Explicit Binds: Effortless Efficiency with and without Trees

We demonstrate a simple and robust program transformation technique that can improve asymptotic time complexity of datamanipulating programs (e.g., produce a linear-time list reversal function from the obvious quadratic one). In the version of the present paper, it applies to monadic inductive datatypes and can be stated in two flavors, through a datatype representation, with an explicit (“frozen”) bind constructor and a special associated defining clause for the fold function, and in a functional form (generalized Church numerals), with a special definition of the bind function in terms of the build constructor. The technique explicates, systematizes, combines and scales a number of ideas known from the literature, achieving a new level of generality.