Related papers: Complete and Easy Bidirectional Typechecking for H…

The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…

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…

Type inference is an application domain that is a natural fit for logic programming (LP). LP systems natively support unification, which serves as a basic building block of typical type inference algorithms. In particular, polymorphic type…

Extending a given language with new dedicated features is a general and quite used approach to make the programming language more adapted to problems. Being closer to the application, this leads to less programming flaws and easier…

DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…

Dynamic languages are praised for their flexibility and expressiveness, but static analysis often yields many false positives and verification is cumbersome for lack of structure. Hence, unit testing is the prevalent incomplete method for…

This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…

Model-checking is one of the most powerful techniques for verifying systems and programs, which since the pioneering results by Knapik et al., Ong, and Kobayashi, is known to be applicable to functional programs with higher-order types…

Dynamic languages such as Python and JavaScript widely use function decorators to extend behavior. In TypeScript, a common way to type such patterns uses Parameters<T> and ReturnType<T>. In practice, this idiom relies on a function-type…

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…

Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…

We address the problem of local type inference for a language based on System F with context-free session types. We present an algorithm that leverages the bidirectional type checking approach to propagate type information, enabling first…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

We generalize the concept of stack one dimension higher, introducing a notion of 2-stack suitable for a trihomomorphism from a 2-category equipped with a bitopology into the tricategory of bicategories. Moreover, we give a characterization…

Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…

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…