Related papers: DeLaM: A Dependent Layered Modal Type Theory for M…

Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…

The requirements engineering (RE) phase is pivotal in developing high-quality software. Integrating advanced modelling techniques with large language models (LLMs) and formal verification in a logical style can significantly enhance this…

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…

Causal discovery from observational data is fundamental to scientific fields like biology, where controlled experiments are often impractical. However, existing methods, including constraint-based (e.g., PC, causalMGM) and score-based…

We propose a novel framework for comprehending the reasoning capabilities of large language models (LLMs) through the perspective of meta-learning. By conceptualizing reasoning trajectories as pseudo-gradient descent updates to the LLM's…

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…

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…

In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of…

Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a…

Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…

This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…

Recent work has shown that Large Language Models (LLMs) are not only a suitable tool for code generation but also capable of generating annotation-based code specifications. Scaling these methodologies may allow us to deduce provable…

Language Workbenches offer language designers an expressive environment in which to create their DSLs. Similarly, research into mechanised meta-theory has shown how dependently typed languages provide expressive environments to formalise…

Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…

Modern foundation models such as large language models (LLMs) and large multi-modal models (LMMs) require a massive amount of computational and memory resources. We propose a new framework to convert such LLMs/LMMs into a reduced-dimension…

The paper introduces a new modular action language, ALM, and illustrates the methodology of its use. It is based on the approach of Gelfond and Lifschitz (1993; 1998) in which a high-level action language is used as a front end for a logic…

Significant efforts has been made to expand the use of Large Language Models (LLMs) beyond basic language tasks. While the generalizability and versatility of LLMs have enabled widespread adoption, evolving demands in application…

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…

In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, and spatial and cohesive type theory. In this…