In The Screwtape Letters, Lewis describes a “materialist magician,” a person who simultaneously engages in magical rituals which have a spiritual purpose and also insists that the realm of the divine is imaginary, in order to highlight the doublethink inherent in folks’ casual invocation of supposedly-spiritual phenomena or beings. Similarly, the article’s author is engaged in a sort of ritualized usage of mathematical concepts, but they ignore the algebraic and logical origins.

When the author writes that “interfaces are adjectives,” they are insisting on a particular linguistic attitude which ignores the history of Carnap’s function words. For example, Carnap would suggest that the word “and” is a functor, and today we often identify this as the tensor product functor of monoidal categories.

This [Haskell typeclass] is the full definition. There is no additional hidden machinery that Haskell is somehow automatically invoking when you “use a Functor”. … What makes a data structure “functorish”? It is having a sensible implementation of fmap, whatever that may be on the data structure. If it has a sensible implementation, we can give it, that makes it a Functor, not the other way around.

Without the algebra, it’s only half-complete. When using GHC, Functor instances can be automatically derived. This relies on the fact that, when we add the algebraic law fmap id == id to our equations, a Haskell datatype can only have one legal and correct Functor instance. If Hask were a category, then Functors would indeed be endofunctors on Hask. The author says that these important details were “glossed over with malice aforethought,” which is a weird flex.

Let me highlight that there’s nothing about “monad” that is somehow “requiring” the implementation on list to be flatmap.

This relies on the fact that, when we add the algebraic law fmap id == id to our equations, a Haskell datatype can only have one legal and correct Functor instance.

Huh. Do you know of a good way to prove this? It certainly seems intuitively true to me, but I don’t have the category theory machinery. (And is it true even in the presence of undefined?)

Overall I think you’re being a bit harsh, and this is as someone that knows Haskell and just enough category theory to be dangerous. The idea of a functor or a monad is plenty useful even in languages that don’t have the academic pedigree that Haskell does, and while you certainly can’t fully appreciate them without category theory, if you want a working programmer’s understanding I think it’s alright to push that aside.

In The Screwtape Letters, Lewis describes a “materialist magician,” a person who simultaneously engages in magical rituals which have a spiritual purpose and also insists that the realm of the divine is imaginary, in order to highlight the doublethink inherent in folks’ casual invocation of supposedly-spiritual phenomena or beings. Similarly, the article’s author is engaged in a sort of ritualized usage of mathematical concepts, but they ignore the algebraic and logical origins.

When the author writes that “interfaces are adjectives,” they are insisting on a particular linguistic attitude which ignores the history of Carnap’s function words. For example, Carnap would suggest that the word “and” is a functor, and today we often identify this as the tensor product functor of monoidal categories.

Without the algebra, it’s only half-complete. When using GHC, Functor instances can be automatically derived. This relies on the fact that, when we add the algebraic law

`fmap id == id`

to our equations, a Haskell datatype can only have one legal and correct Functor instance. If Hask were a category, then Functors would indeed be endofunctors on Hask. The author says that these important details were “glossed over with malice aforethought,” which is a weird flex.Today I learned that there is an exotic list monads package on Hackage.

Huh. Do you know of a good way to prove this? It certainly seems intuitively true to me, but I don’t have the category theory machinery. (And is it true even in the presence of undefined?)

Overall I think you’re being a bit harsh, and this is as someone that knows Haskell and just enough category theory to be dangerous. The idea of a functor or a monad is plenty useful even in languages that don’t have the academic pedigree that Haskell does, and while you certainly can’t fully appreciate them without category theory, if you want a working programmer’s understanding I think it’s alright to push that aside.