A graded dependent type system with a usage-aware semantics (extended version)

11/08/2020 ∙ by Pritam Choudhury, et al. ∙ 0

Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive sums, and a unit type. Since standard operational semantics is resource-agnostic, we develop a heap-based operational semantics and prove a soundness theorem that shows correct accounting of resource usage. Several useful properties, including the standard type soundness theorem, non-interference of irrelevant resources in computation and single pointer property for linear resources, can be derived from this theorem. We hope that our work will provide a base for integrating linearity, irrelevance and dependent types in practical programming languages like Haskell.



There are no comments yet.


page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.