Contents The Curry-Howard correspondence How do proof assistants use the CH correspondence A theorem A proof of the theorem The type checker Limitations of the type checker Mathematical consequences (and proof) Your type checker maybe wrong Conclusion When writing code many of us have been saved time and time again by type checkers: the useful piece of software that ensures you aren’t adding…
Contents Tolstoyan art Zero-knowledge proof A marriage of (or casual relationship between) the two Conclusion In this post I hope to prove to you (get it 😉) in rather uncertain terms, that: Tolstoyan art has the structure of a zero knowledge proof. Currently, this statement is a big nothing-burger, so first we will discuss the high level ideas of Tolstoyan art and zero knowledge proofs. Tolstoyan…
Contents Introduction The explanation Conclusion Introduction While quite a fundamental law in logic, the contrapositive is certainly not immediately intuitive (or at least it was not to me). After someone else expressed a similar feeling, I decided to try and derive some intuition to explain the rule, and I think I have succeeded. This blog could also be treated as an introduction to the…
Contents Introduction Should you read this? The Turing machine The intuitive approach A mathematical approach Languages Words/Strings Languages from words Distinguishing Turing machines with respect to a language A recogniser A decider Distinguishing languages A first result Proof of Turing-recognisability A second, more exciting result Proof of non-decidability A discussion of the proof The…
Contents The problem An example The solution Lemma one Lemma two Conclusion Generalisation What a catchy name! I’d like to explain this problem, and then provide a wordy proof for a general case. All the proofs are hidden in drop downs to motivate you to try them yourself and to make the blog less dense, if you have any questions about the proofs (or anything else), please leave them below!
Contents The structure of the network The new function Arguments Network setup Weight initialisation Initialisation options Bias initialisation Returning The forward pass function Arguments Return value Initialisation All layers but one The one layer Conclusion Appendix The RNG tangent This is the second iteration in the series where we are building a Multi-Layer-Perceptron (MLP) from scratch!…
Hi! I am Max, a first year student at the University of Warwick in the UK where I study discrete mathematics (mathematics, computer science and the large intersection). I love pure mathematics as well as most things software (including Nix and Rust), which I suppose makes my university course a good fit? Also, I play trumpet and violin, and I enjoy classical music (perhaps by extension). Last…