Bartosz Milewski's Programming Cafe | Category Theory, Haskell,...
Bartosz Milewski. Category Theory, Haskell, Concurrency, C++.
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(Weak) Homotopy Equivalences | Bartosz Milewski's Programming Cafe
Previously: Fibrations and Cofibrations. In topology, we say that two shapes are the same if there is a homeomorphism-- an invertible continuous map-- between them. Continuity means that nothing is br...
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Bartosz Milewski's Programming Cafe | Category Theory, Haskell, Concurrency, C++
Category Theory, Haskell, Concurrency, C++
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December | 2011 | Bartosz Milewski's Programming Cafe
2 posts published by Bartosz Milewski during December 2011
Bartoszmilewski.com news digest
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3 months
Previously: Identity Types. Let me first explain why the naive categorical model of dependent types doesn’t work very well for identity types. The problem is that, in such a model, any arrow can be considered a fibration, and therefore interpreted as...
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4 months
Previously: Models of (Dependent) Type Theory. There is a deep connection between mathematics and programming. Computer programs deal with such mathematical objects as numbers, vectors, monoids, functors, algebras, and many more. We can implement such...
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5 months
Models of (Dependent) Type Theory
Previously: (Weak) Factorization Systems. It’s been known since Lambek that typed lambda calculus can be modeled in a cartesian closed category, CCC. Cartesian means that you can form products, and closed means that you can form function types. Loosely...
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6 months
Previously (Weak) Homotopy Equivalences. An average function between sets, is neither surjective nor injective. We can however isolate the two “failure modes” if we insert a third set in between. We can, for instance, pick this set to be the subset of...
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