Related papers: The Relative Monadic Metalanguage
Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…
Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage…
Reinforcement learning (RL) with rule-based reward functions has recently shown great promise in enhancing the reasoning depth and generalization ability of vision-language models (VLMs), while maintaining computational efficiency. In spite…
The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a…
In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic…
We revisit once again the connection between three notions of computation: monads, arrows and idioms (also called applicative functors). We employ monoidal categories of finitary functors and profunctors on finite sets as models of these…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a…
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
Argument mining (AM) is the process of automatically extracting arguments, their components and/or relations amongst arguments and components from text. As the number of platforms supporting online debate increases, the need for AM becomes…
For decades, SQL has been the default language for composing queries, but it is increasingly used as an artifact to be read and verified rather than authored. With Large Language Models (LLMs), queries are increasingly machine-generated,…
Abstract meaning representations (AMRs) are broad-coverage sentence-level semantic representations. AMRs represent sentences as rooted labeled directed acyclic graphs. AMR parsing is challenging partly due to the lack of annotated…
We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Multilingual large language models (LLMs) seem to generalize somewhat across languages. We hypothesize this is a result of implicit vector space alignment. Evaluating such alignment, we see that larger models exhibit very high-quality…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…