Essential Intersection Type Assignment
نویسنده
چکیده
This paper introduces a notion of intersection type assignment on the Lambda Calculus that is a restriction of the BCD-system as presented in [4]. This restricted system is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCD-system. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
منابع مشابه
Intersection Type Assignment Systems
This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCD-system. It is essential in the following sense: it is an almost syntax directed system that satisfies all major propert...
متن کاملPartial Intersection Type Assignment in Applicative Term Rewriting Systems
This paper introduces a notion of partial type assignment on applicative term rewriting systems that is based on a combination of an essential intersection type assignment system, and the type assignment system as defined for ML [16], both extensions of Curry’s type assignment system [11]. Terms and rewrite rules will be written as trees, and type assignment will consists of assigning intersect...
متن کاملIntersection and Union Types in the λμμ̃-calculus
The original λμe μ of Curien and Herbelin has a system of simple types, based on sequent calculus, embodying a Curry-Howard correspondence with classical logic. We introduce and discuss three type assignment systems that are extensions of λμe μ with intersection and union types. The intrinsic symmetry in the λμe μ calculus leads to an essential use of both intersection and union types.
متن کاملCut-elimination in the Strict Intersection Type Assignment System Is Strongly Normalising
This paper defines reduction on derivations in the strict intersection type assignment system of [1], by generalising cut-elimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability using intersection types.
متن کاملResource control and intersection types: an intrinsic connection
In this paper we investigate the λ-calculus, a λ-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and contraction rules in the type assignment system. We introduce directly the class of λ-terms and we provide a new treatment of substitution by its decomposition into atomic steps. ...
متن کامل