Edit detail for SandBoxThisFunctor revision 2 of 2

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.

(1) -> <spad>

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

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

     coerce(x:%):OutputForm == brace [i::OutputForm for i in rep x]
     x = y == rep(x) = rep(y)
     construct(x) == per removeDuplicates(x)$Rep
     parts(x:%):List T == rep x
     join x == construct concat rep2 x</spad>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7834450198179479618-25px001.spad
      using old system compiler.
   MYSET abbreviates domain MySet 
------------------------------------------------------------------------
   initializing NRLIB MYSET for MySet 
   compiling into NRLIB MYSET 
************* USER ERROR **********
available signatures for Rep: 
    NONE
NEED Rep: () -> ?
****** comp fails at level 1 with expression: ******
((DEF (|Rep|) (NIL) (|List| T$)))
****** level 1  ******
x:= (DEF (Rep) (NIL) (List T$))
m:= $EmptyMode
f:=
((((~= #) (= #) (|coerce| #) (|latex| #) ...)))

   >> Apparent user error:
   unspecified error

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?