November 26, 2025
Big‑O? Big Uh‑Oh
Functional Data Structures and Algorithms: a Proof Assistant Approach
Proofs vs speed: comment war over runtime and one-off searches
TLDR: A free ACM book showcases machine-checked proofs for functional algorithms, sparking cheers for rigor. The top debate: it doesn’t prove actual runtime on real code, and binary search’s hidden sorting cost makes one-off lookups faster with a simple scan—proof lovers vs speed skeptics collide.
A new ACM Books release drops a free PDF on data structures and algorithms with machine-checked proofs using Isabelle—cue the community fireworks. Fans of formal math cheer the rigor, while performance hawks roll in asking: but how fast, really? One loud camp says the book proves that code is correct, yet doesn’t prove the speed of the actual code you’d run. User dwohnitmok set the tone with a challenge: can any language prove runtime for the real function, not a neat abstraction? The vibe: “Great theory, show me the stopwatch.”
Then zkmon kicked off a practical reality check: people hype binary search, but forget you must sort first. If you only need a single lookup, just scan once—it’s cheaper than sorting and then searching. Commenters traded memes like “binary search isn’t free” and the classic “benchmarks or it didn’t happen.” The thread split between proof purists (trust the math!) and performance pragmatists (trust the measurements!).
Amid the drama, folks loved that the book is evolving and invites contributions. The top request? Add direct runtime proofs for real code, or at least tie proofs to real-world costs. In short: math brains vs speed demons, with jokes, hot takes, and a reminder that context matters more than cool algorithms.
Key Points
- •The book introduces data structures and algorithms for functional languages with a focus on formal proofs.
- •It covers both functional correctness and running time analysis.
- •A unified inductive-proof approach addresses programs and their running time functions.
- •All proofs are machine-checked using the Isabelle proof assistant.
- •The PDF includes links to Isabelle theories, and the book invites community contributions.