Program = Proof
by Samuel Mimram · first published 2020
83% recommend17% neutral
Why HN recommends it
Mathematically grounded introduction to the Curry-Howard correspondence, covering lambda calculus, intuitionistic logic and dependent type theory; suits readers who want the foundations of programming and proofs.
Summarised by Claude from recommending comments
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…https://www.dropbox.com/s/2umr9ouz0jdelio/1407.pdf?dl=1 * Probabilistic Models of Cognition: https://probmods.org Something that merges logic, types and proofs, perhaps yet to be written. Some good preliminary material: * Program = Proof: https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching... * Concrete Semantics: http://concrete-semantics.org * The Hitchhiker’s Guide to Logical Verification: https://raw.githubusercontent.com/blanchette/logical_verific...…
on “Paradigms of Artificial Intelligence Programming (1992)” ↗…accomplish in each step, and did something functionally equivalent in idiomatic F#. That was fun & challenging. haven't tackled the second part, I'm currently down the rabbit hole with Samuel Mimram's Program = Proof, which I'm just loving and the first book I've seen that focuses on the Curry Howard Isomorphism, covering essential logic, lambda calculus, type theory, and Agda... so good.
on “Crafting Interpreters: A Review” ↗…multiple variable calculus. Analysis is discussed in an appendix. All proofs have a constructive bias, so it's very algorithmic and natural for a CS-minded student. Solutions are in a separate volume. * Program = Proof by Mimram. Discusses logic and computation, and takes you from the basics to depedent type theory and beyond. Uses OCaml and Agda. Freely available at: https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching...
on “Ask HN: Math books that made you significantly better at math?” ↗Program = Proof, Samuel Mimram: https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching.... Also available as hardcopy in Amazon.
on “Ask HN: Best value Comp. Sc. book for 100€?” ↗1. Program = Proof by Samuel Mimram Math foundation of programming. Church–Rosser theorem, Curry–Howard correspondence, intuitionistic logic, theorem proving with dependent types, etc. 2. Rust Atomics and Locks: Low-Level…
on “Ask HN: Any interesting books you have read lately?” ↗…not cover proof assistants. Alternatively you may enjoy these two. The latter is especially thorough, and begins with classical logic: * Concrete Semantics (Isabelle): http://concrete-semantics.org * Program = Proof (Agda): https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching...
on “The Deep Link Equating Math Proofs and Computer Programs” ↗I would highly recommend "PROGRAM = PROOF" by Samuel Mimram. It covers everything from pure lambda calculus through dependent type theory up to homotopy type theory. In comparison to the HoTT book, the book "PROGRAM = PROOF" is oriented less…
on “Principia Mathematica is modern and insightful” ↗There's a book that's explicitly about this, "Program = Proof", and though it's not beginner and needs maybe a light version for earlier learners, is an excellent example.
on “Propositions as Types (2014) [pdf]” ↗The book "Program = Proof" by Samuel Mimram starts with a formula which is true for all n below n = 15 341 178 777 673 149 429 167 740 440 969 249 338 310 889 I don't think you can catch it with any test suite.
on “Formal Methods and the Future of Programming” ↗See also: https://www.amazon.com/PROGRAM-PROOF-Samuel-Mimram/dp/B08C97...
on “Designing a Language Without a Parser” ↗