Pearls of Functional Algorithm Design

Richard Bird takes a radically new approach to algorithm design, namely, design by calculation. These 30 short chapters each deal with a particular programming problem drawn from sources as diverse as games and puzzles, intriguing combinatorial tasks, and more familiar areas such as data compression and string matching. Each pearl starts with the statement of the problem expressed using the functional programming language Haskell, a powerful yet succinct language for capturing algorithmic ideas clearly and simply. The novel aspect of the book is that each solution is calculated from an initial formulation of the problem in Haskell by appealing to the laws of functional programming. Pearls of Functional Algorithm Design will appeal to the aspiring functional programmer, students and teachers interested in the principles of algorithm design, and anyone seeking to master the techniques of reasoning about programs in an equational style.

(Cambridge)

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"Though the writing is crisp, and the explanations lucid, this is not an easy book to read. The difficulty lies in the density of ideas presented. The rewards of persevering are definitely worth it, though. In fact, once immersed, I started to ponder where this material would lead to: which algorithms could be even further generalized, what would many of these algorithms look like if implemented in Coq or Agda, and so forth. This is the effect that all good books have on me: well-presented and well-motivated material strives to become a stepping stone to further discovery. Any serious computer scientist would benefit from reading and properly understanding this book. Jacques Carette, Computing Reviews

(Cambridge)

Richard Bird is Professor of Computer Science at Oxford University Computing Laboratory.

(Cambridge)

Preface; 1. The smallest free number; 2. A surpassing problem; 3. Improving on saddleback search; 4. A selection problem; 5. Sorting pairwise sums; 6. Making a century; 7. Building a tree with minimum height; 8. Unravelling greedy algorithms; 9. Finding celebrities; 10. Removing duplicates; 11. Not the maximum segment sum; 12. Ranking suffixes; 13. The Burrows-Wheeler transform; 14. The last tail; 15. All the common prefixes; 16. The Boyer-Moore algorithm; 17. The Knuth-Morris-Pratt algorithm; 18. Planning solves the rush hour problem; 19. A simple Sudoku solver; 20. The countdown problem; 21. Hylomorphisms and nexuses; 22. Three ways of computing determinants; 23. Inside the convex hull; 24. Rational arithmetic coding; 25. Integer arithmetic coding; 26. The Schorr-Waite algorithm; 27. Orderly insertion; 28. Loopless functional algorithms; 29. The Johnson-Trotter algorithm; 30. Spider spinning for dummies; Index.

(Cambridge)