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www.leviathansecurity.com | ||
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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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jingnanshi.com
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| | | | | Tutorial on automatic differentiation | |
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thenumb.at
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| | | | | [AI summary] This text provides an in-depth exploration of how functions can be treated as vectors, particularly in the context of signal and geometry processing. It discusses the representation of functions as infinite-dimensional vectors, the use of Fourier transforms in various domains (such as 1D, spherical, and mesh-based), and the application of linear algebra to functions for tasks like compression and smoothing. The text also touches on the mathematical foundations of these concepts, including the Laplace operator, eigenfunctions, and orthonormal bases. It concludes with a list of further reading topics and acknowledges the contributions of reviewers. | |
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geriatrixfotogallerie.wordpress.com
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