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Finding patterns is a common act in human intellectual endeavours, and it is a complex challenge tackled by both humans and algorithms. For several decades, musical pattern discovery algorithms have been researched, and researchers have been comparing human-annotated patterns to algorithmic outputs, as well as algorithms to algorithms. However, traditional metrics have not fully captured the rich insights that these comparisons could offer. To contribute to the comparisons between musical pattern discovery mechanisms, this dissertation spans seven chapters. Chapter 1 provides the background of the dissertation, including an overview, research approaches, contexts, scope, thesis statement, and an enumeration of contributions. Chapter 2 delves into the concept of musical patterns and explores the diverse landscape of musical pattern discovery algorithms. Our exploration reveals the complexities surrounding the definition of patterns and the multifaceted nature of these algorithms. Chapter 3 is dedicated to the collection tools for human-annotated musical patterns and the analysis of factors that influence annotations. We observe that musical background impacts annotated patterns; tool interfaces and automatic matching affect the length and frequency of annotations. Chapter 4 introduces four methods tailored for comparing musical pattern discovery algorithms. These methods provide novel insights into the discrepancies between human-annotated patterns and their algorithmically extracted counterparts. These methods provide a more comprehensive approach to comparing algorithms, aiding in the interpretation and evaluation of algorithmic outputs. Chapter 5 implements Pattrans, a Domain-Specific Language (DSL) in the functional language Haskell for comparing musical pattern occurrences through musical transformations. We delve into its design for uncovering the relations between pattern occurrences in a modular way. Chapter 6 employs Pattrans to scrutinise transformations be

When writing functional code that composes multiple recursive functions that operate on a datastrcuture, we often incur a lot of computational overhead allocating memory, only to later read, use, and discard this information. This can be alleviated using fusion, a technique that combines these multiple recursive datastructure traversals into one. This thesis explores shortcut fusion using (Co)Church encodings based on the work of Harper (2011), focusing on two questions: What is needed to reliably achieve fusion in Haskell, and the correctness of these transformations through a formalization in Agda. The first contribution replicates and extends Harper's (Co)Church encodings in Haskell, uncovering optimizer weaknesses and providing practical insights for achieving fusion within Haskell. The second contribution formalizes these encodings in Agda, leveraging parametricity and the category theory described by Harper. The formalization proves the equivalence of these encoded functions to the unencoded ones, showing that the encodings are in fact isomorphisms, as long as parametricity (Wadler, 1989) is assumed. These findings highlight the effectiveness and correctness of shortcut fusion techniques and show the promise of shortcut fusion: Reduce the computational overhead associated with functional programming while retaining its nice, compositional properties., https://github.com/Bigstep22/thesis Repository link The link to the repository in which my work was done. This contains the same data as the artifacts., Computer Science | Software Technology