Related papers: Domain-Specific Languages of Mathematics: Presenti…
This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users.…
At the workshop on Trends in Functional Programming in Education (TFPIE) in 2015 Ionescu and Jansson presented the approach underlying the "Domain Specific Languages of Mathematics" (DSLsofMath) course even before the first course instance.…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many…
We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
In an era dominated by data, the management and utilization of domain-specific language have emerged as critical challenges in various application domains, particularly those with industry-specific requirements. Our work is driven by the…
Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
We present MathDSL, a Domain-Specific Language (DSL) for mathematical equation solving, which, when deployed in program synthesis models, outperforms state-of-the-art reinforcement-learning-based methods. We also introduce a quantitative…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
Multilingual programs, whose implementations are made of different languages, are gaining traction especially in domains, such as web programming, that particularly benefit from the additional flexibility brought by using multiple…