Type Theory

Part 1: Introduction — The Why; early compiler architecture; Nat, Bool, summation, equality; “Core List Machine” introduction — This is the first article in a series describing the creation of FOOL3: “functional object-oriented low-level language” — a functional programming language with a powerful type system (as close to Calculus of Constructions as we can get without making our heads spin) that compiles to .Net and JavaScript as initial…

In a recent pull request written in the Go language I added a method with the signature func(A) D(obfuscated) where types A and D are defined as interfaces. During the pull request review a fellow engineer suggested I replace the type D with a struct citing the Go proverb “accept…

Given their widespread use, I shall assume readers are already familiar with regular expressions (basic knowledge of regular expression notations such as union and Kleene star is sufficient for our purposes) and start my explanation from set-theoretic types. Set-theoretic types treat types in programming languages as sets of values. For…

Let’s talk about two dimensional matrices in Rust. To be precise, two-dimensional matrices written as nested arrays. A simple 2x2 matrix is looks like this: let matrix = [[1, 2], [3, 4]]; A simple 1x1 matrix looks like this: let matrix = [[1]]; The empty (0x0) matrix is… let matrix…

TLDR : Agda + VSCode for HoTT summer school. — Note: This is for the HoTT summer school. You can also use this for agda too, but its main purpose is different. Skip to step 5 to just run it. My system is running Pop-Os 22.04, so I used the Ubuntu installation for everything. I cannot tell what errors might…

Two Logicians Alonzo Church was an American logician. He invented the lambda calculus and used it in 1934 to answer negatively Hilbert and Ackermann’s Entscheidungsproblem, the question of whether there’s an algorithm to solve every yes-or-no mathematical question. Turing got the same result with Turing machines independently a few months later. Haskell…

“Reducing” an array seems to be one of those things that many engineers struggle with at first. So much so that they tend to avoid reductions even though they are comfortable with reduce’s friends (mapping, filtering, etc). I hope that by the end of this article the idea of “reducing”…

In this short text, we explore how one could benefit from juggling with functional and type-theoretic thinking, to solve a concrete common problem found in programming. The language is Java (yet keep your Spring away), and the use case we focus on is the topic of validator trees. The final result we target Throughout the…

Can we have a better real-world application development experience with a better type system? — Any real-world application uses a database or seventeen in the backend. Developing and maintaining such applications has largely remained a nightmare experience, despite many attempts to fix the problem. Enterprise Java Beans, Ruby-on-Rails, Meteor — many tried, but none succeeded in achieving a seemingly straightforward and very desirable goal: