Related papers: Equational Reasoning for MTL Type Classes

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

In recent years, languages like Haskell have seen a dramatic surge of new features that significantly extends the expressive power of their type systems. With these features, the challenge of kind inference for datatype declarations has…

In-context learning (ICL) enables multimodal large language models (MLLMs) to classify images from a few labelled examples. Yet, how these models use the provided context remains opaque. While Chain-of-Thought prompting is widely used,…

Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…

Logical reasoning with large language models (LLMs) has received growing attention. One mainstream approach translates natural language into formal logic and then applies symbolic solvers for deduction. While effective in many tasks, these…

Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…

The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect…

Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…

It is notoriously difficult to control the behavior of reinforcement learning agents. Agents often learn to exploit the environment or reward signal and need to be retrained multiple times. The multi-objective reinforcement learning (MORL)…

Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…

Extensive research on formal verification of machine learning (ML) systems indicates that learning from data alone often fails to capture underlying background knowledge. A variety of verifiers have been developed to ensure that a…

There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…

It often happens that free algebras for a given theory satisfy useful reasoning principles that are not preserved under homomorphisms of algebras, and hence need not hold in an arbitrary algebra. For instance, if $M$ is the free monoid on a…

Transformers have demonstrated remarkable performance in natural language processing and related domains, as they largely focus on sequential, autoregressive next-token prediction tasks. Yet, they struggle in logical reasoning, not…

We introduce a self-play framework for semantic equivalence in Haskell, utilizing formal verification to guide adversarial training between a generator and an evaluator. The framework leverages Liquid Haskell proofs for validating…

Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…

Horn clauses and first-order resolution are commonly used to implement type classes in Haskell. Several corecursive extensions to type class resolution have recently been proposed, with the goal of allowing (co)recursive dictionary…

The field of machine learning (ML) is concerned with the question of how to construct algorithms that automatically improve with experience. In recent years many successful ML applications have been developed, such as datamining programs,…