## Relational Properties of Recursively Defined Domains (1993)

Venue: | In 8th Annual Symposium on Logic in Computer Science |

Citations: | 15 - 2 self |

### BibTeX

@INPROCEEDINGS{Pitts93relationalproperties,

author = {Andrew M. Pitts},

title = {Relational Properties of Recursively Defined Domains},

booktitle = {In 8th Annual Symposium on Logic in Computer Science},

year = {1993},

pages = {86--97},

publisher = {IEEE Computer Society Press}

}

### OpenURL

### Abstract

This paper describes a mixed induction/co-induction property of relations on recursively defined 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/finality 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 relational framework yields a family of induction principles for admissible subsets of general recursively defined domains which extends the principle of structural induction for inductively defined sets. Another instance of the framework yields the co-induction principle studied by the author in [22], by which equalities between elements of recursively defined domains may be proved via `bisimulations'. 1 Introduction A characteristic feature of higher-order functional lan...