Attribute Grammars and Functional Programming Deforestation

The functional programming community is paying increasing attention to static structure-based transformations. For example, generic control operators , such as fold, have been introduced in functional programming to increase the power and applicability of a particular kind of static transformation, called deforestation, which prevents the construction of useless intermediate data structures in function composition. This is achieved by making the structure of the data more explicit in program speciications. We argue that one of the original concepts of Attribute Grammars is precisely to make data structures explicit in program speciications. Furthermore, there exists a powerful static deforestation-like transformation in their context. In this paper, we present similarities between deforestation methods, on the one hand with the functional approach, and on the other hand with the Attribute Grammars approach. In order to gain a grasp of these similarities, we rst make a simple comparison: purely-synthesized Attribute Grammars and rst order folds. In this context, deforestation transformations are equivalent. This allows us to highlight the limitations of the fold formalism and to present how the hy-lomorphism approach generalizes it; hylomorphisms and attribute grammars are surprisingly alike. Finally, we show how the inherited attribute notion in Attribute Grammars solves some transformation problems in higher order functional programs.