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justinpombrio.net | ||
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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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bartoszmilewski.com
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| | | | | This is part 9 of Categories for Programmers. Previously: Functoriality. See the Table of Contents. So far I've been glossing over the meaning of function types. A function type is different from other types. Take Integer, for instance: It's just a set of integers. Bool is a two element set. But a function type a->b... | |
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wimvanderbauwhede.codeberg.page
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| | | | | Algebraic data types are great for building complex data structures, and easy to implement in Raku using roles. | |
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xorshammer.com
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| | | There are many functions from $latex \mathbb{N}$ to $latex \mathbb{N}$ that cannot be computed by any algorithm or computer program. For example, a famous one is the halting problem, defined by $latex f(n) = 0$ if the $latex n$th Turing machine halts and $latex f(n) = 1$ if the $latex n$th Turing machine does not... | ||
