Uniform Proofs of Normalisation and Approximation for Intersection Types
نویسندگان
چکیده
منابع مشابه
Uniform Proofs of Normalisation and Approximation for Intersection Types
We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini’s ones and equivalent to the usual natural deduction style systems. We prove the characterisation theorems of strong and weak normalisation through the proposed ...
متن کاملNon-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...
متن کاملCharacterisation of Approximation and (Head) Normalisation for $\lambda\mu$ using Strict Intersection Types
We study the strict type assignment for λμ that is presented in [7]. We define a notion of approximants of λμ-terms, show that it generates a semantics, and that for each typeable term there is an approximant that has the same type. We show that this leads to a characterisation via assignable types for all terms that have a head normal form, and to one for all terms that have a normal form, as ...
متن کاملCharacterisation of Approximation and (Head) Normalisation for λμ using Strict Intersection Types
We study the strict type assignment for λμ that is presented in [7]. We define a notion of approximants of λμ-terms, show that it generates a semantics, and that for each typeable term there is an approximant that has the same type. We show that this leads to a characterisation via assignable types for all terms that have a head normal form, and to one for all terms that have a normal form, as ...
متن کاملThe heart of intersection type assignment: Normalisation proofs revisited
This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types for a system with ω and a ≤-relation that is contravariant over arrow types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2015
ISSN: 2075-2180
DOI: 10.4204/eptcs.177.2