# Graded Modal Dependent Type Theory

@article{Moon2021GradedMD, title={Graded Modal Dependent Type Theory}, author={Benjamin Moon and Harley D. Eades and Dominic A. Orchard}, journal={Programming Languages and Systems}, year={2021}, volume={12648}, pages={462 - 490} }

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…

## 4 Citations

Idris 2: Quantitative Type Theory in Practice

- Computer ScienceECOOP
- 2021

This paper introduces Idris 2, and describes how QTT has influenced its design, and gives examples of the benefits of QTT in practice including: expressing which data is erased at run time, at the type level; and, resource tracking in the type system leading to type-safe concurrent programming with session types.

A Dependent Dependency Calculus (Extended Version)

- Computer ScienceArXiv
- 2022

A Dependent Dependency Calculus (DDC) is presented, which extends this general idea to the setting of a dependently-typed language, and is used to track both run-time and compile-time irrelevance, enabling faster typechecking and program execution.

Replicate, Reuse, Repeat: Capturing Non-Linear Communication via Session Types and Graded Modal Types

- Computer SciencePLACES@ETAPS
- 2022

This paper shows how graded modal types can be leveraged alongside session types to enable various non-linear concurrency behaviours to be re-introduced in a precise manner in a type system with a linear basis.

Logical Foundations of Quantitative Equality (long version)

- Computer ScienceArXiv
- 2021

A deductive calculus for (Graded) Linear Logic with quantitative equality and the notion of Lipschitz doctrine to give semantics to it is introduced, using the categorical language of Lawvere’s hyperdoctrines.

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