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Title | Poleiro, the Coq blog - |
Description | A blog about the Coq proof assistant and programming |
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WebSite | poleiro.info |
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Location | United States |
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US$330,671
Last updated: 2023-05-13 04:13:51
poleiro.info has Semrush global rank of 32,008,613. poleiro.info has an estimated worth of US$ 330,671, based on its estimated Ads revenue. poleiro.info receives approximately 38,155 unique visitors each day. Its web server is located in United States, with IP address 159.65.233.164. According to SiteAdvisor, poleiro.info is safe to visit. |
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Poleiro Where the Coq lives Main Archives About Feed GitHub December 25, 2019 | Comments Quotients in Coq Quotients are crucial in mathematical practice, and it is a shame that they are not available in Coq’s standard library. There was a recent discussion on the Coq GitHub page on this issue and the consequences of implementing quotients like Lean does, where the eliminator for function types has a reduction rule that breaks pleasant metatheoretic properties such as subject reduction. In this post, we are going to define quotients in Coq with three standard axioms: Functional extensionality Propositional extensionality Constructive definite description (also known as the axiom of unique choice) Check @ functional_extensionality_dep : ∀ A B ( f g : ∀ x : A , B x ), (∀ x : A , f x = g x ) → f = g . Check @ propositional_extensionality : ∀ P Q , ( P ↔ Q ) → P = Q . Check @ constructive_definite_description : ∀ A P , ( exists ! x : A , P x ) → { x : A | P x }. As far as axioms go, these |
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