Domain Convergence

Okay, how is this for a definition of convergence:
An infinite sequence xs :: [()] converges if there exists an n such that for every m > n, xs !! m = xs !! n. In other words, this is a bunch of programs which either halt or don’t, and after some point, either they [...]

Continuous Stream Fusion

I’ve been able to sketch-implement a version of FRP with a strange distinction: Env vs. Behavior. I’ll give you the intuition, then the rest of the article will develop the semantics more fully. I thought “backwards” to discover this (the word “discover” used under the assumption that it has some merit: questionable), [...]

Reactive spaces

My recent days have been spent staring at the ceiling, drawing abstract doodles on a whiteboard, or closing my eyes and watching higher-dimensional images fly through my consciousness. No, I haven’t been on drugs. I’m after a very specific piece of mathematics, to solve a specific problem. But I have no idea [...]

Compact data types

Join me, fellow readers, as I learn some topology by pretending I know something about it.
I recently uploaded Martin Escardó’s infinite search monad to hackage, under the name infinite-search. It is a delightful little thing to play with, and has inspired some deeper thoughts about the connection between computation and topology.
Quick refresher on topology: [...]