Homotopy Type Theory and Univalent Foundations
Homotopy Type Theory and the Univalent Foundations of Mathematics Homotopy type theory refers to a new interpretation of Martin-Löf's constructive type theory into homotopy theory. Propositional equality between intensionally distinct terms is interpreted as homotopy. The interpretation makes use of methods from abstract homotopy theory such as Quillen model categories, as well as related methods
A Neighborhood of Infinity: Monads, a Field Guide
Here are some sketches of monads. I've annotated each with its species. I'm not a great artist and I only saw each of them for a fleeting moment so I had to fill in some details from memory. But I think the sketches are good enough to be able to recognise them in the wild. Click on the 'thumbnail' for the full size image. I'm currently trying to stalk some monads from the continuation family. When
操作的意味論 vs 表示的意味論 - sumiiのブログ
http://d.hatena.ne.jp/ranha/20090615 (via http://d.hatena.ne.jp/yad-EL/20090615/p2) 「諸君らの愛した表示的意味論(R5RS)は死んだ。なぜだ?」 う、これは私も（というか私ごときでは）迂闊に発言できないテーマです…。Scheme (R5RS → R6RS)に固有の事情は知らないので、（もしあれば）メーリングリストなどでの議論を検索したほうが詳しいかもしれません。追記：R5RSの操作的意味論と、その表示的意味論に対するメリットに関しては論文があるようです。 迂闊に発言すると、（一般論としては）「操作的意味論のほうが理論が簡単だから」だと思います。要するにプログラムの「意味」というより「動作」を状態遷移（式の書き換え）で表しているだけなので…。歴史的には、操作的意味論も（仮想機械やインタプリタによる定義から）項
Downloadable Publications
Selected publications by Giuseppe Longo, after 1990 available as .dvi, .ps (some gzipped) or .pdf files by ftp and http 1 - Mathematical Logic and Computer Science. 2 - Cognition and Foundations of Mathematical Knowledge. 3 - Theoretical Biology. 4 - Interfaces Computability, Physics and Biology. 5 - Minima Philosophica. 6 - Minima Economica. 7 - 1980's: Some of the
ICS | Utrecht University
Department of Information and Computing Sciences This is a website used by the ICS in education. If you are looking for more information on our department, go to Information and Computing Sciences. Information regarding your courses can be found in Blackboard. General information regarding ICS courses can be found in Osiris catalog. The archive of the technical reports of our department can be fou
Jones, Gomard, Sestoft: Partial Evaluation
Partial Evaluation and Automatic Program Generation The book Partial Evaluation and Automatic Program Generation gives a comprehensive presentation of partial evaluation: theory, techniques, and applications. It is suitable for self-study, and for graduate courses and advanced undergraduate courses on program transformation techniques. See the preface and the table of contents. Download the full t
The Curry-Howard Correspondence in Haskell
The Curry-Howard correspondence is a mapping between logic and type systems. On the one hand you have logic systems with propositions and proofs. On the other hand you have type systems with types and programs (or functions). As it turns out these two very different things have very similar rules. This article will explore the Curry-Howard correspondence by constructing a proof system using the Ha
A Tutorial Implementation of a Dependently Typed Lambda Calculus
A Tutorial Implementation of a Dependently Typed Lambda Calculus Andres Löh, Conor McBride and Wouter Swierstra We present the type rules for a dependently-typed core calculus together with a straightforward implementation in Haskell. We explicitly highlight the changes necessary to shift from a simply-typed lambda calculus to the dependently-typed lambda calculus. We also describe how to extend o
Programmering som teoribyggnad
Peter Naur Introduktion Denna diskussion är ett bidrag till förståelsen av vad programmering är. Det föreslår att programmering på rätt sätt bör ses som en aktivitet genom vilken programmerarna formar eller uppnår en viss typ av insikt, en teori, om de aktuella frågorna. Detta förslag står i motsats till vad som förefaller vara en vanligare föreställning, att programmering ska ses som en produktio
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Monoids? In my programming language?
Ulisses Costa Blog » Blog Archive » Catamorphisms in Haskell
https://www.cs.chalmers.se/Cs/Research/Logic/book/book.pdf
http://www.maths.gla.ac.uk/~tl/ct/