Random generators for dependent types

Authors:
Peter Dybjer;Qiao Haiyan;Makoto Takeyama
Affiliations:
Department of Computing Science, Chalmers University of Technology, Göteborg, Sweden;Department of Computing Science, Chalmers University of Technology, Göteborg, Sweden;Research Centre for Verification and Semantics, National Institute of Advanced Industrial Science and Technology, Amagasaki Hyogo, Japan
Venue:
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Year:
2004

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Abstract

We show how to write surjective random generators for several different classes of inductively defined types in dependent type theory. We discuss both non-indexed (simple) types and indexed families of types. In particular we show how to use the relationship between indexed inductive definitions and logic programs: the indexed inductive definition of a type family corresponds to a logic program, and generating an object of a type in the family corresponds to solving a query for the logic program. As an example, we show how to write a surjective random generator for theorems in propositional logic by randomising the Prolog search algorithm.