Random generators for dependent types

Paper in proceeding, 2004

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.