Linear β-reduction

Stefano Guerrini
(LIPN, Institut Galilée, Université Paris Nord 13, Sorbonne Paris Cité)

Linear head reduction is a key tool for the analysis of reduction machines for lambda-calculus and for game semantics. Its definition requires a notion of redex at a distance named primary redex in the literature. Nevertheless, a clear and complete syntactic analysis of this rule is missing. We present here a general notion of beta-reduction at a distance and of linear reduction (i.e., not restricted to the head variable), and we analyse their relations and properties. This analysis rests on a variant of the so-called sigma-equivalence that is more suitable for the analysis of reduction machines, since the position along the spine of primary redexes is not permuted. We finally show that, in the simply typed case, the proof of strong normalisation of linear reduction can be obtained by a trivial tuning of Gandy's proof for strong normalisation of beta-reduction.

In Iliano Cervesato and Maribel Fernández: Proceedings Fourth International Workshop on Linearity (LINEARITY 2016), Porto, Portugal, 25 June 2016, Electronic Proceedings in Theoretical Computer Science 238, pp. 44–53.
Published: 17th January 2017.

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