On Isomorphism of "Functional" Intersection and Union Types
نویسندگان
چکیده
منابع مشابه
On Isomorphism of "Functional" Intersection and Union Types
Type isomorphism is useful for retrieving library components, since a function in a library can have a type different from, but isomorphic to, the one expected by the user. Moreover type isomorphism gives for free the coercion required to include the function in the user program with the right type. The present paper faces the problem of type isomorphism in a system with intersection and union ...
متن کاملIsomorphism of intersection and union types
This paper gives a complete characterisation of type isomorphism definable by terms of a λ-calculus in a type system with intersection and union types. Type isomorphism is usually proved using a form of Inversion Lemma to relate terms and types. Currently in the literature no inversion lemma for intersection and union types is provided. Moreover, the subject reduction property does not hold in ...
متن کاملToward Isomorphism of Intersection and Union types
This paper investigates type isomorphism in a λ-calculus with intersection and union types. It is known that in λ-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably, invertible terms are linear terms of a particular shape, called finite hereditary permutators. Typing properties of finite hereditary permutators are then studied in a relevan...
متن کاملIsomorphism of "Functional" Intersection Types
Type isomorphism for intersection types is quite odd, since it is not a congruence and it does not extend type equality in the standard interpretation of types. The lack of congruence is due to the proof theoretic nature of the intersection introduction rule, which requires the same term to be the subject of both premises. A partial congruence can be recovered by introducing a suitable notion o...
متن کاملSession Types = Intersection Types + Union Types
We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the resulting theory overcomes some important defects of related behavioral theories. In particular, intersections and unions provide a native solution to the pro...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2015
ISSN: 2075-2180
DOI: 10.4204/eptcs.177.5