Typing Local Definitions and Conditional Expressions with Rank 2 Intersection (Extended Abstract)

Abstract

Abstract. We introduce a variant of the system of rank 2 intersection types with new typing rules for local definitions (let-expressions and letrec-expressions) and conditional expressions (if-expressions and case-expressions). These extensions are a further step towards the use of intersection types in "real" programming languages.

Strict intersection types for the Lambda Calculus

“…The key idea for this system is to restrict the set of types to those of the shape (σ 1 ∩ · · · ∩σ n )→τ, where the σ i are types that do not contain intersections. This kind of type later was used outside the context of the λ-calculus [8,9,28,30,58]; many decidable restrictions of various ranks were later defined by [45], [46].…”

Rank 2 intersection types for local definitions and conditional expressions

“…An extended abstract describing a preliminary version of the system presented in this paper appeared as Damiani [2000].…”

A conjunctive type system for useless-code elimination

“…The key idea is that of performing Hindley/Milner type inference and useless-code detection at the same type. Since rank 2 conjunctive type inference algorithms for ML-like functional languages have been proposed in the literature (Jim 1996;Damiani 2000b) (see also Banerjee (1997), where a type-based closure analysis based on the rank 2 type system of Jim (1996) is proposed), an interesting possibility could be that of modifying such algorithms to detect useless code (as done in Kobayashi (2000) for the Hindley/Milner type inference algorithm). Further opportunities might come from more powerful conjunctive type inference algorithms such as those based on finite rank conjunction types (Kfoury and Wells 1999) and polar types (Jim 2000).…”