A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the first ACM SIGPLAN international conference on Functional programming
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Terminiation of permutative conversions in intuitionistic Gentzen calculi
Theoretical Computer Science - Special issue: Gentzen
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
CPS Translations and Applications: The Cube and Beyond
Higher-Order and Symbolic Computation
Standardization and Confluence for a Lambda Calculus with Generalized Applications
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Continuation models are universal for lambda-mu-calculus
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Strong normalization proofs by CPS-translations
Information Processing Letters
Permutative conversions in intuitionistic multiary sequent calculi with cuts
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
A sequent calculus for type theory
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Monadic Translation of Intuitionistic Sequent Calculus
Types for Proofs and Programs
A calculus of multiary sequent terms
ACM Transactions on Computational Logic (TOCL)
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The intuitionistic fragment of the call-by-name version of Curien and Herbelin's ???µ???-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed λ-calculus. Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's λµ-calculus. The embedding simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding.