rep == List(R -> S) --morphism(f) == per([f 1]) --elt(f, r)
 == (rep(f)(1))(r) 
 You can't use `macro parameter character #' in horizontal mode.
l.115 ...  --morphism(f)                     == (#
                                                  2; f(#1))
 You can't use `macro parameter character #' in horizontal mode.
l.115 ...rphism(f)                     == (#2; f(#
                                                  1))
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<inserted text> 
                $
l.120 


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