Practical dependent type checking using twin types
Paper in proceeding, 2020

People writing proofs or programs in dependently typed languages can omit some function arguments in order to decrease the code size and improve readability. Type checking such a program involves filling in each of these implicit arguments in a type-correct way. This is typically done using some form of unification.

One approach to unification, taken by Agda, involves sometimes starting to unify terms before their types are known to be equal: in some cases one can make progress on unifying the terms, and then use information gleaned in this way to unify the types. This flexibility allows Agda to solve implicit arguments that are not found by several other systems. However, Agda's implementation is buggy: sometimes the solutions chosen are ill-typed, which can cause the type checker to crash.

With Gundry and McBride's twin variable technique one can also start to unify terms before their types are known to be equal, and furthermore this technique is accompanied by correctness proofs. However, so far this technique has not been tested in practice as part of a full type checker.

We have reformulated Gundry and McBride's technique without twin variables, using only twin types, with the aim of making the technique easier to implement in existing type checkers (in particular Agda). We have also introduced a type-agnostic syntactic equality rule that seems to be useful in practice. The reformulated technique has been tested in a type checker for a tiny variant of Agda. This type checker handles at least one example that Coq, Idris, Lean and Matita cannot handle, and does so in time and space comparable to that used by Agda. This suggests that the reformulated technique is usable in practice.

type checking

dependent types

unification

Author

Víctor López Juan

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Nils Anders Danielsson

University of Gothenburg

TyDe 2020 - Proceedings of the 5th ACM SIGPLAN International Workshop on Type-Driven Development, co-located with ICFP 2020

11-23

5th ACM SIGPLAN International Workshop on Type-Driven Development
Virtual Event, USA,

Roots

Basic sciences

Subject Categories

Computer Science

DOI

10.1145/3406089.3409030

Related datasets

Benchmark data for "Practical Dependent Type Checking Using Twin Types" [dataset]

DOI: 10.5281/zenodo.3924267

More information

Latest update

9/22/2023