2 4 D ec 2 00 5 — Review , submitted to JoLLI — Kees Doets and Jan van Eijck “ The Haskell Road to Logic , Maths and Programming ”

In university curricula, the subjects of programming and maths and logic tend to be separated. For instance, in the typical computer-science curriculum, mathematics and logic are taught according to the (dry) mathematical tradition, perhaps with modern concessions to help the less abstract minds. One sort of concession is to illustrate the implementability of selected mathematical concepts in some programming language, be it C, Fortran, or others. Another sort of concession is to hint at the usefulness of systems like Maple or Mathematica — systems that are probably more appreciated by mathematicians than applied, programming-minded computer scientists. By contrast, programming courses are almost certainly focused on a specific programming paradigm and on a specific language. Logic and maths may show up in such courses as a sort of “application domain”, while competing with many other domains. For instance, a typical course on the programming language Haskell is likely to emphasize Haskell’s strengths in the areas of abstract-data type specification and combinator libraries for domain-specific languages. The authors of the book at hand have succeeded in amalgamating the themes of maths, logic and Haskell programming in a mutually beneficial manner. The “Haskell road to Logic, Maths and Programming” by Kees Doets and Jan van Eijck is not an introduction to functional programming or the programming language Haskell. (There exist such introductions to Haskell, indeed; cf. the excellent textbooks by Thompson and Hudak [12, 5].) By contrast, the book at hand is about logic and maths, while it uses Haskell for the executable and strongly typed manifestation of the various mathematical notions at the level of declarative programming. To the best of the knowledge of this referee, there