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v2 (2008-01-29)

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A semantic measure of the execution time in Linear Logic

Daniel De Carvalho 1, Michele Pagani 2, Lorenzo Tortora De Falco 3

(2008)

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 (proof-)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 define a size on every experiment of a net, and we precisely relate the number of cut-elimination steps of every stratified reduction sequence to the size of a particular experiment. Finally, we 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.

1:	CALLIGRAMME (INRIA Lorraine - LORIA)
	INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2:	Preuves, Programmes et Systèmes (PPS)
	CNRS : UMR7126 – Université Paris VII - Paris Diderot
3:	Dipartimento di Filosofia dell'Universita Roma Tre
	Universita Roma Tre

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Computer Science/Logic in Computer Science

inria-00206099, version 3

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From: Daniel De Carvalho <>

Submitted on: Friday, 1 February 2008 19:38:22

Updated on: Saturday, 2 February 2008 11:40:54