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Article Dans Une Revue Theoretical Computer Science Année : 2011

A semantic measure of the execution time in linear logic

Résumé

We give a semantic account of the execution time (i.e. the number of cut elimination steps leading to the normal form) of an untyped MELL net. We first prove that: 1) a net is head-normalizable (i.e. normalizable at depth 0) if and only if its interpretation in the multiset based relational semantics is not empty and 2) a net is normalizable if and only if its exhaustive interpretation (a suitable restriction of its interpretation) is not empty. We then give a semantic measure of execution time: we prove that we can compute the number of cut elimination steps leading to a cut free normal form of the net obtained by connecting two cut free nets by means of a cut-link, from the interpretations of the two cut free nets. These results are inspired by similar ones obtained by the first author for the untyped lambda-calculus.

Dates et versions

hal-00698976 , version 1 (18-05-2012)

Identifiants

Citer

Michele Pagani. A semantic measure of the execution time in linear logic. Theoretical Computer Science, 2011, 412 (20), pp.1884-1902. ⟨10.1016/j.tcs.2010.12.017⟩. ⟨hal-00698976⟩
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