Related papers: Ill-Typed Programs Don't Evaluate

We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…

We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…

This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…

The present paper shows meta-programming turn programming, which is rich enough to express arbitrary arithmetic computations. We demonstrate a type system that implements Peano arithmetics, slightly generalized to negative numbers. Certain…

Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming…

Benefits of static type systems are well-known: they offer guarantees that no type error will occur during runtime and, inherently, inferred types serve as documentation on how functions are called. On the other hand, many type systems have…

The severity of type II errors is frequently ignored when deriving a multiple testing procedure, even though utilizing it properly can greatly help in making correct decisions. This paper puts forward a theory behind developing a multiple…

We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…

We propose a type system for a calculus of contracting processes. Processes can establish sessions by stipulating contracts, and then can interact either by keeping the promises made, or not. Type safety guarantees that a typeable process…

We present a new type system combining occurrence typing, previously used to type check programs in dynamically-typed languages such as Racket, JavaScript, and Ruby, with dependent refinement types. We demonstrate that the addition of…

The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…

Type analyses of logic programs which aim at inferring the types of the program being analyzed are presented in a unified abstract interpretation-based framework. This covers most classical abstract interpretation-based type analyzers for…

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…

We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers…