Re: [stack] possibilities for macros in a typed language

Apologies if this is formatted strangely... replying via broken webmail.

>> > In Cat "dup apply" has the type "(A (A (B -> C) -> D) -> D)"
>>
>> I'm not convinced this is useful. As a trivial example, it assigns
>> '[swap] dup apply' the type 'A b -> A (C -> D) b'. Your system then
>> rejects this type because (C -> D) is unknowable.
>
> You are incorrect.
> Cat infers the type as: ('a -> ('b 'c -> 'c 'b) 'a)
> Why would you claim otherwise?

My derivation is at the end of the email. I've yet to actually use the Cat
interpreter so perhaps I made an incorrect assumption.

Out of curiosity, what type does Cat give '[swap] dup'? Is it not 'A -> A
(B c d -> B d c) (B c d -> B d c)'? If not, why?

>> I was speaking here primarily from a pedagogical standpoint. With
>> macros, you can no longer state that every space-delineated token is a
>> function.
>
> This is already not the case in Joy or Cat. (e.g. in Cat "define",
> "[", "]", "{", "}").

Yes, yes. I meant that '3' is a function, '[1 2 3]' is a function, et
cetera. Replace "token" with "valid syntactic entity" or some such.

- John

;; (initial composition)
E -> E (F g h        -> F h g)        ;; [swap]
     A (A   (B -> C) -> D    ) -> D   ;; dup apply

;; D -> F h g
E -> E (F g h        -> F h g)
     A (A   (B -> C) -> F h g) -> F h g

;; h -> (B -> C)
E -> E (F g (B -> C) -> F (B -> C) g)
     A (A   (B -> C) -> F (B -> C) g) -> F (B -> C) g

;; A -> F g
E -> E   (F g (B -> C) -> F (B -> C) g)
     F g (F g (B -> C) -> F (B -> C) g) -> F (B -> C) g

;; E -> F g
F g -> F g (F g (B -> C) -> F (B -> C) g)
       F g (F g (B -> C) -> F (B -> C) g) -> F (B -> C) g

F g -> F (B -> C) g