Related papers: Transitivity of Subtyping for Intersection Types
To design type systems that use subtyping, we have to make tradeoffs. Deep subtyping is more expressive than shallow subtyping, because deep subtyping compares the entire structure of types. However, shallow subtyping is easier to reason…
Intersection and union types denote conjunctions and disjunctions of properties. Using bidirectional typechecking, intersection types are relatively straightforward, but union types present challenges. For union types, we can case-analyze a…
Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…
The lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…
We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
We study the question of extending the BCD intersection type system with additional type constructors. On the typing side, we focus on adding the usual rules for product types. On the subtyping side, we consider a generic way of defining a…
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…
We introduce a method to evaluate untyped lambda terms by combining the theory of traversals, a term-tree traversing technique inspired from Game Semantics, with judicious use of the eta-conversion rule of the lambda calculus. The traversal…
Resolution and subtyping are two common mechanisms in programming languages. Resolution is used by features such as type classes or Scala-style implicits to synthesize values automatically from contextual type information. Subtyping is…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
Prior work has extended the deep, logical connection between the linear sequent calculus and session-typed message-passing concurrent computation with equi-recursive types and a natural notion of subtyping. In this paper, we extend this…
Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
We study an assignment system of intersection types for a lambda-calculus with records and a record-merge operator, where types are preserved both under subject reduction and expansion. The calculus is expressive enough to naturally…
A cornerstone of the theory of lambda-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational…
Refining and extending previous work by Retor\'e, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz…
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure {\lambda}-calculus, the calculus with explicit substitutions {\lambda}S, and the calculus with explicit…