  A theory of recursive definitions has been mechanized in Isabelle's
Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization
of particular recursive definitions for use in verification, semantics proofs
and other computational reasoning. Inductively defined sets are expressed as
least fixedpoints, applying the Knaster-Tarski Theorem over a suitable set.
Recursive functions are defined by well-founded recursion and its derivatives,
such as transfinite recursion. Recursive data structures are expressed by
applying the Knaster-Tarski Theorem to a set, such as V[omega], that is closed
under Cartesian product and disjoint sum. Worked examples include the
transitive closure of a relation, lists, variable-branching trees and mutually
recursive trees and forests. The Schr\"oder-Bernstein Theorem and the soundness
of propositional logic are proved in Isabelle sessions.
