Syntax-Directed Semantics

The subject of this book is the investigation of tree transducers. Tree trans­ ducers were introduced in theoretical computer science in order to study the general properties of formal models which give semantics to context-free languages in a syntax-directed way. Such formal models include attribute grammars with synthesized attributes only, denotational semantics, and at­ tribute grammars (with synthesized and inherited attributes). However, these formal models share certain constituents which are irrelevant in the investi­ gation of the general properties considered in this book. In particular, we can abstract (a) from derivation trees of the context-free grammar and take trees over some ranked alphabet, (b) from the semantic domain of the model and use the initial term algebra instead, and finally (c) from the machine­ oriented computation paradigm, which maintains the incarnation information of recursive function calls, and take a term rewriting semantics instead. Ap­ plying these three abstraction steps to attribute grammars with synthesized attributes only, to denotational semantics, and to attribute grammars we obtain the concepts of top-down tree transducer, macro tree transducer, and attributed tree transducer, respectively. The macro attributed tree transducer combines the concepts of the macro tree transducer and the attributed tree transducer. This book explores the general properties of these four types of tree transducers.