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blog.jle.im | ||
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sitr.us
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| | | | | Dependent types provide an unprecedented level of type safety. A quick example is a type-safe printf implementation. They are also useful for theorem proving. According to the Curry-Howard correspondence, mathematical propositions can be represented in a program as types. An implementation that satisfies a given type serves as a proof of the corresponding proposition. In other words, inhabited types represent true propositions. | |
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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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jdh.hamkins.org
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| | | This will be a series of self-contained lectures on the philosophy of mathematics, given at Oxford University in Michaelmas term 2019. We will be meeting in the Radcliffe Humanities Lecture Room at | ||
