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Tue 21 Jan 2020 10:30 - 10:51 at Maurepas - Mechanized metatheory Chair(s): Benjamin C. Pierce

The mechanisation of the meta-theory of programming languages is still considered hard and requires considerable effort. When formalising properties of the extension of a language, one hence wants to reuse definitions and proofs. But type-theoretic proof assistants use inductive types and predicates to formalise syntax and type systems, and these definitions are closed to extensions. Available approaches for modular syntax are either inapplicable to type theory or add a layer of indirectness by requiring complicated encodings of types.

We present a concise, transparent, and accessible approach to modular syntax with binders by adapting Swierstra’s Data Types à la Carte approach to the Coq proof assistant in an ad-hoc way. Our approach relies on two phases of code generation: We extend the Autosubst~2 tool and allow users to specify modular syntax with binders in a HOAS-like input language. To state and automatically compose modular functions and lemmas, we implement commands based on MetaCoq. We support modular syntax, functions, predicates, and theorems.

We demonstrate the practicality of our approach by modular proofs of preservation, weak head normalisation, and strong normalisation for several variants of mini-ML.

Tue 21 Jan
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10:30 - 11:35: CPP 2020 - Mechanized metatheory at Maurepas
Chair(s): Benjamin C. PierceUniversity of Pennsylvania
CPP-2020-papers10:30 - 10:51
Yannick ForsterSaarland University, Kathrin StarkSaarland University, Germany
DOI Pre-print Media Attached
CPP-2020-papers10:51 - 11:13
Tomás DíazIMFD Chile, Federico OlmedoUniversity of Chile & IMFD Chile, Éric TanterUniversity of Chile
DOI Pre-print Media Attached File Attached
CPP-2020-papers11:13 - 11:35
Danil AnnenkovConcordium Blockchain Research Center, Aarhus University, Jakob Botsch NielsenConcordium Blockchain Research Center, Aarhus University, Bas SpittersConcordium Blockchain Research Center, Aarhus University
DOI Pre-print Media Attached File Attached