Principal type scheme and unification for intersection type discipline
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Complete restrictions of the intersection type discipline
Theoretical Computer Science
Lambda-calculus, types and models
Lambda-calculus, types and models
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
Une Extension de la Theorie des Types en lambda-Calcul
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Standardization and Confluence for a Lambda Calculus with Generalized Applications
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Intersection types for explicit substitutions
Information and Computation
THEORETICAL PEARLS: A bargain for intersection types: a simple strong normalization proof
Journal of Functional Programming
Intersection and Union Types in the λμμ~-calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Permutative conversions in intuitionistic multiary sequent calculi with cuts
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Completing Herbelin's programme
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Simple proofs of characterizing strong normalization for explicit substitution calculi
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Characterising strongly normalising intuitionistic sequent terms
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Note: A note on preservation of strong normalisation in the λ-calculus
Theoretical Computer Science
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This paper gives a characterisation, via intersection types, of the strongly normalising proof-terms of an intuitionistic sequent calculus where LJ easily embeds. The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary λ-calculus. The completeness of the typing system is obtained from subject expansion at root position. Next we use our result to analyze the characterisation of strong normalisability for three classes of intuitionistic terms: ordinary λ-terms, ΛJ-terms λ-terms with generalised application, and λx-terms λ-terms with explicit substitution. We explain via our system why the type systems in the natural deduction format for ΛJ and λx known from the literature contain extra, exceptional rules for typing generalised application or substitution; and we show a new characterisation of the β-strongly normalising λ-terms, as a corollary to a PSN-result, relating the λ-calculus and the intuitionistic sequent calculus. Finally, we obtain variants of our characterisation by restricting the set of assignable types to sub-classes of intersection types, notably strict types. In addition, the known characterisation of the β-strongly normalising λ-terms in terms of assignment of strict types follows as an easy corollary of our results.