Principal type scheme and unification for intersection type discipline
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Intersection type assignment systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
What are principal typings and what are they good for?
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher order unification via explicit substitutions
Information and Computation
A Decidable Intersection Type System based on Relevance
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
PLILPS '95 Proceedings of the 7th International Symposium on Programming Languages: Implementations, Logics and Programs
Characterization of the Principal Type of Normal Forms in an Intersection Type System
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
The λse-calculus does not preserve strong normalisation
Journal of Functional Programming
Journal of Functional Programming
Principality and type inference for intersection types using expansion variables
Theoretical Computer Science
Intersection types for explicit substitutions
Information and Computation
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The λ-calculus with de Bruijn indices, called λdB, assembles each α-class of λ-terms into a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism satisfying important properties like principal typing, which allows the type system to include features such as data abstraction (modularity) and separate compilation. To be closer to computation and to simplify the formalisation of the atomic operations involved in β-contractions, several explicit substitution calculi were developed most of which are written with de Bruijn indices. Although untyped and simply types versions of explicit substitution calculi are well investigated, versions with more elaborate type systems (e.g., with intersection types) are not. In previous work, we presented a version for λdB of an intersection type system originally introduced to characterise principal typings for β-normal forms and provided the characterisation for this version. In this work we introduce intersection type systems for two explicit substitution calculi: the λσ and the λse. These type system are based on a type system for λdB and satisfy the basic property of subject reduction, which guarantees the preservation of types during computations.