Theoretical Computer Science
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proof-nets and the Hilbert space
Proceedings of the workshop on Advances in linear logic
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A λ-calculus with explicit weakening and explicit substitution
Mathematical Structures in Computer Science
Resource operators for λ-calculus
Information and Computation
Perpetuality for Full and Safe Composition (in a Constructive Setting)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Strong normalization property for second order linear logic
Theoretical Computer Science
Jumping boxes: representing lambda-calculus boxes by jumps
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Confluence of pure differential nets with promotion
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
A prismoid framework for languages with resources
Theoretical Computer Science
Extending the explicit substitution paradigm
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
On Explicit Substitution with Names
Journal of Automated Reasoning
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We refine the simulation technique introduced in Di Cosmo and Kesner (1997) to show strong normalisation of $\l$-calculi with explicit substitutions via termination of cut elimination in proof nets (Girard 1987). We first propose a notion of equivalence relation for proof nets that extends the one in Di Cosmo and Guerrini (1999), and show that cut elimination modulo this equivalence relation is terminating. We then show strong normalisation of the typed version of the $\ll$-calculus with de Bruijn indices (a calculus with full composition defined in David and Guillaume (1999)) using a translation from typed $\ll$ to proof nets. Finally, we propose a version of typed $\ll$ with named variables, which helps to give a better understanding of the complex mechanism of the explicit weakening notation introduced in the $\ll$-calculus with de Bruijn indices (David and Guillaume 1999).