A fixedpoint approach to implementing (Co)inductive definitions

Abstract

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 other conveniences. It also handles coinductive definitions: simply replace the least fixedpoint by a greatest fixedpoint. This represents the first automated support for coinductive definitions.The method has been implemented in Isabelle's formalization of ZF set theory. It should be applicable to any logic in which the Knaster-Tarski Theorem can be proved. Examples include lists of n elements, the accessible part of a relation and the set of primitive recursive functions. One example of a coinductive definition is bisimulations for lazy lists.KeywordsInduction RuleElimination RuleIntroduction RuleInductive DefinitionMinor PremiseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.