A Translation from Attribute Grammars to Catamorphisms

Let AG be an attribute grammar, with underlying context free grammar G and attribute evaluation rules A . The function that decorates —according to A— a parse tree with attribute values and then delivers the synthesized attribute value of the root node, is denoted [[A]] . We translate G into a functor F such that any parse tree for G is an element of the initial F -algebra. The attribute evaluation rules A are translated to a function φ such that ([F| φ]) is, in a precise sense, equivalent to [[A]] .