Mechanical Analysis of Finite Idempotent Relations

We use the technique of interactive theorem proving to develop the theory and an enumeration technique for finite idempotent relations. Starting from a short mathematical characterization of finite idempotents defined and proved in Isabelle/HOL, we derive first an iterative procedure to generate all instances of idempotents over a finite set. From there, we develop a more precise theoretical characterization giving rise to an efficient predicate that can be executed in the programming language ML. Idempotent relations represent a very basic, general mathematical concept but the steps taken to develop their theory with the help of Isabelle/HOL are representative for developing algorithms from a mathematical specification. (Research for this paper has been partly performed in collaboration with J.W. Sanders, University of Oxford and has been supported by grant ARC D/03/20258 of the German Academic Exchange Service (DAAD).)

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