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• W2951685654 abstract "Since the very beginning of the theory of linear logic it is known how to represent the $lambda$-calculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of sharing---the exponentials---and a micro-step operational semantics, while the $lambda$-calculus has no sharing and a small-step operational semantics. Here we show that the emph{linear substitution calculus}, a simple refinement of the $lambda$-calculus with sharing, is isomorphic to proof nets at the operational level. Nonetheless, two different terms with sharing can still have the same proof nets representation---a further result is the characterisation of the equality induced by proof nets over terms with sharing. Finally, such a detailed analysis of the relationship between terms and proof nets, suggests a new, abstract notion of proof net, based on rewriting considerations and not necessarily of a graphical nature." @default.
• W2951685654 created "2019-06-27" @default.
• W2951685654 creator A5046873607 @default.
• W2951685654 date "2018-08-10" @default.
• W2951685654 modified "2023-09-26" @default.
• W2951685654 title "Proof Nets and the Linear Substitution Calculus" @default.
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• W2951685654 hasPublicationYear "2018" @default.
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