Related papers: Separated and Shared Effects in Higher-Order Langu…

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…

This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…

Probabilistic programming languages, which exist in abundance, are languages that allow users to calculate probability distributions defined by probabilistic programs, by using inference algorithms. However, the underlying inference…

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human…

The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…

We describe a denotational semantics for an abstract effect system for a higher-order, shared-variable concurrent programming language. We prove the soundness of a number of general effect-based program equivalences, including a…

The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…

We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…

Deep compositional models of meaning acting on distributional representations of words in order to produce vectors of larger text constituents are evolving to a popular area of NLP research. We detail a compositional distributional…

Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…

Human languages differ widely in their forms, each having distinct sounds, scripts, and syntax. Yet, they can all convey similar meaning. Do different languages converge on a shared neural substrate for conceptual meaning? We used language…

Randomized controlled trials are a cornerstone of medicine and the social sciences as they enable reliable estimates of causal effects. However, they are costly and time-consuming to conduct, motivating interest in predicting causal effects…

A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the…

Instead of a monolithic programming language trying to cover all features of interest, some programming systems are designed by combining together simpler languages that cooperate to cover the same feature space. This can improve usability…

We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…

Deep learning is moving towards increasingly sophisticated optimization objectives that employ higher-order functions, such as integration, continuous optimization, and root-finding. Since differentiable programming frameworks such as…

Many complex generative systems use languages to create structured objects. We consider a model of random languages, defined by weighted context-free grammars. As the distribution of grammar weights broadens, a transition is found from a…

Large Language Models (LLMs) increasingly exhibit strong reasoning abilities, often attributed to their capacity to generate chain-of-thought-style intermediate reasoning. Recent work suggests that exposure to code can further enhance these…

The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…