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The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose $F^\omega_{..}$, a rigorous…
Linear and substructural types are powerful tools, but adding them to standard functional programming languages often means introducing extra annotations and typing machinery. We propose a lightweight substructural type system design that…
SHACL and OWL are two prominent W3C standards for managing RDF data. These languages share many features, but they have one fundamental difference: OWL, designed for inferring facts from incomplete data, makes the open-world assumption,…
Many of the machine learning (ML) tasks are focused on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) leading to a huge communication overhead. Federated learning…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
Recognition and classification of Figurative Language (FL) is an open problem of Sentiment Analysis in the broader field of Natural Language Processing (NLP) due to the contradictory meaning contained in phrases with metaphorical content.…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
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.…
The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a…
GADTs were introduced in Haskell's eco-system more than a decade ago, but their interaction with several mainstream features such as type classes and functional dependencies has a lot of room for improvement. More specifically, for some…
Large Language Models (LLMs) have exhibited impressive generation capabilities, but they suffer from hallucinations when solely relying on their internal knowledge, especially when answering questions that require less commonly known…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
This paper proposes a functional foundation for model driven engineering that unifies model construction, metamodels, templates, and transformations under a single formalism: the model expression algebra. In this algebra, models are values,…
This paper presents a novel methodological framework for detecting and classifying latent constructs, including frames, narratives, and topics, from textual data using Open-Source Large Language Models (LLMs). The proposed hybrid approach…
Evaluating instruction following in Large Language Models requires decomposing instructions into verifiable requirements and assessing satisfaction--tasks currently dependent on manual annotation and uniform criteria that do not align with…
We contribute the first denotational semantics of polymorphic dependent type theory extended by an equational theory for general (higher-order) reference types and recursive types, based on a combination of guarded recursion and…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…
Deep learning has been popularized by its recent successes on challenging artificial intelligence problems. One of the reasons for its dominance is also an ongoing challenge: the need for immense amounts of computational power. Hardware…