Relating System F and Lambda2: A Case Study in Coq, Abella and Beluga ...

We give three formalisations of a proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system (PTS) variant Lambda2. This is established by reducing the typability problem of F to Lambda2 and vice versa. A key challenge is the treatment of variab...

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Bibliographic Details
Main Authors: Kaiser, Jonas, Pientka, Brigitte, Smolka, Gert
Format: Conference Object
Language:English
Published: Schloss Dagstuhl – Leibniz-Zentrum für Informatik 2017
Subjects:
Pure Type Systems
System F
de Bruijn Syntax
Higher-Order Abstract Syntax
Contextual Reasoning
Beluga
Beluga*
Online Access:https://dx.doi.org/10.4230/lipics.fscd.2017.21
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.21
Description
Summary:We give three formalisations of a proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system (PTS) variant Lambda2. This is established by reducing the typability problem of F to Lambda2 and vice versa. A key challenge is the treatment of variable binding and contextual information. The formalisations all share the same high level proof structure using relations to connect the type systems. They do, however, differ significantly in their representation and manipulation of variables and contextual information. In Coq, we use pure de Bruijn indices and parallel substitutions. In Abella, we use higher-order abstract syntax (HOAS) and nominal constants of the ambient reasoning logic. In Beluga, we also use HOAS but within contextual modal type theory. Our contribution is twofold. First, we present and compare a collection of machine-checked solutions to a non-trivial theoretical result. Second, we propose our proof as a benchmark, complementing the POPLmark ... : LIPIcs, Vol. 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017), pages 21:1-21:19 ...

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