The Clustering of Lambda Terms by Using Embeddings

Keywords: Pure Lambda Calculus, Clustering Analysis, Pretrained Embedding, Hidden Space


Relevance. The importance of optimizing compilers and interpreters for functional programming languages, mainly through the lens of Lambda Calculus, is paramount in addressing the increasing complexity and performance requirements in software engineering. The emphasis of this study lies in this critical area, aiming to leverage advanced machine learning techniques to enhance identification and application of code reduction strategy.

Goal. The primary goal is to improve the performance and efficiency of compilers and interpreters by deepening the understanding of program code reduction strategies within Lambda Calculus. The research is aimed at using machine learning to convert lambda terms into feature vectors, facilitating the exploration of optimal reduction strategies.

Research methods. The study employs a comprehensive approach, generating a wide range of lambda terms for analysis. It utilizes OpenAI's text embedding model to transform these terms into embedding vectors, employing clustering analyses (DBSCAN with Euclidean measurements) and visualizations (PCA and t-SNE) to identify patterns and assess feature separability. The research navigates the complexities of choosing between specific and universal reduction strategies.

The results.  Findings have revealed clear distinctions among lambda term representations within the embedding vectors, supporting the hypothesis that cluster analysis can uncover identifiable patterns. However, the challenges have been encountered due to OpenAI Embeddings' training being generally focused on human-readable text and code, and that complicates the precise representation of Lambda Calculus terms.

Conclusions. This exploration underscores the challenges in pinpointing the optimal reduction strategy for Lambda Calculus terms, highlighting the limitations of current mathematical models and the need for tailored machine learning applications. Despite the hurdles with the OpenAI Embeddings model's adaptability, the research offers significant insight into the potential of machine learning to refine the optimization processes of compilers and interpreters in functional programming environments.


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Author Biography

Oleksandr Deineha, V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine

PhD student




How to Cite
Deineha, O. (2023). The Clustering of Lambda Terms by Using Embeddings. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 59, 16-23.