On Constructor Rewrite Systems and the Lambda Calculus

Ugo Dal Lago 1, 2 Simone Martini 1, 2
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In particular, weak call-by-value beta-reduction can be simulated by an orthogonal constructor term rewrite system in the same number of reduction steps. Conversely, each reduction in a term rewrite system can be simulated by a constant number of beta-reduction steps. This is relevant to implicit computational complexity, because the number of beta steps to normal form is polynomially related to the actual cost (that is, as performed on a Turing machine) of normalization, under weak call-by-value reduction. Orthogonal constructor term rewrite systems and lambda-calculus are thus both polynomially related to Turing machines, taking as notion of cost their natural parameters.
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https://hal.inria.fr/hal-00909372
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Submitted on : Tuesday, November 26, 2013 - 11:08:16 AM
Last modification on : Friday, July 5, 2019 - 1:18:51 AM

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Ugo Dal Lago, Simone Martini. On Constructor Rewrite Systems and the Lambda Calculus. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, 8 (3). ⟨hal-00909372⟩

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