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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2014.72
URN: urn:nbn:de:0030-drops-54921
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5492/
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Danvy, Olivier ; Keller, Chantal ; Puech, Matthias

Typeful Normalization by Evaluation

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Abstract

We present the first typeful implementation of Normalization by Evaluation for the simply typed lambda-calculus with sums and control operators: we guarantee type preservation and eta-long (modulo commuting conversions), beta-normal forms using only Generalized Algebraic Data Types in a general-purpose programming language, here OCaml; and we account for sums and control operators with Continuation-Passing Style. First, we implement the standard NbE algorithm for the implicational fragment in a typeful way that is correct by construction. We then derive its call-by-value continuation-passing counterpart, that maps a lambda-term with sums and call/cc into a CPS term in normal form, which we express in a typed dedicated syntax. Beyond showcasing the expressive power of GADTs, we emphasize that type inference gives a smooth way to re-derive the encodings of the syntax and typing of normal forms in Continuation-Passing Style.

BibTeX - Entry

@InProceedings{danvy_et_al:LIPIcs:2015:5492,
  author =	{Olivier Danvy and Chantal Keller and Matthias Puech},
  title =	{{Typeful Normalization by Evaluation}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{72--88},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Hugo Herbelin and Pierre Letouzey and Matthieu Sozeau},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5492},
  URN =		{urn:nbn:de:0030-drops-54921},
  doi =		{10.4230/LIPIcs.TYPES.2014.72},
  annote =	{Keywords: Normalization by Evaluation, Generalized Algebraic Data Types, Continuation-Passing Style, partial evaluation}
}

Keywords: Normalization by Evaluation, Generalized Algebraic Data Types, Continuation-Passing Style, partial evaluation
Seminar: 20th International Conference on Types for Proofs and Programs (TYPES 2014)
Issue Date: 2015
Date of publication: 29.09.2015


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