Enumerating Well-Typed Terms Generically

We use generic programming techniques to generate well-typed lambda terms. We encode well-typed terms by generalized algebraic datatypes (GADTs) and existential types. The Spine approach (Hinze et al. 2006; Hinze and Löh 2006) to generic programming supports GADTs, but it does not support the definition of generic producers for existentials. We describe how to extend the Spine approach to support existentials and we use the improved Spine to define a generic enumeration function. We show that the enumeration function can be used to generate the terms of simply typed lambda calculus.