Deforesting in Accumulating Parameters via Type-Directed Transformations

Classical deforestation methods fail to compose functions with accumulating parameters, which are function arguments to which intermediate result accumulates. This paper proposes a new deforestation method which solves this problem. The method is comprised of a few transformation steps, each of which is guided by type information. Though our solution draws its fundamental idea from a deforestation method that has been developed for attribute grammars, it is not merely a recast of an existing technique to another formalism. The new method provides a type-based account for the existing attribute grammar deforestation process. Further, it can deforest a class of functions that the attribute grammar deforestation cannot. These advantages are demonstrated by a few examples. It is also shown that the new method is as powerful as another method that has been developed for macro tree transducer composition.