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www.joachim-breitner.de | ||
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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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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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hookrace.net
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jamesmills.co.uk
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| | | Every now and then you will probably find yourself in the need to use a custom function in your Laravel application. I cannot think of one project which I have worked on where I haven't needed to add a quick and easy custom function. Our controllers don't contain actions outside of the 7 resource actions [...] | ||
