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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