This paper presents a fixedpoint approach to inductive definitions. Instead of using a syntactic test such as "strictly positive," the approach lets definitions involve any operators that have been proved monotone. It is conceptually simple, which has allowed the easy implementation of mutual recursion and iterated definitions. It also handles coinductive definitions: simply replace the least fixedpoint by a greatest fixedpoint. The method

This working paper develops a Tofte-Talpin style region inference system... this paper have been formalized in Isabelle and all proofs have been mechanically verified.

Abstract. Several more or less algebraic approaches to model checking are presented and compared with each other with respect to their range of applications and their degree of automation. All of them have been implemented and tested in our Haskell-based formal-reasoning system Expander2. Besides realizing and integrating state-of-the art proof and computation rules the system admits rarely restricted specifications of the models to be checked in terms of rewrite rules and functional-logic programs. It also offers flexible features for visualizing and even animating models and computations. Indeed, this paper does not present purely theoretical work. Due to the increasing abstraction potential of programming languages like Haskell the boundaries between developing a formal system and implementing it or making it ‘user-friendly ’ as well as between systems developed in different communities become more and more obsolete. The individual topics discussed in the paper reflect this observation. 1