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Mirroring Call-By-Need, or Values Acting Silly

Authors Beniamino Accattoli , Adrienne Lancelot

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Beniamino Accattoli
  • Inria & LIX, Ecole Polytechnique, UMR 7161, France
Adrienne Lancelot
  • Inria & LIX, Ecole Polytechnique, UMR 7161, France
  • Université Paris Cité, CNRS, IRIF, Paris, France

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Beniamino Accattoli and Adrienne Lancelot. Mirroring Call-By-Need, or Values Acting Silly. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FSCD.2024.23

Abstract

Call-by-need evaluation for the λ-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name and call-by-value, namely silly duplications by-name and silly erasures by-value. We validate the design of the call-by-silly calculus via rewriting properties and multi types. In particular, we mirror the main theorem about call-by-need - that is, its operational equivalence with call-by-name - showing that call-by-silly and call-by-value induce the same contextual equivalence. This fact shows the blindness with respect to efficiency of call-by-value contextual equivalence. We also define a call-by-silly strategy and measure its length via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
Keywords
  • Lambda calculus
  • intersection types
  • call-by-value
  • call-by-need

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