Related papers: Principal Typing for Intersection Types, Forty-Fiv…

We present a type system to guarantee termination of pi-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. We show that our…

We study Milner's lambda-calculus with partial substitutions. Particularly, we show confluence on terms and metaterms, preservation of \b{eta}-strong normalisation and characterisation of strongly normalisable terms via an intersection…

We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…

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…

Gradual typing is an approach to integrating static and dynamic typing within the same language, and puts the programmer in control of which regions of code are type checked at compile-time and which are type checked at run-time. In this…

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…

We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…

Linear type systems need to keep track of how programs use their resources. The standard approach is to use context splits specifying how resources are (disjointly) split across subterms. In this approach, context splits redundantly echo…

Multi types---aka non-idempotent intersection types---have been used to obtain quantitative bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the same time the number of evaluation steps and the size of…

This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource aware type systems, named U and E, for a lambda-calculus…

Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…

The type used to print an early modern book can give scholars valuable information about the time and place of its production as well as its producer. Recognizing such type is currently done manually using both the character shapes of `M'…

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 this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…

Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast…

Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…

On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…

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 the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the…

The lambda-cube is a famous pure type system (PTS) cube of eight powerful explicit type systems that include the simple, polymorphic and dependent type theories. The lambda-cube only types Strongly Normalising (SN) terms but not all of…