Light Affine Logic (Proof Nets, Programming Notation, P-Time Correctness and Completeness)

Andrea Asperti; Luca Roversi

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arXiv · cs/0006010

Light Affine Logic (Proof Nets, Programming Notation, P-Time Correctness and Completeness)

Andrea Asperti·Luca Roversi

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Abstract

This paper is a structured introduction to Light Affine Logic, and to its intuitionistic fragment. Light Affine Logic has a polynomially costing cut elimination (P-Time correctness), and encodes all P-Time Turing machines (P-Time completeness). P-Time correctness is proved by introducing the Proof nets for Intuitionistic Light Affine Logic. P-Time completeness is demonstrated in full details thanks to a very compact program notation. On one side, the proof of P-Time correctness describes how the complexity of cut elimination is controlled, thanks to a suitable cut elimination strategy that exploits structural properties of the Proof nets. This allows to have a good catch on the meaning of the ``paragraph'' modality, which is a peculiarity of light logics. On the other side, the proof of P-Time completeness, together with a lot of programming examples, gives a flavor of the non trivial task of programming with resource limitations, using Intuitionistic Light Affine Logic derivations as programs.

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BibTeX RIS

Andrea Asperti, Luca Roversi. 2000-06-05. Light Affine Logic (Proof Nets, Programming Notation, P-Time Correctness and Completeness). https://arxiv.org/abs/cs/0006010

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