Algorithms through the lens of symbolic pattern matching
The blog post discusses symbolic pattern matching using the Symbolica framework, covering its applications in programming and graph theory, and methods for analyzing graph properties and automorphisms.
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The blog post discusses the use of symbolic pattern matching in algorithms, particularly through the computational framework Symbolica. It highlights the prevalence of pattern matching in various domains, including programming, mathematics, and graph theory. The author, Ben Ruijl, illustrates how to implement mathematical expressions and algorithms using Symbolica, starting with basic examples like the factorial function and progressing to more complex structures such as graphs. The post explains how to represent graphs as mathematical expressions, manipulate them using pattern matching, and extract properties like connectivity and cycles. It also introduces techniques for counting vertices and edges in a graph and determining the number of loops using Euler's formula. The author emphasizes the elegance of using pattern matching for algorithm design, even if it may not always be the most efficient approach. The post concludes with a discussion on graph automorphisms, exploring how to find self-maps of a graph through relabeling vertices and edges. Overall, the article serves as a guide to understanding and applying symbolic pattern matching in computational algorithms.
- Symbolica is a computational framework for symbolic pattern matching.
- The blog covers applications of pattern matching in programming, mathematics, and graph theory.
- It demonstrates how to represent and manipulate graphs using mathematical expressions.
- The author explains methods for analyzing graph properties, including connectivity and cycles.
- The post concludes with insights on graph automorphisms and self-mapping techniques.
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2 commentsI really do like how you have smoothly integrated this into Python. Though the symbolic pattern matching is well pretty amazing and make me think about things a little different now. You could probably implement something like this in Julia with it's macros and flexibility in manipulating the AST. I hate Python, but I'm forced to bow to the ecosystem.
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