Relational Properties of Recursively

This paper describes a mixed induction/co-induction property of relations on recursively deened domains. We work within a general framework for relations on domains and for actions of type constructors on relations introduced by O'Hearn and Tennent 20], and draw upon Freyd's analysis 7] of recursive types in terms of a simultaneous initiality//nality property. The utility of the mixed induction/co-induction property is demonstrated by deriving a number of families of proof principles from it. One instance of the rela-tional framework yields a family of induction principles for admissible subsets of general recursively de-ned domains which extends the principle of structural induction for inductively deened sets. Another instance of the framework yields the co-induction principle studied by the author in 22], by which equalities between elements of recursively deened domains may be proved viàbisimulations'.