Related papers: Type Classes for Lightweight Substructural Types
Type classes are an elegant extension to traditional, Hindley-Milner based typing systems. They are used in modern, typed languages such as Haskell to support controlled overloading of symbols. Haskell 98 supports only single-parameter and…
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
This paper describes a tool suite for the ACL2 programming language which incorporates certain ideas from the Hindley-Milner paradigm of functional programming (as exemplified in popular languages like ML and Haskell), including a "typed"…
Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate…
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…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We previously developed a polymorphic type system and a type checker for a multithreaded lock-based polymorphic typed assembly language (MIL) that ensures that well-typed programs do not encounter race conditions. This paper extends such…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
In recent projects on operating-system verification, C and C++ data types are often formalized using a semantics that does not fully specify the precise byte encoding of objects. It is well-known that such an underspecified data-type…
CLASS is a proof-of-concept general purpose linear programming language, flexibly supporting realistic concurrent programming idioms, and featuring an expressive linear type system ensuring that programs (1) never misuse or leak stateful…
The fact that Applicative type class allows one to express simple parsers in a variable-less combinatorial style is well appreciated among Haskell programmers for its conceptual simplicity, ease of use, and usefulness for semi-automated…
Situation calculus has been widely applied in Artificial Intelligence related fields. This formalism is considered as a dialect of logic programming language and mostly used in dynamic domain modeling. However, type systems are hardly…