License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.20
URN: urn:nbn:de:0030-drops-180049
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Dal Lago, Ugo ; Hoshino, Naohiko ; Pistone, Paolo

On the Lattice of Program Metrics

LIPIcs-FSCD-2023-20.pdf (0.9 MB)


In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as those based on the interpretation of terms in metric spaces and those obtained by generalizing observational equivalence. We also introduce a new one, called the interactive metric, built by applying the well-known Int-Construction to the category of metric complete partial orders. Our aim is then to understand how these metrics relate to each other, i.e., whether and in which cases one such metric refines another, in analogy with corresponding well-studied problems about program equivalences. The results we obtain are twofold. We first show that the metrics of semantic origin, i.e., the denotational and interactive ones, lie in between the observational and equational metrics and that in some cases, these inclusions are strict. Then, we give a result about the relationship between the denotational and interactive metrics, revealing that the former is less discriminating than the latter. All our results are given for a linear lambda-calculus, and some of them can be generalized to calculi with graded comonads, in the style of Fuzz.

BibTeX - Entry

  author =	{Dal Lago, Ugo and Hoshino, Naohiko and Pistone, Paolo},
  title =	{{On the Lattice of Program Metrics}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-180049},
  doi =		{10.4230/LIPIcs.FSCD.2023.20},
  annote =	{Keywords: Metrics, Lambda Calculus, Linear Types}

Keywords: Metrics, Lambda Calculus, Linear Types
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023

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