Intersection types for explicit substitutions

Reductions, Intersection Types, and Explicit Substitutions

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...

Principal Typings in a Restricted Intersection Type System for Beta Normal Forms with De Bruijn Indices

The λ-calculus with de Bruijn indices assembles each α-class of λterms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable λ-terms, that is a term is normalisable if and only if it is typeable. To be closer to computations and to simplify the formalisation of the atomic operations involved in β-contra...

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...

Non-idempotent intersection types and strong normalisation

We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure λ-calculus, the calculus with explicit substitutions λS, and the calculus with explicit substitutions, contractions and weakenings λlxr. In each of the three calculi, a term is typable if and only if it is strongly normalising, as it is the case in (many) systems wi...