A strong call-by-need calculus (original) (raw)

A strong call-by-need calculusArticle

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Thibaut Balabonski;Antoine Lanco;Guillaume Melquiond

We present a call-by-need lambda\lambdalambda-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit substitutions and subsumes the existing strong-call-by-need strategy, but allows for more reduction sequences, and often shorter ones, while preserving the neededness. The calculus is shown to be normalizing in a strong sense: Whenever a lambda\lambdalambda-term t admits a normal form n in the lambda\lambdalambda-calculus, then any reduction sequence from t in the calculus eventually reaches a representative of the normal form n. We also exhibit a restriction of this calculus that has the diamond property and that only performs reduction sequences of minimal length, which makes it systematically better than the existing strategy. We have used the Abella proof assistant to formalize part of this calculus, and discuss how this experiment affected its design. In particular, it led us to derive a new description of call-by-need reduction based on inductive rules.

Volume: Volume 19, Issue 1

Secondary volumes: Selected Papers of the 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Published on: March 24, 2023

Accepted on: January 24, 2023

Submitted on: November 3, 2021

Keywords: Computer Science - Logic in Computer Science