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Implicative Formulae in the `Proofs as Computations' Analogy.

Asperti, Andrea; Ferrari, Gian Luigi; Gorrieri, Roberto

In: Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, 1990, San Francisco, CA, USA, pages 59-71. New York, NY, USA: ACM, 1990.

Abstract: A correspondence between the subset of Linear Logic and Place/Transition Nets has been previously established. The authors study the fundamental connecitve of linear implication; the introduction of linear implication allows them to observe the net at a lower, more decentralized level of atomicity, where the preemption of each resource needed for the firing of a transition is represented as a separate move. They give a conservative theorem relating computations at different levels of abstraction. The categorical semantics establishes a tight correspondence among Petri nets, monoidal closed categories and tensor theories.

Keywords: implicative formula; linear logic; place/transition net; categorical semantics; monoidal closed category; tensor theory.

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