This paper describes a set of theorem proving tools based on a new derived principle of definition in HOL, namely the introduction of relations inductively defined by a set of rules. Such inductive definitions abound in computer science. Example application areas include reasoning about structured operational semantics, type judgements, transition relations for process algebras, reduction relations, and compositional proof systems. The package described in this paper automates the derivation of certain inductive definitions involved in these applications and provides the basic tools needed for reasoning about the relations introduced by them. 1 Introduction The HOL user community has a strong tradition of taking a purely definitional approach to using higher order logic. That is, the syntax of the logic is extended with new notation not simply by postulating axioms to give meaning to it, but rather by defining it in terms of existing expressions of the logic that already have the requ...

: Inductively defined relations are among the basic mathematical tools of computer science. Examples include evaluation and computation relations in structural operational semantics, labelled transition relations in process algebra semantics, inductively-defined typing judgements, and proof systems in general. This paper describes a set of HOL theorem-proving tools for reasoning about such inductively defined relations. We also describe a suite of worked examples using these tools. First printed: August 1992 Parts of this report have previously appeared as: T. Melham, `A Package for Inductive Relation Definitions in HOL', in Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications, Davis, August 1991, edited by M. Archer, J. J. Joyce, K. N. Levitt, and P. J. Windley (IEEE Computer Society Press, 1992), pp. 350--357. Contents Introduction 4 1 Inductive definitions 5 1.1 Rule induction : : : : : : : : : : : : : : : : : : : : : : : : :...