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 relative 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 a prototype implementation of 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.


  • 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.