Eberhard Karls Universität Tübingen

Mathematisch-Naturwissenschaftliche FakultätProgramming Languages and Software Technology

First-class functors

Yufei Cai
Yufei Cai
, Paolo Giarrusso
Paolo G. Giarrusso
, Klaus Ostermann
Klaus Ostermann


This is the homepage of the first-class functors project. Our goal is to support as many datatype-related functors as first-class objects as possible, as conveniently as possible. So far we managed to practically support regular functors and demonstrate type-soundness in the presence of higher-kinded functors.

Source code

The source code of a prototype library for first-class regular functors is available for free under the MIT license:

CREG: First-Class Regular Functors.

Email us questions.


Here are some slides of a talk at IFIP WG2.11 (Jan. 2015) by Klaus Ostermann
Klaus Ostermann

Paper (POPL 2016): System F-omega with Equirecursive Types for Datatype-generic Programming


Technical report version with full proofs.

Slides of paper presentation.

Abstract: Traversing an algebraic datatype by hand requires boilerplate code which duplicates the structure of the datatype. Datatype-generic programming (DGP) aims to eliminate such boilerplate code by decomposing algebraic datatypes into type constructor applications from which generic traversals can be synthesized. However, different traversals require different decompositions, which yield isomorphic but unequal types. This hinders the interoperability of different DGP techniques.

In this paper, we propose Fωμ, an extension of the higher-order polymorphic lambda calculus Fω with records, variants, and equirecursive types. We prove the soundness of the type system, and show that type checking for first-order recursive types is decidable with a practical type checking algorithm. In our soundness proof we define type equality by interpreting types as infinitary λ-terms (in particular, Berarducci-trees). To decide type equality we β-normalize types, and then use an extension of equivalence checking for usual equirecursive types.

Thanks to equirecursive types, new decompositions for a datatype can be added modularly and still interoperate with each other, allowing multiple DGP techniques to work together. We sketch how generic traversals can be synthesized, and apply these components to some examples.

Since the set of datatype decomposition becomes extensible, System Fωμ enables using DGP techniques incrementally, instead of planning for them upfront or doing invasive refactoring.


Paper accepted at POPL

Our paper on equirecursive types in System Fω, with title “System Fω with Equirecursive Types for Datatype-generic Programming”, has been accepted for presentation at the annual Symposium on Principles of Programming Languages.
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