Handbook of Practical Logic and Automated Reasoning

John Harrison’s Handbook of Practical Logic and Automated Reasoning strongly reminds me of Donald Knuth’s The Art of Computer Programming. Both clearly are masterpieces. And both scare me. They are so comprehensive, so erudite, and the information density is so high, that one really has to pay attention to get the most from the exposition. Also, both are a bit idiosyncratic. On the other hand, reading those books is an utter pleasure, because everything is so beautifully presented and there is so much to learn. The Handbook of Practical Logic and Automated Reasoning then, is about automation in mathematical logic. Theorem proving with a computer only becomes practical when mundane proof tasks are performed automatically (the two main types of automation being ‘decision procedures’ and ‘proof search’). The best interactive theorem provers are those in which this kind of automation has been developed furthest. The Handbook is a comprehensive treatment of this kind of automation. The book consists of three strains that have been woven together expertly. The first strain consists of English prose, treating the topics of the book in computer science style. The second strain is a mathematical treatment consisting of definitions and theorems with full mathematical proofs. And the third strain is the source code of a computer program in the programming language OCaml, that implements everything that is being treated in detailed working code. When reading the book one can ignore the second and third strains without losing understanding of the subject. If one thinks ‘Yes, I believe that that theorem holds, I am not interested in the details of the proof right now’, one can skip over the proof without getting lost. Or if one thinks, ‘Yes, I roughly understand how that works, I believe that it can be implemented’, one can skip over the program source without problems too. However, if one is interested in the details of either the mathematics or the implementation, it is all there. If one strips the English from the book, one gets the full source of a beautiful self-contained theorem prover. The book even includes the source for mundane things like parsing and pretty-printing. It shows the power of functional program-