License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TLCA.2015.107
URN: urn:nbn:de:0030-drops-51580
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5158/
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Biernacki, Dariusz ; Polesiuk, Piotr

Logical Relations for Coherence of Effect Subtyping

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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.

BibTeX - Entry

@InProceedings{biernacki_et_al:LIPIcs:2015:5158,
  author =	{Dariusz Biernacki and Piotr Polesiuk},
  title =	{{Logical Relations for Coherence of Effect Subtyping}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{107--122},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Thorsten Altenkirch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5158},
  URN =		{urn:nbn:de:0030-drops-51580},
  doi =		{10.4230/LIPIcs.TLCA.2015.107},
  annote =	{Keywords: type system, coherence of subtyping, logical relation, control effect, continuation-passing style}
}

Keywords: type system, coherence of subtyping, logical relation, control effect, continuation-passing style
Collection: 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)
Issue Date: 2015
Date of publication: 15.06.2015

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