Every Distributive is Representable
Functor is actually
Representable”, as the documentation for
Representable tells us straight away, and yet it is far from obvious why that should be the case. At first glance,
Distributive, the dual to
Traversable, appears to have little if anything to do with
Representable, the class for functors isomorphic to functions. The goal of this post is making this connection explicit. In the process, we will tease out a fair amount of information about the two classes, and also contemplate what makes it tricky to fully bridge the gap to
Read more - February 7, 2022
Divisible and the Monoidal Quartet
A recent blog post by Gabriella Gonzalez, Co-Applicative programming style, has sparked discussion on ergonomic ways to make use of the
Divisible type class. The conversation pointed to an interesting rabbit hole, and jumping into it resulted in these notes, in which I attempt to get a clearer view of picture of the constellation of monoidal functor classes that
Divisible belongs to. The gist of it is that “
Divisible is a contravariant
Decidable is a contravariant
Alternative” is not a full picture of the relationships between the classes, as there are a few extra connections that aren’t obvious to the naked eye.
Read more - November 12, 2021
Idempotent Applicatives, Parametricity, and a Puzzle
Some applicative functors are idempotent, in the sense that repeating an effect is the same as having it just once. An example and a counterexample are
IO, respectively (contrast
Just 3 *> Just 3 with
print 3 *> print 3). More precisely, idempotency means that
f <$> u <*> u = (\x -> f x x) <$> u. Given the informal description I began with, though, one might wonder whether the simpler property
u *> u = u, which seems to capture the intuition about repeated effects, is equivalent to the usual idempotency property. In this post, I will tell how I went about exploring this conjecture, as well as a few things I learnt about parametricity along the way.
Read more - April 1, 2019
Traversable: A Remix
Traversable is a fun type class. It lies at a crossroad, where many basic Haskell concepts meet, and it can be presented in multiple ways that provide complementary intuitions. In this post,
Traversable will be described from a slightly unusual point of view, or at least one that is not put into foreground all that often. We will suspend for a moment the picture of walking across a container while using an effectful function, and instead start by considering what can be done with effectful functions.
Read more - May 19, 2017
What's in a Fold: The Basic Catamorphism in recursion-schemes
This article is meant as an accessible introduction to the most basic recursion scheme, the catamorphism. It won’t engage in deep dives into theory, or survey practical motives for using recursion schemes – that will be covered by the further reading suggestions at the end. Rather, its main goal is simply offering a concrete presentation of how folds can be generalised. This presentation will be done in terms of the types and combinators used by the recursion-schemes library, so that the article doubles as an introduction to some of its key conventions.
Read more - March 10, 2017
Casual Hacking With stack, Reloaded
It has been quite a while since I wrote about how to use stack for casual play outside of the context of a conventional Haskell project. In the meantime, stack has gained a feature called the global project which in many cases makes it possible to do quick experiments with essentially no setup, while still taking advantage of the infrastructure provided through stack.
Read more - February 26, 2017