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bartoszmilewski.com | ||
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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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www.jeremykun.com
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| | | | | Previously in this series we've seen the definition of a category and a bunch of examples, basic properties of morphisms, and a first look at how to represent categories as types in ML. In this post we'll expand these ideas and introduce the notion of a universal property. We'll see examples from mathematics and write some programs which simultaneously prove certain objects have universal properties and construct the morphisms involved. | |
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degoes.net
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| | | | | Functional programming has a bit of jargon, but that doesn't have to stop you from understanding core concepts | |
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philpapers.org
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