Computing with generic trees in Agda

Abstract

Dependently-typed programming languages offer powerful new means of abstraction, allowing the programmer to work generically across data structures. However, using the standard generic encoding of tree-like data structures (the W-types), we soon notice a caveat: the computational behaviour of W-types does not quite match their first-order counterparts. Here, we show how a tweak to the definition of W-types avoids this caveat, making the generic definition work just as well as the direct one.