Logic is Algebra · HackerPapers discussions

Logic is Algebra — mentioned by practal

Thu, 21 Nov 2024 10:32:06 GMT

This interplay between intuition and logic is exactly what makes the magic happen. You need intuition to feel your way forward, and then logic to solidify your progress so far, and also for ideas maybe not directly accessible via intuition only. I've experienced that myself, and it is even well-documented, because I wrote technical reports and such at each stage. My discovery of Abstraction Logic went through various stages: 1) First, I had a vague vision of how I want to do mathematics on a computer, based on my experience in interactive theorem proving, and what I didn't like about the…

Paper and discussion history. A mention is not an endorsement.

Logic is Algebra — HN submission

Thu, 28 Sep 2023 16:12:42 GMT

(Abstraction) Logic is (abstraction) Algebra [PDF]

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Logic is Algebra — mentioned by practal

Thu, 28 Sep 2023 08:11:29 GMT

I think the important idea from math for programming, and pretty much everything else, is that of a function that operates on functions. You can build on that important idea in different general ways, for example category theory, or type theory. There is a much simpler way of making this idea the foundation of pretty much everything though, see my report "Logic is Algebra" [1]. I've simplified matters further since then (for example, instead of the somewhat unfamiliar notation (lambda x. D P[x]) you write now lambda(D, x. P[x]) (maybe I should even go as far as just writing "lambda(D, x =>…

Paper and discussion history. A mention is not an endorsement.