The Beta Cube

We define a big-step-style template for reduction strategies that can be instantiated to the foremost (and more) reduction strategies of the pure lambda calculus. We implement the template in Haskell as a parametric monadic reducer whose fixed points are reduction strategies. The resulting code is clean and abstracts away from the machinery required to guarantee semantics preservation for all strategies in lazy Haskell. By interpreting some parameters as boolean switches we obtain a reduction strategy lattice or beta cube which captures the strategy space neatly and systematically. We define a hybridisation function that generates hybrid strategies by composing a base and a subsidiary strategy from the cube. We prove an absorption theorem which states that subsidiaries are left-identities of their hybrids. More properties from the cube remain to be explored.