Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti - Archive ouverte HAL Access content directly
Reports (Technical Report) Year : 2024

Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti

Abstract

Proof assistants such as Coq implement a type theory featuring three important features: impredicativity, cumulativity and product covariance. This combination has proven difficult to be expressed in the logical framework Dedukti, and previous attempts have failed in providing an encoding that is proven confluent, sound and conservative. In this work we solve this longstanding open problem by providing an encoding of these three features that we prove to be confluent, sound and to satisfy a restricted (but, we argue, strong enough) form of conservativity. Our proof of confluence is a contribution by itself, and combines various criteria and proof techniques from rewriting theory. Our proof of soundness also contributes a new strategy in which the result is shown in terms of an inverse translation function, fixing a common flaw made in some previous encoding attempts.
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Dates and versions

hal-04470850 , version 1 (21-02-2024)
hal-04470850 , version 2 (07-05-2024)

Identifiers

  • HAL Id : hal-04470850 , version 2

Cite

Thiago Felicissimo, Théo Winterhalter. Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti. Deducteam - Inria Paris-Saclay / ENS Paris-Saclay. 2024. ⟨hal-04470850v2⟩
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