Syntax-Directed Semantics
Formal Models Based on Tree Transducers
Published on 6. December 2012
X, 269 pages
978-3-642-72248-6 (ISBN)
Description
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.
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Content
1. Introduction.- 1.1 Syntax-Directed Semantics.- 1.2 Tree Transducers.- 1.3 Theory of Compositions of Classes of Tree Transformations.- 1.4 Other Formal Models.- 1.5 Outline of the Book.- 1.6 Bibliographic Notes.- 2. Basic Notions and Notations.- 2.1 Sets and Relations.- 2.2 Partial Orders.- 2.3 Directed Graphs.- 2.4 Derivation Systems.- 2.5 Semigroups, Strings and Languages.- 2.6 String Rewrite Systems.- 2.7 Grammars.- 2.8 Notions on Trees.- 3. Top-Down Tree Transducers.- 3.1 Basic Definitions.- 3.2 Induced Tree Transformation.- 3.3 Characterization of Top-Down Tree Transformations.- 3.4 Height Property.- 3.5 Subclasses of TOP.- 3.6 Composition and Decomposition Results.- 3.7 Composition Semigroup Generated by TOP, l-TOP, and HOM.- 3.8 Bibliographic Notes.- 4. Macro Tree Transducers.- 4.1 Basic Definitions.- 4.2 Induced Tree Transformation.- 4.3 Characterization of Macro Tree Transformations.- 4.4 Height Property.- 4.5 Composition and Decomposition Results.- 4.6 Bibliographic Notes.- 5. Attributed Tree Transducers.- 5.1 Basic Definitions.- 5.2 Induced Tree Transformation.- 5.3 Characterization of Attributed Tree Transformations.- 5.4 Height and Subtree Properties.- 5.5 Composition and Decomposition Results.- 5.6 Bibliographic Notes.- 6. Comparison of Induced Tree Transformation Classes.- 6.1 Comparison of M AC and ATT.- 6.2 Inclusion Diagram Based on TOP, YIELD, ATT, and M AC.- 6.3 Composition Semigroup Generated by TOP, ATT, and MAC.- 6.4 Bibliographic Notes.- 7. Macro Attributed Tree Transducers.- 7.1 Basic Definitions.- 7.2 Induced Tree Transformation.- 7.3 Characterization of Macro Attributed Tree Transformations.- 7.4 Composition and Decomposition Results.- 7.5 Height Property.- 7.6 Bibliographic Notes.- 8. Two Examples.- 8.1 The Specification Language.- 8.2 Contextual Analysis.- 8.3 Insertion into 2-3 Trees.- 8.4 Bibliographic Notes.
