Instantiate the type of the “rest” parameter of a variadic polymorphic procedure when arity is not known in advance in typed Racket

Question

Let's say I want to transpose a 2 x n "matrix" (list of lists) mat. The idiomatic way of doing so in racket is

(apply map list mat)

To do the same thing in typed/racket, I have to help the type checker a little. The type of map in that case is

(All (c a b ...) 
  (-> (-> a b ... b c) (Listof a) (Listof b) ... b (Listof c)))

Since I'm dealing with a 2 x n matrix, I must instantiate both a and b as Number:

(apply (inst map (Listof Number) Number Number) 
       (inst list Number)
       mat)

If mat was a 3 x n matrix,

(apply (inst map (Listof Number) Number Number Number)
       (inst list Number)
       mat)

Would do the trick. Now, let's say that I'm dealing with an m x n matrix where m is some unknown positive integer. Is there a general way of instantiating map that would work for any value of m?

I think this is exactly what you want stackoverflow.com/a/44864244/718349 — Sorawee Porncharoenwase

pfournier pfournier · Accepted Answer · 2019-01-10T19:40:55

Thank you Sorawee Porncharoenwase, that pretty much solved my problem. Here's what I've done:

Define a polymorphic zip function as in the link provided:

(: zip (∀ (a) (-> (Listof a) (Listof a) * (Listof (Listof a)))))
(define (zip lst . lsts)
  (apply map (inst list a) lst lsts))

Apply it to mat:

(apply zip (car mat) (cdr mat))

Instantiate the type of the “rest” parameter of a variadic polymorphic procedure when arity is not known in advance in typed Racket

1 Answers