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homotopytypetheory.org | ||
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xorshammer.com
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| | | | | The Axiom of Choice is usually introduced as a non-constructive axiom that mathematicians used to care about but don't really pay much attention to anymore. It's true that mainstream mathematicians often don't pay much attention to it, but it turns out that AC isn't inherently non-constructive: it depends on what the base system it's being... | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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bartoszmilewski.com
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| | | | | This is part 13 of Categories for Programmers. Previously: Limits and Colimits. See the Table of Contents. Monoids are an important concept in both category theory and in programming. Categories correspond to strongly typed languages, monoids to untyped languages. That's because in a monoid you can compose any two arrows, just as in an untyped... | |
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blog.sigfpe.com
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| | | [AI summary] An in-depth technical exploration demonstrating how Haskell monads can be formally defined as monoids in the category of endofunctors using abstract categorical logic and functional programming code. | ||
