
Proof nets for the Displacement calculus
We present a proof net calculus for the Displacement calculus and show i...
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Neural Proof Nets
Linear logic and the linear λcalculus have a long standing tradition in...
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Formal Smallstep Verification of a Callbyvalue Lambda Calculus Machine
We formally verify an abstract machine for a callbyvalue lambdacalcul...
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Sharing Equality is Linear
The λcalculus is a handy formalism to specify the evaluation of higher...
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Towards a Homotopy Domain Theory (HoDT)
A favourable environment is proposed for the achievement of λmodels wit...
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A theory of linear typings as flows on 3valent graphs
Building on recently established enumerative connections between lambda ...
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Divergence and unique solution of equations
We study proof techniques for bisimilarity based on unique solution of e...
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Proof Nets and the Linear Substitution Calculus
Since the very beginning of the theory of linear logic it is known how to represent the λcalculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of sharingthe exponentialsand a microstep operational semantics, while the λcalculus has no sharing and a smallstep operational semantics. Here we show that the linear substitution calculus, a simple refinement of the λcalculus with sharing, is isomorphic to proof nets at the operational level. Nonetheless, two different terms with sharing can still have the same proof nets representationa 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.
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