From mathematics to map-reduce
There's more mathematics to programming than meets the eye. This post will highlight one such connection that explains the link between map-reduce and category theory. I will then conclude with some wild speculation about what this might imply for future programming paradigms. This post assumes that you already know Haskell and explains the mathematics behind the map-reduce using Haskell concepts
Monads Made Difficult
Monads Made Difficult Caveat: This is not a monad tutorial, you should not read this to understand monads initially. If you aren’t already comfortable with monads and have used them in production code, please don’t read this. It will not impart any intution. This is a short, fast and analogy-free introduction to Haskell monads derived from a categorical perspective. This assumes you are familiar w
Categories for the Working Haskeller | SkillsCast
8th October 2014 in London There are 7 other SkillsCasts available from Haskell eXchange 2014 Please log in to watch this conference skillscast. In this talk, I hope to explain a little bit about how categories can help the working Haskeller. I'll focus on two aspects: categories as an organising principle, helping us to manage generic libraries; and categories as a reasoning principle, helping us
A Neighborhood of Infinity: A Partial Ordering of some Category Theory applied to Haskell
A Partial Ordering of some Category Theory applied to Haskell I've had a few requests from people wanting to teach themselves applications of Category Theory to Haskell based on posts I've made. I've made things difficult by posting stuff at random levels of difficulty and without any kind of organising thread through them. So here's an attempt to list a bunch of posts related to aspects of catego
モノイドからモナドを作る - 檜山正幸のキマイラ飼育記 (はてなBlog)
モニャドセミナー3をやってから一週間以上経過しちゃったんですが、だいぶ遅れた補足です。なぜ補足が必要かというと、当日の後半、なにかに憑かれてラリラリだったから。ホワイトボードでの説明でグダグダだったところを少しはクリアにしよう、と。説明のストーリーや記号法は、セミナー当日のものとほぼ同じにしました。そのため、慣用の記法とは少しずれたところがあります。例えば、「μ」を使うところで「δ」を使ったりとか。 この記事は、あまり実例がなくて定義ばっかりの印象かもしれませんが、モニャドセミナーが事例中心だから、いいとしましょう。それと、やっぱりどっかで定義を確認することは必要なんです。確認作業では、つまんないタルイ計算が続きますが、我慢してヤッテ。 内容： モノイドの復習 直積による掛け算関手 掛け算関手の繰り返し適用 2回適用を1回につぶす自然変換δ クライスリ結合 クライスリ圏 ●モノイドの復習
The Comonad.Reader » Recursion Schemes: A Field Guide (Redux)
About a year back I posted a field guide of recursion schemes on this blog and then lost it a few months later when I lost a couple of months of blog entries to a crash. I recently recovered the table of recursion schemes from the original post thanks to Google Reader's long memory and the help of Jeff Cutsinger. The following recursion schemes can be found in category-extras, along with variation
Category Theory and Haskell 3 : Algebras and Monads
Posted by alpheccar - Jul 02 2007 at 21:10 CEST This is the third part of my serie about Haskell and category theory. In the previous post, I described a bit the Hask category and some categorical constructs. The goal of this text is to understand the meaning of a recursive type like List. For that, we will have to understand what is a free algebra and have a quick look at the relationship with
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