A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular look-ahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular look-ahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular look-ahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...

We present a technique to prevent the construction of intermediate data structures in functional programs, which is based on results from the theory of tree transducers. We first decompose function definitions, which correspond to macro tree transducers, into smaller pieces. Under certain restrictions...

. Two well-known formalisms for the specication and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with look-ahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to dene the output tree in terms of the input tree. The attributed tree transducer is an attribute grammar in which all attributes are trees; it is preceded by a look-ahead phase in which all attributes have nitely many values. The main result is that these formalisms are equivalent, i.e., that the attributed tree transducer with look-ahead is an appropriate implementation model for the tree transductions that are speciable in mso logic. This result holds for mso graph transducers that produce trees with shared subtrees. If no sharing is allowed, the attributed tree transducer satises the single use restriction. 1 Introduction Formulas of monadic second order (mso) logic can be used to express properti...

Abstract. This paper describes the Java Language Extender framework, a tool that allows one to create new domain-adapted languages by importing domain-specific language extensions into an extensible implementation of Java 1.4. Language extensions may define the syntax, semantic analysis, and optimizations of new language constructs. Java and the language extensions are specified as higher-order attribute grammars. We describe several language extensions and their implementation in the framework. For example, one embeds the SQL database query language into Java and statically checks for syntax and type errors in SQL queries. The tool supports the modular specification of composable language extensions so that programmers can import into Java the unique set of extensions that they desire. When extensions follow certain restrictions, they can be composed without requiring any implementation-level knowledge of the language extensions. The tools automatically compose the selected extensions and the Java host language specification. 1

Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. In order to do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.

We compare transformations for the elimination of intermediate results in first-order functional programs. We choose the well known deforestation technique of Wadler and composition techniques from the theory of tree transducers, of which the implementation of functional programs yet does not take advantage. We identify syntactic classes of function definitions for which both techniques deliver equally efficient results and for which one technique is more powerful than the other.

Unfortunately, the class of transformations computed by linear extended top-down tree transducers with regular look-ahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it is demonstrated that every linear epsilon-free extended top-down tree transducer with regular look-ahead can be implemented by a linear multi bottom-up tree transducer. The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by top-down tree transducers with itself. More precisely, it constitutes the composition closure of the class of transformations computed by nite-copying top-down tree transducers.

We study the problem to transform functional programs, which intensively use append functions (like inefficient list reversal), into programs, which use accumulating parameters instead (like efficient list reversal). We give an (automatic) transformation algorithm for our problem and identify a class of functional programs, namely restricted 2-modular tree transducers, to which it can be applied. Moreover, since we get macro tree transducers as transformation result and since we also give the inverse transformation algorithm, we have a new characterization for the class of functions induced by macro tree transducers.

Abstract. The first main result is that if a macro tree translation is of linear size increase, i.e., if the size of every output tree is linearly bounded by the size of the corresponding input tree, then the translation is MSO definable (i.e., definable in monadic second-order logic). This gives a new characterization of the MSO definable tree translations in terms of macro tree transducers: they are exactly the macro tree translations of linear size increase. The second main result is that given a macro tree transducer, it can be decided whether or not its translation is MSO definable, and if it is then an equivalent MSO transducer can be constructed. Similar results hold for attribute grammars, which define a subclass of the macro tree translations.

Attributed tree transducers are abstract models to study properties of attribute grammars. One abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input, instead of derivation trees of a context-free grammar. In this paper we show that with respect to the generating power this is not an abstraction, i.e., we show that attributed tree transducers and attribute grammars generate the same class of term (or tree) languages. To prove this, a number of results concerning the generating power of top-down tree transducers are established, which are interesting in their own. We also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes. The latter result is achieved by proving a hierarchy of classes of tree languages generated by context-free hypergraph grammars with respect to their rank. 1 Introduction Attribute grammars...