What is PLUS times PLUS?
Why Hacker News recommends it
Mentioned in lambda calculus and combinator threads as a visual entry point to the topic.
What it is
2swap explores lambda calculus using John Tromp's lambda diagrams, with animated beta-reductions, asking what PLUS times PLUS gives. It touches on Church encodings and the equivalence of Turing machines and lambda calculus.
Recommended by 1 HN commenters across 1 different months, 2025 to 2026.
What Hacker News said
Recommends contraposit · 2026-04 · on “Optimal Strategy for Connect 4”
I also liked the one on lambda calculus. I hope one day we will be able to find interpretation of what it actually means for PLUS Times Plus. Maybe this is how we will explore nonstandard arithmetic. What is PLUS times PLUS? [this video]
Cites diginova · 2025-07 · on “How to draw lambda diagrams (2020)”
True, thanks for clarification that would be this one - [LINK] as I just started learning lambda calculus and this one helped Also this is where I got the interest from - [this video]
Cites csense · 2025-11 · on “Interactive λ-Reduction”
I don't know much about any of this, and I'm far from an expert on the lambda calculus. But I skimmed paper by OP, which is informative: [LINK] The lambda calculus is an alternate model of computation created by Alonzo Church in the 1930s. It's basically a restricted programming language where the only things you can do are define anonymous functions, and apply those anonymous functions to input variables or the output of other functions. The Lambda calculus statement And = λp.λq.p q p is more conventionally notated as And(p, q) = p(q(p)). You can reduce lambda expressions -- basically, this is "Simplifying this program as far as possible" what you expect a good optimizing compiler to do. Wh
Cites bntr · 2026-02 · on “Show HN: Visual Lambda Calculus – a thesis project (2008) revived for the web”
For comparison: factorial(3) visualized in two different notations. John Tromp's Lambda Diagrams (via 2swap): [this video] Bubble Notation: [LINK]
Cites observationist · 2026-03 · on “Combinators”
Combinators are math, and a little like Lisp - building functions from primitives and operations with the ability to apply them, where even the notion of variables are functions - functions all the way down. The y combinator is this: λf.(λx.x x)(λx.f(x x)) Lambda diagrams get you visualizations like this: [LINK] When considering logic and functions, when thinking in the space of combinators, you can ask questions like "What is Plus times Plus" and have a sensible result. [this video] Combinators are awesome. The site linked by OP is a specific collection of combinators with bird names, riffing on the "To Mock a Mockingbird" puzzle book and subsequent meme of giving combinators bird names.