Related papers: A Type Checker for a Logical Framework with Union …

The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…

Subtyping is a crucial ingredient of session type theory and its applications, notably to programming language implementations. In this paper, we study effective ways to check whether a session type is a subtype of another by applying a…

We propose a model checking algorithm to test properties of systems that are expressed in the multi-agent temporal logic ATL+. The specificities of this algorithm are: it is on-the-fly, generating states only when they are needed, and it…

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…

We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination…

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…

Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…

This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…

Scalable and automatic formal verification for concurrent systems is always demanding. In this paper, we propose a verification framework to support automated compositional reasoning for concurrent programs with shared variables. Our…

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…

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…

Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…

We present a type inference algorithm for lambda-terms in Elementary Affine Logic using linear constraints. We prove that the algorithm is correct and complete.

Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…

The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…

A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…

There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…

We propose an approach on model checking information flow for imperative language with procedures. We characterize our model with pushdown system, which has a stack of unbounded length that naturally models the execution of procedural…