Abstract

A theory of recursive deflnitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive deflnitions for use in veriflcation, semantics proofs and other computational reasoning. Inductively deflned sets are expressed as least flxedpoints, applying the Knaster-Tarski The- orem over a suitable set. Recursive functions are deflned by well-founded recursion and its derivatives, such as transflnite recursion. Recursive data structures are expressed by applying the Knaster-Tarski Theorem to a set, such as V!, 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 Schroder-Bernstein Theorem and the soundness of propositional logic are proved in Isabelle sessions.

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