Related papers: Equational Reasoning for MTL Type Classes
In order to automate verification process, regulatory rules written in natural language need to be translated into a format that machines can understand. However, none of the existing formalisms can fully represent the elements that appear…
Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…
Monads play an important role in both the syntax and semantics of modern functional programming languages. The problem of combining them has been of profound interest at least since the 90s, and different approaches have been employed to…
This paper extends Escardo and Oliva's selection monad to the selection monad transformer, a general monadic framework for expressing backtracking search algorithms in Haskell. The use of the closely related continuation monad transformer…
Applicative functors are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell. Applicative functors are to be preferred to monads when the structure of a computation…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We introduce a variant of modal logic, dubbed EXISTENTIAL COUNTING MODAL LOGIC (ECML), which captures a vast majority of problems known to be tractable in single exponential time when parameterized by treewidth. It appears that all these…
Large language models (LLMs) have developed impressive performance and strong explainability across various reasoning scenarios, marking a significant stride towards mimicking human-like intelligence. Despite this, when tasked with several…
We present a new type system with support for proofs of programs in a call-by-value language with control operators. The proof mechanism relies on observational equivalence of (untyped) programs. It appears in two type constructors, which…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
While functional programming is an efficient way to express complex software, functional programming languages have a steep learning curve. Haskell can be challenging to learn for students who were only introduced to imperative programming.…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in document understanding. However, their reasoning processes remain largely black-box, making it difficult to ensure reliability and trustworthiness,…
Large Language Models (LLMs) have shown remarkable performance on complex reasoning tasks, especially when equipped with long chain-of-thought (CoT) reasoning. However, eliciting long CoT typically requires large-scale reinforcement…
In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain…
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…
Large Language Models (LLMs) excel in generating personalized content and facilitating interactive dialogues, showcasing their remarkable aptitude for a myriad of applications. However, their capabilities in reasoning and providing…