I'm trying to write an instance of Applicative for my ZipList and I'm getting some confusing results.
data List a =
Nil
| Cons a (List a)
deriving (Eq, Show)
newtype ZipList' a =
ZipList' (List a)
deriving (Eq, Show)
instance Applicative ZipList' where
pure = ZipList' . flip Cons Nil
(<*>) (ZipList' Nil) _ = ZipList' Nil
(<*>) _ (ZipList' Nil) = ZipList' Nil
(<*>) (ZipList' (Cons f fs)) (ZipList' (Cons x xs)) =
ZipList' $ Cons (f x) (fs <*> xs)
It works as expected for ZipLists of length 1 or 2:
> ZipList' (Cons (*2) (Cons (+9) Nil)) <*> ZipList' (Cons 5 (Cons 9 Nil))
ZipList' (Cons 10 (Cons 18 Nil))
But when I go to 3+, I get some odd results:
> ZipList' (Cons (*2) (Cons (+99) (Cons (+4) Nil))) <*> ZipList' (Cons 5 (Cons 9 (Cons 1 Nil)))
ZipList' (Cons 10 (Cons 108 (Cons 100 (Cons 13 (Cons 5 Nil)))))
The result should be a ZipList of 10, 108, 5 -- but somehow 100 and 13 are crashing the party.
So I tried pulling my function out of the instance so that I could inspect the type that Haskell infers:
(<**>) (ZipList' Nil) _ = ZipList' Nil
(<**>) _ (ZipList' Nil) = ZipList' Nil
(<**>) (ZipList' (Cons f fs)) (ZipList' (Cons x xs)) =
ZipList' $ Cons (f x) (fs <**> xs)
but it won't compile!
17-applicative/list.hs:94:26: error:
• Couldn't match expected type ‘ZipList' (a0 -> b0)’
with actual type ‘List (a -> b)’
• In the first argument of ‘(<**>)’, namely ‘fs’
In the second argument of ‘Cons’, namely ‘(fs <**> xs)’
In the second argument of ‘($)’, namely ‘Cons (f x) (fs <**> xs)’
• Relevant bindings include
xs :: List a (bound at 17-applicative/list.hs:93:49)
x :: a (bound at 17-applicative/list.hs:93:47)
fs :: List (a -> b) (bound at 17-applicative/list.hs:93:26)
f :: a -> b (bound at 17-applicative/list.hs:93:24)
(<**>) :: ZipList' (a -> b) -> ZipList' a -> ZipList' b
(bound at 17-applicative/list.hs:91:1)
The error tells me that I'm trying to pass a List where a ZipList is expected, which I can see. But how then did my Applicative instance even compile?
