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Integrating Linear and Dependent Types by Krishnaswami, Neelakantan R.; Pradic, Pierre; Benton, Nick is a Computer Science article available to read on EtoBox.

What is Integrating Linear and Dependent Types about?

In this paper, we show how to integrate linear types with type dependency, by extending the linear/non-linear calculus of Benton to support type dependency. Next, we give an application of this calculus by giving a proof-theoretic account of imperative programming, which requires extending the calculus with computationally irrelevant quantification, proof irrelevance, and a monad of computations. We show the soundness of our theory by giving a realizability model in the style of Nuprl, which permits us to validate not only the beta-laws for each type, but also the eta-laws. These extensions permit us to decompose Hoare triples into a collection of simpler type-theoretic connectives, yielding a rich equational theory for dependently-typed higher-order imperative programs. Furthermore, both the type theory and its model are relatively simple, even when all of the extensions are considered.

Who reads Integrating Linear and Dependent Types?

Author

Krishnaswami, Neelakantan R.; Pradic, Pierre; Benton, Nick

Publisher

Association for Computing Machinery; Special Interest Group on Computer Graphics, Association for Computing Machinery; Association for Computing Machinery (ACM) (ISSN 0362-1340)

Published

2015

Language

EN

Field

Computer Science (Physical Sciences)