An error (?) in the jigsaw puzzle at page 121

[jfet97]

Not sure about that, maybe I've misunderstood something but...

This is the BiComp Bifunctor presented at page 120

newtype BiComp bf fu gu a b = BiComp (bf (fu a) (gu b))

instance (Bifunctor bf, Functor fu, Functor gu) => Bifunctor (BiComp bf fu gu) where 
  bimap f1 f2 (BiComp x) = BiComp ((bimap (fmap f1) (fmap f2)) x)

So f1 and f2 are "normal" functions that are mapped firstly by the Functors fu and gu respectively, then are mapped together by the Bifunctor bf. As expected, f1 and f2 are presented in this way at page 121:

f1 :: a -> a'
f2 :: b -> b'

Therefore, the expected signature for the bimap function of the BiComp Bifunctor shouldn't be: (a -> a') -> (b -> b') -> bf (fu a) (gu b) -> bf (fu a') (gu b')? Corresponding to the given definition of bimap that is: f1 -> f2 -> BiComp x -> ...

I'm asking because it is presented differently at page 121: (fu a -> fu a') -> (fu b -> fu b') -> bf (fu a) (gu b) -> bf (fu a') (gu b')

[BartoszMilewski]

It's a different bimap. The first one is for BiComp bf fu gu the last one is for bf. These different implementations are not marked by the name fo the bifuncor, because GHC figures that out. Maybe a subscript bimap_{bf} would help?

[jfet97]

Uh, I've completely misunderstood the sentence "The outer bimap breaks through the outer bf layer", most likely because English is not my mother tongue. Anyway shame on me because I should have thought that you weren't talking about the Bicomp's bimap. Now taking a closer look, I see that it's the bf's bimap type signature 😅

Obviously, in my case, a subscript bimap_{bf} would have been very helpful, but honestly, I'm in no position to suggest anything 😅😅😅