The Duality of Construction

We explore the duality of construction and deconstruction in the presence of different evaluation strategies. We characterize an evaluation strategy by the notion of substitutability, given by defining what is a value and a co-value, and we present an equational theory that takes the strategy as a parameter. The theory may be extended with new logical connectives, in the form of user-defined data and co-data types, which are duals of one another. Finally, we explore a calculus with composite evaluation strategies that allow for more flexibility over evaluation order by mingling multiple primitive strategies within a single program.