Toward Isomorphism of Intersection and Union types
نویسندگان
چکیده
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 relevant type inference system with intersection and union types for linear terms. In particular, an isomorphism preserving reduction between types is defined. Reduction of types is confluent and terminating, and induces a notion of normal form of types. The properties of normal types are a crucial step toward the complete characterisation of type isomorphism. The main results of this paper are, on one hand, the fact that two types with the same normal form are isomorphic, on the other hand, the characterisation of the isomorphism between types in normal form, modulo isomorphism of arrow types.
منابع مشابه
Isomorphism 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 کاملOn 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 کاملON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...
متن کاملGeneral definitions for the union and intersection of ordered fuzzy multisets
Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...
متن کاملCompleteness and Soundness results for X with Intersection and Union Types
This paper defines intersection and union type assignment for the sequent calculus X , a substitution-free language that enjoys the Curry-Howard correspondence with respect to Gentzen’s sequent calculus for classical logic. We show that this notion is complete (i.e. closed for subject-expansion), and show that the non-logical nature of both intersection and union types disturbs the soundness (i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012