[racket] TR: Making recursive types as subtypes of non-recursive types

You're very close -- you just need to give inference a little more
help.  This definition works:

(: card* (All (a) ((Set* a) -> Hereditary-Set)))
(define (card* A)
  ((inst card (U a (Set* a))) A))

My brain was injured thinking about those types, though. :)

On Wed, Feb 22, 2012 at 7:11 PM, Neil Toronto <neil.toronto at gmail.com> wrote:
> I'd like to use the same functions to operate on both "flat" container types
> and arbitrarily nested container types. More precisely, I want a type for
> `Set*' that allows this program otherwise unchanged:
>
>
> #lang typed/racket
>
> (struct: Empty-Set ())
> (struct: (a) Opaque-Set ([error-thunk : (-> a)]))   ; Phantom type
>
> (define-type (Set a) (U Empty-Set (Opaque-Set a)))  ; Flat sets
> (define-type (Set* a) (Rec T (Set (U a T))))        ; Nested sets
>
> ;; Type of "pure" sets, currently doing double-duty for cardinals:
> (define-type Hereditary-Set (Set* Nothing))
>
> ;; Cardinality operator
> (: card (All (a) ((Set a) -> Hereditary-Set)))
> (define (card A) (error 'card "unimplementable"))
>
> (: card* (All (a) ((Set* a) -> Hereditary-Set)))
> (define (card* A)
>  (card A))  ; checking fails here
>
>
> I think the problem is that a (U a T) isn't a subtype of `a' - it's a
> supertype. But I can't figure out how to make a recursive type that's a
> subtype of its corresponding "flat" type.
>
> Neil ⊥
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-- 
sam th
samth at ccs.neu.edu