May 18, 2026
Math rock, but make it code
Profunctor Equipment in Haskell
A brainy Haskell demo drops, and the comments instantly beg for plain English
TLDR: A Haskell post turned a very abstract math-programming idea into toy code checked by the compiler, aiming to make it easier to grasp. The community’s main reaction was blunt: cool in theory, but readers want plain-English explanations and real-world uses before they’ll buy in.
A tiny but very on-brand nerd storm erupted after a post tried to make an ultra-abstract Haskell concept feel a little more real with toy code the compiler can check. The author’s pitch was basically: yes, this topic is wildly academic, but here’s a hands-on version in Haskell so humans can poke at it without needing a full futuristic math-powered language. Translation for normal people: someone built a miniature demo for a very advanced programming idea and said, in so many words, they trust the compiler more than AI. That alone is enough to make the functional programming crowd nod solemnly.
But the actual drama was in the reaction. One commenter delivered the cleanest drive-by in the thread: they were “hoping for applications.” Ouch. That’s the eternal internet struggle right there—show me why this matters in real life, not just that it’s elegant. Another reader voiced the much bigger mood: these posts always seem like they’re hiding something cool, but they feel locked behind a wall of math. That kicked open the classic debate between the theory lovers and the practical crowd: is the beauty the point, or do writers need to meet readers halfway?
The funniest subtext? The article tried to be more approachable, and the comments basically replied, “Respectfully, we are still lost.” It’s less a flame war than a familiar tech melodrama: one side bringing category-theory wizardry, the other side waving a giant sign that says “Can I get this in normal-person?”
Key Points
- •The article presents a compiler-checkable toy implementation of profunctor equipment in Haskell, limited to a single category with endofunctors and endoprofunctors.
- •It models the Haskell category of types and functions as the only 0-cell, uses `Functor` for vertical 1-cells, and `Profunctor` for horizontal 1-cells.
- •A 2-cell is represented as a natural transformation via the type `Cell f g h j = forall a c . h a c -> j (f a) (g c)`.
- •The article defines both horizontal and vertical composition of cells, with vertical composition relying on a `Procompose` type implemented using an existential type to represent a coend.
- •Companions and conjoints are implemented through the library types `Costar` and `Star`, with explicit unit and counit cell definitions provided for each.