Related papers: Explicit Refinement Types
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
Lighthouse projects such as CompCert, seL4, IronFleet, and DeepSpec have demonstrated that full verification of entire systems is feasible by establishing a refinement relation between an abstract system specification and an executable…
Precisely modeling complex systems like cyber-physical systems is challenging, which often render model-based system verification techniques like model checking infeasible. To overcome this challenge, we propose a method called LAR to…
Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…
Erlang's dynamic typing discipline can lead to runtime errors that persist even after process restarts. Some of these runtime errors could be prevented through static type checking. While Erlang provides a type specification language, the…
Dependent types provide a lightweight and modular means to integrate programming and formal program verification. In particular, the types of programs written in dependently typed programming languages (Agda, Idris, F*, etc.) can be used to…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
Programming languages like P4 enable specifying the behavior of network data planes in software. However, with increasingly powerful and complex applications running in the network, the risk of faults also increases. Hence, there is growing…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
Model-driven design of software for safety-critical applications often relies on mathematically grounded techniques such as the B method. Such techniques consist in the successive applications of refinements to derive a concrete…
Type classes are one of Haskell's most popular features and extend its type system with ad-hoc polymorphism. Since their conception, there were useful features that could not be offered because of the desire to offer two correctness…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
All formalizations of session types rely on linear types for soundness as session-typed communication channels must change their type at every operation. Embedded language implementations of session types follow suit. They either rely on…