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PREUVES, PROGRAMMES et SYSTÈMES |  |
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PREUVES, PROGRAMMES et SYSTÈMES | |
| HAL: hal-00153136, version 1 |
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| Symposium on Logic in Computer Science (LICS '07), Wroclaw : Pologne (2007) |
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| Light Logics and Optimal Reduction: Completeness and Complexity. |
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| Patrick Baillot 1Paolo Coppola 2 |
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| (2007) |
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| Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial (elementary, resp.) bound; on the other hand these terms can also be evaluated by optimal reduction using the abstract version of Lamping's algorithm. The first reduction is global while the second one is local and asynchronous. We prove that for LAL (EAL, resp.) typed terms, Lamping's abstract algorithm also admits a polynomial (elementary, resp.) bound. We also show its soundness and completeness (for EAL and LAL with type fixpoints), by using a simple geometry of interaction model (context semantics). |
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| 1: | Laboratoire d'informatique de Paris-nord (LIPN) |
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CNRS : UMR7030 – Université Paris XIII - Paris Nord |
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| 2: | Dipartimento di Matematica e Informatica, Università di Udine |
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Università di Udine |
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| 3: | Preuves, Programmes et Systèmes (PPS) |
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CNRS : UMR7126 – Université Paris VII - Paris Diderot |
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| 4: | Università di Bologna (UNIBO) |
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Università degli studi di Bologna |
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| Subject | : | Computer Science/Logic in Computer Science |
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| lambda calculus – linear logic – implicit computational complexity – optimal reduction – proof-nets |
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| hal-00153136, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00153136 | |
| oai:hal.archives-ouvertes.fr:hal-00153136 | |
| From: Patrick Baillot | |
| Submitted on: Friday, 8 June 2007 13:48:31 | |
| Updated on: Tuesday, 19 June 2007 19:08:24 | |
