Mark P Jones: Typing Haskell in Haskell
REVISED VERSION Last updated: Thanksgiving day, November 23, 2000 Abstract Haskell benefits from a sophisticated type system, but implementors, programmers, and researchers suffer because it has no formal description. To remedy this shortcoming, we present a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a notation that is familiar
Typed Tagless-Final Interpretations: Introductory Course
The first course on typed tagless-final embeddings of domain-specific languages has been presented at the Spring School on Generic and Indexed Programming (SSGIP) <http://www.comlab.ox.ac.uk/projects/gip/school.html> at Wadham College, Oxford, UK on 22nd to 26th March 2010. This page collects the notes for the course in the form of the extensively commented Haskell and OCaml code. Lecture Notes In
Type arithmetic - HaskellWiki
Type arithmetic (or type-level computation) are calculations on the type-level, often implemented in Haskell using functional dependencies to represent functions. A simple example of type-level computation are operations on Peano numbers: data Zero data Succ a class Add a b ab | a b -> ab, a ab -> b instance Add Zero b b instance (Add a b ab) => Add (Succ a) b (Succ ab) Many other representations
A Neighborhood of Infinity: The Categorification of the Naturals
A heavyweight looking title, but this post is really about nothing more than doing arithmetic. Peano Arithmetic I've seen many articles on type level arithmetic. They all seem to share the idea that the Haskell type system can be made to perform computations by treating types as symbols that can be manipulated according to rules. But every article I have seen seems to miss the important idea that
full-sessions-0.6.1 - keigoiの日記
full-sessionsの新バージョン 0.6.1 を HackageDBにアップロード しました。 full-sessions は、Haskellにおけるマルチスレッド/ネットワークプログラミングのライブラリです。 Sessionモナドという新しいモナドを使ってプログラムを書きます。 チャネルの型表現にπ計算の型理論の一つであるセッション型を採用しています。セッション型のおかげで、チャネルの「使われ方（プロトコル）」がスレッド間で整合していることを実行前の型検査によりチェックできます。これにより、ある種のデッドロックや型の不整合は型検査で排除できるようになります。 さらにHaskellの型推論でセッション型を推論させれば、プログラムがチャネルを意図通りに使っていることを型表現からチェックできます。 full-sessions は、HList等で見られるような型レベルプログラミングのテク
Unusual Polymorphism
Parametric polymorphism is the parameterization of a term by a type, permitting the term to be used in differently-typed contexts. Types of polymorphic terms contain universal quantification. For the sake of inference and ease of type checking, mainstream functional programming languages restrict where in the type the quantifiers may appear and what they quantify over. The Hindley-Milner system, o
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Simon Peyton-Jones - Microsoft Research
Generalized zipWithN
Scala for Haskell
Data Types a la Carte | Lambda the Ultimate
Welcome to spoonville: Typefuck
Sorting Type-Heterogeneous Values with Type Families