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Register a new userFrom Regexes to Parsing Expression Grammars
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Added by
S\\'ergio Medeiros
Publication date
2012
fields
Informatics Engineering
and research's language is
English
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Most scripting languages nowadays use regex pattern-matching libraries. These regex libraries borrow the syntax of regular expressions, but have an informal semantics that is different from the semantics of regular expressions, removing the commutativity of alternation and adding ad-hoc extensions that cannot be expressed by formalisms for efficient recognition of regular languages, such as deterministic finite automata. Parsing Expression Grammars are a formalism that can describe all deterministic context-free languages and has a simple computational model. In this paper, we present a formalization of regexes via transformation to Parsing Expression Grammars. The proposed transformation easily accommodates several of the common regex extensions, giving a formal meaning to them. It also provides a clear computational model that helps to estimate the efficiency of regex-based matchers, and a basis for specifying provably correct optimizations for them.
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Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient implementations of PEG libraries in several programming languages. A frequently missed feature of PEGs is left recursion, which is commonly used in Context-Free Grammars (CFGs) to encode left-associative operations. We present a simple conservative extension to the semantics of PEGs that gives useful meaning to direct and indirect left-recursive rules, and show that our extensions make it easy to express left-recursive idioms from CFGs in PEGs, with similar results. We prove the conservativeness of these extensions, and also prove that they work with any left-recursive PEG. PEGs can also be compiled to programs in a low-level parsing machine. We present an extension to the semantics of the operations of this parsing machine that let it interpret left-recursive PEGs, and prove that this extension is correct with regards to our semantics for left-recursive PEGs.
Context-Free Grammars (CFGs) and Parsing Expression Grammars (PEGs) have several similarities and a few differences in both their syntax and semantics, but they are usually presented through formalisms that hinder a proper comparison. In this paper we present a new formalism for CFGs that highlights the similarities and differences between them. The new formalism borrows from PEGs the use of parsing expressions and the recognition-based semantics. We show how one way of removing non-determinism from this formalism yields a formalism with the semantics of PEGs. We also prove, based on these new formalisms, how LL(1) grammars define the same language whether interpreted as CFGs or as PEGs, and also show how strong-LL(k), right-linear, and LL-regular grammars have simple language-preserving translations from CFGs to PEGs.
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they do not cover a large class of hypergraph languages (e.g. languages consisting of star graphs). In this paper, we introduce a weak Greibach normal form, whose definition corresponds to the lexicalized normal form for string grammars, and prove that every context-free hypergraph language (with nonsubstantial exceptions) can be generated by a grammar in this normal form. The proof presented in this paper generalizes a corresponding one for string grammars with a few more technicalities.
Higher-order grammars are extensions of regular and context-free grammars, where non-terminals may take parameters. They have been extensively studied in 1980s, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result.
Existing deep models for code tend to be trained on syntactic program representations. We present an alternative, called Neural Attribute Grammars, that exposes the semantics of the target language to the training procedure using an attribute grammar. During training, our model learns to replicate the relationship between the syntactic rules used to construct a program, and the semantic attributes (for example, symbol tables) constructed from the context in which the rules are fired. We implement the approach as a system for conditional generation of Java programs modulo eleven natural requirements. Our experiments show that the system generates constraint-abiding programs with significantly higher frequency than a baseline model trained on syntactic program representations, and also in terms of generation accuracy.
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