Mondriλn: A Visual Programming Language Based on the Lambda Calculus

The lambda calculus is a core part of every functional programming class. However, students often find it difficult to grasp, especially the process of beta reduction. Hence, representing lambda terms and the beta reduction process visually could improve its comprehensibility to students and motivate them to learn more about the subject. The goal was to design a visual language for the representation of lambda terms which can aid students’ understanding of lambda calculus. In addition, the language aims to be visually pleasing, simple to draw and reason about on paper, and straightforward to read for humans. A proof of concept application should be created to ensure that the implementation of this language is feasible.

The team conducted research about existing visual esoteric programming languages and visual lambda calculus representations. The results of this research influenced the design of the language. Additionally, the SVG format was chosen for storing the visual representations. Mondriλn uses coloured rectangles and their relative positions to represent lambda terms. This design was inspired by the Dutch painter Piet Mondrian. The language allows for artistic freedom without sacrificing its understandability. Furthermore, it is able to represent all lambda terms, only limited by the number of colours displayable on screens. The proof of concept application is implemented as a command line tool and supports generating images from lambda terms, parsing a lambda term from an image and performing beta reduction on them. This proves that it is possible to implement the language we envisioned. Mondriλn appears to make lambda terms simpler to understand, particularly when it comes to the beta reduction process.

While the language shows promise, its potential usefulness to students remains an open question. Further evaluation is needed to determine how effectively it can aid students’ understanding of lambda calculus, with a particular focus on the beta reduction process. Some unresolved issues remain in the proof of concept application, for example, when handling large lambda terms. A next step to improve the usability of the system could be to develop a web-based interface, which could also offer additional features. Overall, this project provides a good starting point for further development. By addressing the aforementioned limitations and opportunities for enhancement, the system can become even more usable and effective.