parenz.wordpress.com

hub.darcs.net

co-dan :: hub.darcs.net

http://hub.darcs.net/co-dan

Mdash; my patches to darcs, branch of darcs-screened. Mdash; mirror of http:/ darcs.net/releases/branch-2.10. Mdash; Darcs Benchmarking Utility. Http:/ wiki.darcs.net/Benchmarks. Mdash; mirror of http:/ darcs.net/screened for SoC15. Mdash; darcs repository web UI and hosting app. This is the main darcsden trunk, which also runs hub.darcs.net. Http:/ hub.darcs.net. Mdash; darcs repository web UI and hosting app. This is the main darcsden trunk, which also runs hub.darcs.net. Http:/ hub.darcs.net.

covariant.me

Haskell reading list

http://www.covariant.me/notes/haskell-links.html

Last updated: July 23, 2015. An small collection of Haskell reading material. A marvelous guide by Stephen Diehl: What I Wish I Knew When Learning Haskell. List folds as structural transformations. Simon Peyton Jones’ article on. Flipping arrows in coBurger king. Interesting post by Ed Yang about some category theory notions you might find in Haskell;. A shocking revelation that monads are actually burritos! Mostly about Lenses as defined in the. A whole bunch of functional pearls. The history of Haskell.

covariant.me

The λ-calculus

http://www.covariant.me/notes/lambda-calc.html

Last updated: October 30, 2014. Notes and fun facts about lambda calculus. Klop’s fixed point combinator. Klop’s fixed point combinator. Y-combinator, defined as. Y = λf.(λx. f (x x) (λx. f (x x). Is a fairly-known logical combinator used for defining recursive functions. However, it is not the only combinator of such kind. Jan Klop has discovered a fixed-point combinator (Y k ). Defined as (Y k = LLLLLLLLLLLLLLLLLLLLLLLLLL ). L = λabcdefghijklmnopqstuvwxyzr. r (thisisafixedpointcombinator).

covariant.me

A note on the universes in the groupoid model of type theory

http://www.covariant.me/notes/groupoid_univ.html

Last updated: May 21, 2015. A note on the universes in the groupoid model of type theory. We start by assuming a meta-theoretical universe ({ cal V} ). We call a groupoid (X ). If both objects and morphisms of (X ). Are in ({ cal V} ). By ({ mathbf{ mathord{Gpd} } ). We denoted a category of small groupoids, restricting the morphisms to only isomorphisms of groupoids. Thus, ({ mathbf{ mathord{Gpd} } ). Is a groupoid as well, ({ mathbf{ mathord{Gpd} } in { mathbf{ mathord{GPD} } ). Mathbf{ mathord{Gpd} } ).

covariant.me

Existential Quantification in Haskell

http://www.covariant.me/notes/existential-quantification.html

Last updated: January 24, 2014. Existential Quantification in Haskell. Existential quantification in Haskell is a topic that arises from time to time, because it is confusing for the newcomers. I remember being perplexed by it myself. In datatypes (and newtypes) declarations is a powerful mechanism that can be used to incapsulate information or even provide stronger type guarantees. Why is it called existential quantification when we are using a universal quantifier? Above you can see the example usage of.

covariant.me

Representable functors in Haskell

http://www.covariant.me/notes/rep-functors.html

Last updated: February 15, 2014. Representable functors in Haskell. F : C to Set ). If it is isomorphic to (Hom(A, -) ). For some (A ). Denoted as (F simeq Hom(A,-) ). Since we are talking about Haskell, I’ll also use the ( a to -) ). Notation instead of (Hom(a, -) ). The object (A ). For a functor (F ). Usually, the isomorphism between the functor is given by two natural transformations. Throughout the text the letters ( alpha ). And ( beta ). Beta : F Rightarrow (a to -) ). For a representing object.

covariant.me

Basic Category Theory in Coq

http://www.covariant.me/notes/coq-categories.html

Last updated: January 28, 2014. Basic Category Theory in Coq. Problems, issues, experience. I am working on an implementation of the basic category theory in Coq. This page should be updated when appropriate. You can browse the repository online. Or you can clone it to your computer using darcs. Darcs get http:/ covariant.me/repos/cat/. Definition of a category,. Typeclass, notation for Hom-sets and composition;. Definition of a functor, id functor;. Definition of a setoid morphism;.