Strict intersection types for the Lambda Calculus

Abstract

This version has all proofs included, rather than accumulated in an appendix.

Retractions in Intersection Types

“…We write Γ ⊢ N : σ with σ = i∈I µ i as short for Γ ⊢ N : µ i for all i ∈ I. The inversion lemma is as expected, for a proof see [1].…”

“…The type system considered in this paper is a notational variant of the essential intersection assignment introduced in [1].…”

“…If µ ∼ ω it is trivial. Otherwise the inhabitants of µ must have hnfs, see [1] for a proof. Let µ = σ 1 → .…”

“…In [1] it is proved that each intersection type is equivalent to an intersection of strict types. Owing to this property and the idempotence of the intersection type constructor, we can show that a simple retraction between intersection types implies a set of retractions between strict types.…”

“…We choose to investigate retraction for the essential intersection type assignment system introduced in [1]. This system has the same typeability power of the standard system [3] and a less permissive type syntax.…”