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Mechanical Analysis of Finite Idempotent Relations

Kammüller F.

Fundamenta Informaticae

2011

Vol. 107, nr 1

43-65

We use the technique of interactive theoremproving 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