Intersection types for explicit substitutions

Intersection types for explicit substitutions

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not...

Explicit Substitutions and Intersection Types

Calculi of explicit substitutions have been introduced to give an account to the substitution process in lambda calculus. The idea is to introduce a notation for substitutions explicitely in the calculus. In other words one makes substitutions first class citizens whereas the classical lambda calculus leaves them in the meta-theory. Originally, the expression “explicit substitution” and the con...

Reductions, Intersection Types, and Explicit Substitutions

Dependent Types and Explicit Substitutions

We present a dependent-type system for a λ-calculus with explicit substitutions. In this system, meta-variables, as well as substitutions, are first-class objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.

Intersection Type Systems and Explicit Substitutions Calculi

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 a...