Edit detail for SandBoxThisFunctorFriCAS revision 1 of 1

In a domain and in categories referenced in a domain the notation % represents "this domain" (or self in some programming languages). So we commonly write for example:

  with
    f: (%,%) -> %

to indicate a function f which takes a pair of values in this domain and returns a value in this same domain - whatever domain we happen to be talking about in this context.

But what if we are interested in the domain as a functor? Suppose I was writing an "endofunctor" domain constructor like Set and I wanted to treat constructions like Set Set R, i.e. sets of sets as something special. E.g.

)abbrev domain MYSET MySet
--#pile
--#include "axiom"
--MonadCat(T:SetCategory,M:SetCategory->SetCategory):Category == with
--  join: M M T -> M T

MySet(T:SetCategory): SetAggregate(T) with
     finiteAggregate
     join: MySet % -> %
   == add
     Rep := List T
     rep(x:%):Rep == x pretend Rep
     per(x:Rep):% == x pretend %

     Rep2 == List List T
     rep2(x:MySet %):Rep2 == x pretend Rep2
     per2(x:Rep2):MySet % == x pretend MySet %

     coerce(x:%):OutputForm ==
       brace(map(coerce$T, rep x)$ListFunctions2(T,OutputForm))
     ((x:%) = (y:%)):Boolean == (rep(x) = rep(y))$Rep
     construct(x:List T):% == per(removeDuplicates(x)$Rep)
     parts(x:%):List T == rep x
     join(x:MySet %):% ==
       construct(concat(rep2 x)$List(T))$%

     copy(x:%):% == per(copy(rep x)$Rep)
     empty():% == per(empty()$Rep)
     map(f:T->T,x:%):% == per(map(f,rep x)$Rep)
     brace():% == empty()$%
     brace(x:List(T)):% == construct(x)$%
     set():% == empty()$%
     set(x:List(T)):% == construct(x)$%

     -- dummy exports as required by Aldor
     _<(x:%, y:%):Boolean == true
     intersect(x:%, y:%):% == empty()$%
     difference(x:%, y:%):% == empty()$%
     subset?(x:%, y:%):Boolean == true
     union(x:%, y:%):% == empty()$%
     if T has ConvertibleTo(InputForm) then
       convert(x:%):InputForm == convert(rep(x))$Rep

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8570179011506836244-25px001.spad
      using old system compiler.
   MYSET abbreviates domain MySet 
------------------------------------------------------------------------
   initializing NRLIB MYSET for MySet 
   compiling into NRLIB MYSET 
   compiling local rep : $ -> Rep
      MYSET;rep is replaced by x 
Time: 0.01 SEC.

   compiling local per : Rep -> $
      MYSET;per is replaced by x 
Time: 0 SEC.

************* USER ERROR **********
available signatures for Rep2: 
    NONE
NEED Rep2: () -> ?
****** comp fails at level 1 with expression: ******
((DEF (|Rep2|) (NIL) (NIL) (|List| (|List| T$))))
****** level 1  ******
$x:= (DEF (Rep2) (NIL) (NIL) (List (List T$)))
$m:= $EmptyMode
$f:=
((((|per| #)) ((|per| #) (|rep| #)) ((|rep| #) (|#| #) (< #) (<= #) ...)))

   >> Apparent user error:
   unspecified error

)sh MySet

 MySet  is a domain constructor
 Abbreviation for MySet is MYSET 
 This constructor is not exposed in this frame.
------------------------------- Operations --------------------------------

   >> System error:
   The function BOOT::|MySet| is undefined.

MySet(Integer) has MonadCat(Integer,MySet)

   MySet is an unknown constructor and so is unavailable. Did you mean 
      to use -> but type something different instead?

m1:MySet(Integer) := construct([1,2,3])$MySet(Integer)

   MySet is an unknown constructor and so is unavailable. Did you mean 
      to use -> but type something different instead?
m2:MySet(Integer) := construct([4,5,6])$MySet(Integer)

   MySet is an unknown constructor and so is unavailable. Did you mean 
      to use -> but type something different instead?
ml:=[m1,m2]

(1)

mm:MySet MySet Integer := construct([m1,m2])$MySet(MySet(Integer))

   MySet is an unknown constructor and so is unavailable. Did you mean 
      to use -> but type something different instead?
join mm

   There are no exposed library operations named join but there are 2 
      unexposed operations with that name. Use HyperDoc Browse or issue
                              )display op join
      to learn more about the available operations.

   Cannot find a definition or applicable library operation named join 
      with argument type(s) 
                                Variable(mm)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.