The Granule Project

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The Granule project is an ambitious research project whose focus is to capture more and more intensional properties of programs at the type-level, that is, how a program computes not just what it computes. Our primary mechanism for doing this is via the relatively new notion of graded types in concert with other typing mechanisms like linear types and dependent types. For example, graded modal types can be combined with linear types to make resource sensitivity an integral aspect of a programming language, precisely enforcing resource usage throughout the language. Other examples include capturing fine-grained information about side effects, data use, privacy levels, cost, and permissions via various kinds of (co)effect types captures via graded modal types.

Our project spans theoretical and practical work. We are actively developing an implementation of a language with graded, linear, and indexed types called Granule based on our research. In addition, we are developing a new dependent type theory that will greatly expand the expressive power of Granule’s type system. This is currently implemented in another language called Gerty.


  • April 2024 paper

    We are excited to announce two new publications from our group:

  • September 2023 staff

    Riccardo Bianchini is visiting us for two weeks in September, and talking about his work on multi-graded Featherweight Java.

  • July 2023 misc

    Dominic presented the work of the Granule project in 6 hours of teaching at the Scottish Programming Languages and Verification summer school.

  • January 2023 staff

    Congratulations to Dr Marco Paviotti on getting a lectureship at Kent! Thankfully Marco will still be working with us in his new role. Well done Marco!

  • May 2022 staff

    We are very pleased to welcome Dr Marco Paviotti to the project at the University of Kent. Marco joins as a Senior Research Associate with expertise in semantics, category theory, recursion schemes, and mathematical logic.

  • March 2022 paper

    Daniel and Dominic have a new paper accepted at PLACES 2022 on capturing various kinds of non-linear communication and concurrent behaviour in a type-based discipline by combining session types and graded types.

  • February 2022 paper

    Daniel and Dominic have a pearl accepted to ECOOP 2022 on how linear functions consuming values can be understood algebraically as a multiplicative inverse to the type of those values, discussing some of the applications using both Haskell and Granule. This paper won a Distinguished Paper Award and a Distinguished Artifact Award.

  • January 2022 paper

    Daniel, Michael and Dominic have a paper accepted to ESOP 2022 on unifying the closely related notions of linearity and uniqueness in a single type system, and implementing this theory to demonstrate the practical benefits of uniqueness types in Granule.

  • January 2022 award

    Daniel has been awarded first place in the Student Research Competition at POPL 2022, for his ongoing work on unifying the closely related concepts of linearity, uniqueness and ownership using Granule’s expressive type system.

  • June 2021 paper

    The Granule project has an abstract accepted for presentation at TLLA 2021:

  • May 2021 job award

    Harley has been awarded a National Science Foundation grant on:

    Semantically and Practically Generalizing Graded Modal Types

    to recruit a PhD Student and continue his work on exploring the expressive power of the theory of graded modal types. Checkout the blog post here.

  • March 2021 implementation

    We are excited to release Gerty v0.1.0, our implementation of our work on graded modal dependent type theory.

  • December 2020 paper

    • We made an “end of the year review” video summarising what we have been up to in 2020. Watch on Youtube.

    • Ben, Harley, and Dominic have a new paper on a new graded modal dependent type theory entitled “Graded Modal Dependent Type Theory”. To appear at ESOP 2021. Find the preprint here.

  • November 2020 paper

    Harley has a new paper on a new graded dependent type system called \(\GraD{}\) entitled “A graded dependent type system with a usage-aware semantics”, joint work with Pritram Choudhury, Richard A. Eisenberg, and Stephanie Weirich. To appear at POPL 2021. Find the preprint here.

  • October 2020 paper

    We have two new draft papers online (under review):

  • September 2020 paper award

    Jack and Dominic have a new paper about program synthesis from linear and graded modal types, demonstrated in Granule, accepted to LOPSTR 2020, entitled “Resourceful Program Synthesis from Graded Linear Types”. The version from the pre-proceedings can be found here. This paper won the LOPSTR 2020 Best Paper Award.

  • June 2020 paper

    The Granule project had three abstracts accepted for presentation at LINEARITY/TLLA 2020:

    • Jack Hughes and Dominic Orchard. Deriving distributive laws for graded linear types
    • Aubrey Bryant and Harley Eades III. The Graded Lambek Calculus
    • Harley Eades III and Dominic Orchard. Grading Adjoint Logic

    For full access to each abstract see the Publications section.

  • April 2020 paper

    Dominic has a new paper capturing classical data flow analysis via graded monadic semantics accepted to FSCD 2020, entitled “Data-flow analyses as effects and graded monads”, joint with Andrej Ivašković and Alan Mycroft. in the proceedings here.

  • March 2020 job

    The Granule project is hiring a 2-year post-doctoral researcher to work at the University of Kent! Details of how to apply here. Closing date for applications is Friday 8th May 2020.

  • March 2020 paper

    We have a new paper on the relationship between graded monads and parameterised monads accepted to MSFP 2020. Preprint available online, updated to the final version soon.