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.FSCD.2020.15
URN: urn:nbn:de:0030-drops-123376
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12337/
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Ivašković, Andrej ; Mycroft, Alan ; Orchard, Dominic

Data-Flow Analyses as Effects and Graded Monads

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LIPIcs-FSCD-2020-15.pdf (0.8 MB)

Abstract

In static analysis, two frameworks have been studied extensively: monotone data-flow analysis and type-and-effect systems. Whilst both are seen as general analysis frameworks, their relationship has remained unclear. Here we show that monotone data-flow analyses can be encoded as effect systems in a uniform way, via algebras of transfer functions. This helps to answer questions about the most appropriate structure for general effect algebras, especially with regards capturing control-flow precisely. Via the perspective of capturing data-flow analyses, we show the recent suggestion of using effect quantales is not general enough as it excludes non-distributive analyses e.g., constant propagation. By rephrasing the McCarthy transformation, we then model monotone data-flow effects via graded monads. This provides a model of data-flow analyses that can be used to reason about analysis correctness at the semantic level, and to embed data-flow analyses into type systems.

BibTeX - Entry

@InProceedings{ivakovi_et_al:LIPIcs:2020:12337,
  author =	{Andrej Iva{\v{s}}ković and Alan Mycroft and Dominic Orchard},
  title =	{{Data-Flow Analyses as Effects and Graded Monads}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Zena M. Ariola},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12337},
  URN =		{urn:nbn:de:0030-drops-123376},
  doi =		{10.4230/LIPIcs.FSCD.2020.15},
  annote =	{Keywords: data-flow analysis, effect systems, graded monads, correctness}
}

Keywords: data-flow analysis, effect systems, graded monads, correctness
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020
Supplementary Material: Code and additional proofs: https://doi.org/10.5281/zenodo.3784967

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