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A Package for Inductive Relation Definitions in HOL
 in Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications
, 1992
"... 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 o ..."
Abstract

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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...