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
Migrating a Project to stack
This post consists of notes on how I converted one of my Haskell projects to stack. It provides a small illustration of how flexible stack can be in accomodating project organisation quirks on the way towards predictable builds.
Read more - July 27, 2015
It is widely agreed that the laws of the
Applicative class are not pretty to look at.
pure id <*> v = v -- identity
pure f <*> pure x = pure (f x) -- homomorphism
u <*> pure y = pure ($ y) <*> u -- interchange
pure (.) <*> u <*> v <*> w = u <*> (v <*> w) -- composition
Monad laws, in comparison, not only look less odd to begin with but can also be stated in a much more elegant way in terms of Kleisli composition
(<=<). Shouldn’t there be an analogous nice presentation for
Applicative as well? That became a static question in my mind while I was studying applicative functors many moons ago. After finding surprisingly little commentary on this issue, I decided to try figuring it out by myself.
Read more - July 6, 2015
What Does fmap Preserve?
A common way of introducing
fmap is saying that it only changes the values in a container, and not its structure. Leaving behind the the functors-as-containers metaphor, we can convey the same idea by saying that
fmap leaves the context of the values in a
Functor unchanged. But what, exactly, is the “context” or “structure” being preserved? “It depends on the functor”, though correct, is not an entirely satisfactory answer. The functor laws, after all, are highly abstract, and make no mention of anything a programmer would be inclined to call “structure” (say, the skeleton of a list); and yet the preservation we alluded to follows from them. After struggling a bit with this question, I realised that the incompatibility is only apparent. This post shows how the tension can be resolved through the mediation of parametricity and naturality, two concepts from different domains that are intertwined in Haskell.
Read more - June 2, 2014
Lenses You Can Make at Home
The most striking traits of the
lens library are its astonishing breadth and generality. And yet, the whole edifice is built around van Laarhoven lenses, which are a simple and elegant concept. In this hands-on exposition, I will show how the
Lens type can be understood without prerequisites other than a passing acquaintance with Haskell functors. Encouraging sound intuition in an accessible manner can go a long way towards making
lens and lenses less intimidating.
Read more - April 26, 2014