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International Conference on Interactive Theorem Proving

ITP 2015: Interactive Theorem Proving pp 453–468Cite as

Pattern Matches in HOL:

A New Representation and Improved Code Generation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9236))

Abstract

Pattern matching is ubiquitous in functional programming and also very useful for definitions in higher-order logic. However, it is not directly supported by higher-order logic. Therefore, the parsers of theorem provers like HOL4 and Isabelle/HOL contain a pattern-compilation algorithm. Internally, decision trees based on case constants are used. For non-trivial case expressions, there is a big discrepancy between the user’s view and the internal representation.

This paper presents a new general-purpose representation for case expressions that mirrors the input syntax in the internal representation closely. Because of this close connection, the new representation is more intuitive and often much more compact. Complicated parsers and pretty printers are no longer required. Proofs can more closely follow the user’s intentions, and code generators can produce better code. Moreover, the new representation is more general than the currently used representation, supporting guards, patterns with multiple occurrences of the same bound variable, unbound variables, arithmetic expressions in patterns, and more. This work has been implemented in the HOL4 theorem prover and integrated into CakeML’s proof-producing code generator.

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Notes

  1. 1.

    The code can be found under: https://github.com/HOL-Theorem-Prover/HOL/examples/pattern_matches.

  2. 2.

    Compare function CASEWISE in define.ml.

  3. 3.

    See patternMatchesSyntax.

  4. 4.

    See e. g. PMATCH_SIMP_ss or PMATCH_REMOVE_GUARDS_ss.

  5. 5.

    See PMATCH_LIFT_BOOL_ss.

  6. 6.

    See e. g. PMATCH_CASE_SPLIT_ss.

  7. 7.

    See COMPUTE_REDUNDANT_ROWS_INFO_OF_PMATCH and

    PMATCH_IS_EXHAUSTIVE_CONSEQ_CONV.

  8. 8.

    See PMATCH_REMOVE_REDUNDANT_ss.

  9. 9.

    See /src/1/PmatchHeuristics.sig in the HOL4 sources.

  10. 10.

    See e. g. HOL4’s Description Manual Sect. 4.5.2 or Isabelle/HOL’s manual Defining Recursive Functions in Isabelle/HOL Sect. 10.1.

  11. 11.

    See PMATCH_IS_EXHAUSTIVE_CONSEQ_CONV.

  12. 12.

    See PMATCH_REMOVE_REDUNDANT_ss.

  13. 13.

    Our code generator renames variables. Here x has become v5, for example.

  14. 14.

    The exceptions are non-constructor patterns that are not part of a constructor family.

References

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Acknowledgements

The second author was partially supported by the Royal Society UK and the Swedish Research Council.

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Authors and Affiliations

  1. Independent Scholar, Brechen, Germany

    Thomas Tuerk

  2. CSE Department, Chalmers University of Technology, Gothenburg, Sweden

    Magnus O. Myreen

  3. Computer Laboratory, University of Cambridge, Cambridge, UK

    Magnus O. Myreen & Ramana Kumar

Authors
  1. Thomas Tuerk
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  2. Magnus O. Myreen
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  3. Ramana Kumar
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Corresponding author

Correspondence to Thomas Tuerk .

Editor information

Editors and Affiliations

  1. Department of Informatics, King's College London, London, United Kingdom

    Christian Urban

  2. PLA University of Science and Technology, Nanjing, China

    Xingyuan Zhang

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Tuerk, T., Myreen, M.O., Kumar, R. (2015). Pattern Matches in HOL:. In: Urban, C., Zhang, X. (eds) Interactive Theorem Proving. ITP 2015. Lecture Notes in Computer Science(), vol 9236. Springer, Cham. https://doi.org/10.1007/978-3-319-22102-1_30

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  • DOI: https://doi.org/10.1007/978-3-319-22102-1_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22101-4

  • Online ISBN: 978-3-319-22102-1

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