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homotopytypetheory.org | ||
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pavpanchekha.com
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adam.chlipala.net
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| | | | | [AI summary] This text provides an in-depth exploration of advanced Coq proof techniques, focusing on manual proofs, recursion, and induction principles for complex data structures. It covers topics like nested inductive types, custom induction principles, and the design philosophy behind Coq's approach to proof automation. The text includes detailed examples of proof scripts, such as manual proofs for discrimination and injectivity of constructors, and discusses the use of tactics like discriminate and injection. It also touches on the implementation of functions like pred and the role of hints in improving proof readability and automation. | |
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bartoszmilewski.com
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| | | | | Previously: Modeling Identity Types. On first viewing, the identity type seems odd. Does it make sense to replace the traditional yes/no equality predicate with an elaborate type of equality proofs? In fact the father or modern type theory Martin Löf had his doubts, and initially tried to reflect all identity proofs into more basic judgmental... | |
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text.marvinborner.de
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| | | This article describes a variadic extension to the default fixed-point combinator namely the Y-combinator. We do this by translating the Scheme code from a paper to bruijn (pure lambda calculus). | ||
