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A Tutorial Implementation of a Dependently Typed Lambda Calculus

Löh A., McBride C., Swierstra W.

Fundamenta Informaticae

2010

Vol. 102, nr 2

177-207

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 our core language with data types and write several small example programs. The article is accompanied by an executable interpreter and example code that allows immediate experimentation with the system we describe.

δ for Data: Differentiating Data Structures

Abbott M., Altenkirch T., McBride C., Ghani N.

Fundamenta Informaticae

2005

Vol. 65, nr 1,2

1-28

This paper and our conference paper (Abbott, Altenkirch, Ghani, and McBride, 2003b) explain and analyse the notion of the derivative of a data structure as the type of its one-hole contexts based on the central observation made by McBride (2001). To make the idea precise we need a generic notion of a data type, which leads to the notion of a container, introduced in (Abbott, Altenkirch and Ghani, 2003a) and investigated extensively in (Abbott, 2003). Using containers we can provide a notion of linear map which is the concept missing from McBride's first analysis. We verify the usual laws of differential calculus including the chain rule and establish laws for initial algebras and terminal coalgebras.