Logical relations for coherence of effect subtyping
Abstract
A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing.
Keywords
Cite
@article{arxiv.1710.09469,
title = {Logical relations for coherence of effect subtyping},
author = {Dariusz Biernacki and Piotr Polesiuk},
journal= {arXiv preprint arXiv:1710.09469},
year = {2023}
}