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Explore the mathematical derivation and implementation of Fenwick trees (binary indexed trees) through this 23-minute conference presentation from ICFP 2025. Begin with segment trees as a foundational, purely functional approach to maintaining sequences with efficient updates and range queries, then follow the equational reasoning that leads to the optimized Fenwick tree implementation. Understand how the seemingly mysterious bitwise operations on indices emerge naturally from mathematical transformations, demystifying one of computer science's most elegant data structures. Learn through a Haskell embedded domain-specific language (EDSL) designed for operations on infinite two's complement binary numbers, making the abstract concepts concrete and verifiable. Gain insight into how complex algorithmic optimizations can be systematically derived rather than discovered through trial and error.
