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www.jeremykun.com | ||
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rakhim.org
[AI summary] A summary of Bartosz Milewski's talk exploring the equivalence between type theory, logic, category theory, and computer science through concepts like composition, Curry-Howard isomorphism, and continuations. |
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bartoszmilewski.com
In the previous instalment of Category Theory for Programmers we talked about the category of types and functions. If you're new to the series, here's the Table of Contents. You can get real appreciation for categories by studying a variety of examples. Categories come in all shapes and sizes and often pop up in unexpected... |
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www.greaterwrong.com
Maybe you've heard about something called a Chu space around here. But what the heck is a Chu space? And whatever it is, does it really belong with all the rich mathematical structures we know and love? Say you have some stuff. What can you do with it? Maybe it's made of little pieces, and you can do a different thing with each little piece. But maybe the pieces are structured in a certain way, and you aren't allowed to do anything that would break this structure. A Chu space is a versatile way of formalizing anything like that! |
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kuruczgy.com
[AI summary] The article explores the intersection of functional programming and logic through the lens of dependent types. It begins with foundational concepts like type constructors and inductive types, then delves into the Curry-Howard isomorphism, which links programs to mathematical proofs. The discussion covers how types represent propositions, functions as implications, and inductive types as proof strategies. Examples include defining logical relations like less than or equal to and equality, and demonstrating how to prove properties like universal quantification and mathematical identities. The article concludes with an overview of resources for further study in proof assistants like Coq and Idris, emphasizing the practical applications of dependent... |
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