The formal power of one-visit attribute grammars

An attribute grammar is one-visit if the attributes can be evaluated by walking through the derivation tree in such a way that each subtree is visited at most once. One-visit (1V) attribute grammars are compared with one-pass left-to-right (L) attribute grammars and with attribute grammars having only one synthesized attribute (1S).\ud \ud Every 1S attribute grammar can be made one-visit. One-visit attribute grammars are simply permutations of L attribute grammars; thus the classes of output sets of 1V and L attribute grammars coincide, and similarly for 1S and L-1S attribute grammars. In case all attribute values are trees, the translation realized by a 1V attribute grammar is the composition of the translation realized by a 1S attribute grammar with a deterministic top-down tree transduction, and vice versa; thus, using a result of Duske e.a., the class of output languages of 1V (or L) attribute grammars is the image of the class of IO macro tree languages under all deterministic top-down tree transductions

Interpretation and reduction of attribute grammars

An attribute grammar (AG) is in reduced form if in all its derivation trees every attribute contributes to the translation. We prove that, eventhough AG are generally not in reduced form, they can be reduced, i.e., put into reduced form, without modifying their translations. This is shown first for noncircular AG and then for arbitrary AG. In both cases the reduction consists of easy (almost syntactic) transformations which do not change the semantic domain of the AG. These easy transformations are formalized by introducing the notion of AG interpretation as an extension to AG of the concept of context-free grammar form. Finally we prove that any general algorithm for reducing even the simple class of L-AG needs exponential time (in the size of the input AG) infinitely often

Symbol–Relation Grammars: A Formalism for Graphical Languages

AbstractA common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol–Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes

Tree automata and attribute grammars

The translational mechanism of attribute grammars using tree automata are investigated. The pushdown tree-to-string transducer with a certain synchronization facility as a model to realize transformations by attribute grammars is proposed and its basic properties using tree-walking finite state automata are studied. To demonstrate the utility of this model, it is shown that noncircular attribute grammars are equally powerful as arbitrary attribute grammars, and a method is provided to show that a certain type of transformations is impossible by attribute grammars

Simple multi-visit attribute grammars

An attribute grammar is simple multi-visit if each attribute of a nonterminal has a fixed visit-number associated with it such that, during attribute evaluation, the attributes of a node which have visit-number j are computed at the jth visit to the node. An attribute grammar is l-ordered if for each nonterminal a linear order of its attributes exists such that the attributes of a node can always be evaluated in that order (cf. the work of Kastens).\ud \ud An attribute grammar is simple multi-visit if and only if it is l-ordered. Every noncircular attribute grammar can be transformed into an equivalent simple multi-visit attribute grammar which uses the same semantic operations.\ud \ud For a given distribution of visit-numbers over the attributes, it can be decided in polynomial time whether the attributes can be evaluated according to these visit-numbers. The problem whether an attribute grammar is simple multi-visit is NP-complete

Generalizing input-driven languages: theoretical and practical benefits

Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families

Tools and libraries to model and manipulate circular programs

This paper presents techniques to model circular lazy programs in a strict, purely functional setting. Circular lazy programs model any algorithm based on multiple traversals over a recursive data structure as a single traversal function. Such elegant and concise circular programs are defined in a (strict or lazy) functional language and they are transformed into efficient strict and deforested, multiple traversal programs by using attribute grammars-based techniques. Moreover, we use standard slicing techniques to slice such circular lazy programs. We have expressed these transformations as an Haskell library and two tools have been constructed: the HaCirctool that refactors Haskell lazy circular programs into strict ones, and the OCirctool that extends Ocaml with circular definitions allowing programmers to write circular programs in Ocaml notation, which are transformed into strict Ocaml programs before they are executed. The first benchmarks of the different implementations are presented and show that for algorithms relying on a large number of traversals the resulting strict, deforested programs are more efficient than the lazy ones, both in terms of runtime and memory consumption.(undefined