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www.chriswarbo.net | ||
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eklausmeier.goip.de
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| | | | | [AI summary] This article explains the mathematical method of diagonalization, using Cantor's proof of uncountability and Turing's halting problem as primary examples. | |
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kuruczgy.com
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| | | | | [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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math.andrej.com
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| | | | | [AI summary] A technical discussion distinguishing between proof by contradiction and proof of negation within the context of classical and intuitionistic logic. | |
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bartoszmilewski.com
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| | | This is part 31 of Categories for Programmers. Previously: Lawvere Theories. See the Table of Contents. There is no good place to end a book on category theory. There's always more to learn. Category theory is a vast subject. At the same time, it's obvious that the same themes, concepts, and patterns keep showing up... | ||
