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 lawrencecpaulson.github.io
Inductive definitions
| | blog.sigfpe.com
A Neighborhood of Infinity: Self-referential logic via self-referential circuits
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| | www.themathdoctors.org
A Few Inductive Fibonacci Proofs - The Math Doctors
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| | adam.chlipala.net
InductiveTypes
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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.
| | thinking-about-science.com
18.16 The square root of minus 1 and complex numbers - Thinking about Science with David Hukins
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| It may seem that this post is about very abstract mathematics. But the ideas explained here are very useful for explaining oscillations and waves (post 18.11), especially when combined with the concept of the number e (post 18.15). Counting is like moving along the line in the picture above - from left to right. When...