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European Symposium on Programming

ESOP 2021: Programming Languages and Systems pp 462–490Cite as

Graded Modal Dependent Type Theory

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12648)

Abstract

Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with quantitative dataflow tracking, usually via a semiring-like structure which provides analysis on variables (often called ‘quantitative’ or ‘coeffect’ theories). We present Graded Modal Dependent Type Theory (Grtt for short), which equips a dependent type theory with a general, parameterizable analysis of the flow of data, both in and between computational terms and types. In this theory, it is possible to study, restrict, and reason about data use in programs and types, enabling, for example, parametric quantifiers and linearity to be captured in a dependent setting. We propose Grtt, study its metatheory, and explore various case studies of its use in reasoning about programs and studying other type theories. We have implemented the theory and highlight the interesting details, including showing an application of grading to optimising the type checking procedure itself.

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Authors and Affiliations

  1. University of Kent, Canterbury, UK

    Benjamin Moon & Dominic Orchard

  2. Augusta University, Augusta, USA

    Harley Eades III

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  1. Benjamin Moon
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  2. Harley Eades III
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  1. Imperial College, London, UK

    Nobuko Yoshida

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Moon, B., Eades III, H., Orchard, D. (2021). Graded Modal Dependent Type Theory. In: Yoshida, N. (eds) Programming Languages and Systems. ESOP 2021. Lecture Notes in Computer Science(), vol 12648. Springer, Cham. https://doi.org/10.1007/978-3-030-72019-3_17

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