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A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
Monads have become a powerful tool for structuring effectful computations in functional programming, because they make the order of effects explicit. When translating pure code to a monadic version, we need to specify evaluation order…
Natural language contexts display logical regularities with respect to substitutions of related concepts: these are captured in a functional order-theoretic property called monotonicity. For a certain class of NLI problems where the…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Extending Mart\'in Escard\'o's effectful forcing technique, we give a new proof of a well-known result: Brouwer's monotone bar theorem holds for any bar that can be realized by a functional of type $(\mathbb{N} \to \mathbb{N}) \to…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by…
This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…
This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…