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ionathan.ch | ||
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homotopytypetheory.org
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| | | | | For a while, Mike Shulman and I (and others) have wondered on and off whether it might be possible to represent all higher inductive types (i.e. with constructors of arbitrary dimension) using just 1-HIT's (0- and 1-cell constructors only), somewhat analogously with the reduction of all standard inductive types to a few specific instances -... | |
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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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qchu.wordpress.com
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| | | Let $latex k$ be a commutative ring. A popular thing to do on this blog is to think about the Morita 2-category $latex \text{Mor}(k)$ of algebras, bimodules, and bimodule homomorphisms over $latex k$, but it might be unclear exactly what we're doing when we do this. What are we studying when we study the Morita... | ||
