Proof Nets and Explicit Substitutions
Roberto Di Cosmo,Delia Kesner,Emmanuel Polonovski +2 more
- pp 63-81
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The simulation technique introduced in [10] is refined to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets and a version of typed λl with named variables is proposed which helps to better understand the complex mechanism of the explicit weakening notation.Abstract:
We refine the simulation technique introduced in [10] to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets [13]. We first propose a notion of equivalence relation for proof nets that extends the one in [9], and we show that cut elimination modulo this equivalence relation is terminating. We then show strong normalization of the typed version of the λl-calculus with de Bruijn indices (a calculus with full composition defined in [8]) using a translation from typed λl to proof nets. Finally, we propose a version of typed λl with named variables which helps to better understand the complex mechanism of the explicit weakening notation introduced in the λl-calculus with de Bruijn indices [8].read more
Citations
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Posted ContentDOI
Study of Behaviours via Visitable Paths
TL;DR: In this article, a design is viewed as a set of coherent paths, where a visitable path is a path in a design or a set that may be traversed by interaction with a design of the orthogonal of the set.
Intuitionistic Differential Nets and Resource Lambda-Calculus
TL;DR: The translation of Boudol's untypedλ-calculus with multiplicities extended withalinear-nonlinearreduction ` ala Ehrhard and Regnier’s differentialinteractionnets with theexponentialbox ofLinearLogic is directed and adjusted to give a translation of the exponential reduction and confluence of the full one.
Proceedings Article
Strong Normalization of the Typed lambda ws-calculus
René David,Bruno Guillaume +1 more
TL;DR: The lambda ws-calculus as mentioned in this paper is a lambda calculus with explicit substitutions, and it is known to preserve strong normalization of usual lambda calculus and to be strongly normalizable for simply typed lambda terms.
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