Graph Interpolation Grammars: a Rule-based Approach to the Incremental Parsing of Natural Languages

Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a syntactic representation of a sentence as each successive lexeme is read. A GIG rule specifies a set of parse configurations that trigger its application and an operation to perform on a matching configuration. Rules are partly context-sensitive; furthermore, they are reversible, meaning that their operations can be undone, which allows the parsing process to be nondeterministic. These two factors confer enough expressive power to the formalism for parsing natural languages.Comment: 41 pages, Postscript onl

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

Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

Towards Zero-Overhead Disambiguation of Deep Priority Conflicts

**Context** Context-free grammars are widely used for language prototyping and implementation. They allow formalizing the syntax of domain-specific or general-purpose programming languages concisely and declaratively. However, the natural and concise way of writing a context-free grammar is often ambiguous. Therefore, grammar formalisms support extensions in the form of *declarative disambiguation rules* to specify operator precedence and associativity, solving ambiguities that are caused by the subset of the grammar that corresponds to expressions. **Inquiry** Implementing support for declarative disambiguation within a parser typically comes with one or more of the following limitations in practice: a lack of parsing performance, or a lack of modularity (i.e., disallowing the composition of grammar fragments of potentially different languages). The latter subject is generally addressed by scannerless generalized parsers. We aim to equip scannerless generalized parsers with novel disambiguation methods that are inherently performant, without compromising the concerns of modularity and language composition. **Approach** In this paper, we present a novel low-overhead implementation technique for disambiguating deep associativity and priority conflicts in scannerless generalized parsers with lightweight data-dependency. **Knowledge** Ambiguities with respect to operator precedence and associativity arise from combining the various operators of a language. While *shallow conflicts* can be resolved efficiently by one-level tree patterns, *deep conflicts* require more elaborate techniques, because they can occur arbitrarily nested in a tree. Current state-of-the-art approaches to solving deep priority conflicts come with a severe performance overhead. **Grounding** We evaluated our new approach against state-of-the-art declarative disambiguation mechanisms. By parsing a corpus of popular open-source repositories written in Java and OCaml, we found that our approach yields speedups of up to 1.73x over a grammar rewriting technique when parsing programs with deep priority conflicts--with a modest overhead of 1-2 % when parsing programs without deep conflicts. **Importance** A recent empirical study shows that deep priority conflicts are indeed wide-spread in real-world programs. The study shows that in a corpus of popular OCaml projects on Github, up to 17 % of the source files contain deep priority conflicts. However, there is no solution in the literature that addresses efficient disambiguation of deep priority conflicts, with support for modular and composable syntax definitions