A Predictable Unification Algorithm for Coq Featuring Universe Polymorphism and Overloading

Speaker: Matthieu Sozeau , INRIA

Date: Wednesday, April 29, 2015

Time: 11:00 AM to 12:00 PM

Public: Yes

Location: 32-G449 (Patil/Kiva)

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Host: Adam Chlipala, CSAIL

Contact: Adam Chlipala, adamc@csail.mit.edu

Relevant URL: http://www.pps.univ-paris-diderot.fr/~sozeau/

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Reminders to: seminars@csail.mit.edu, pl@csail.mit.edu

Reminder Subject: TALK: A Predictable Unification Algorithm for Coq Featuring Universe Polymorphism and Overloading

Unification is a core component of every proof assistant or programming language featuring dependent types. In many cases, it must deal with higher-order problems up to conversion. Since unification in such conditions is undecidable, unification algorithms may include several heuristics to solve common problems. However, when the stack of heuristics grows large, the result and complexity of the algorithm can become unpredictable.

We present a full description of a new unification algorithm for the Calculus of Inductive Constructions (the base logic of Coq), including universe polymorphism, canonical structures (the overloading mechanism baked into Coq’s unification), and a small set of useful heuristics. We implemented our algorithm, and tested it on several libraries, providing evidence that the selected set of heuristics suffices for large developments.

Joint work with Beta Ziliani (MPI Saarbrucken)

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Created by Adam Chlipala Email at Sunday, April 26, 2015 at 8:09 PM.