Grammar Analysis and Parsing by Abstract Interpretation

Cousot, Patrick; Cousot, Radhia

doi:10.1007/978-3-540-71322-7_9

Cited by 9 publications

(6 citation statements)

References 17 publications

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“…We showed how abstract interpretation of the maximal trace semantics of a simple grammar-based language, akin the semantics of context-free grammars and push-down automata [35], can provide a comprehensive view of most well-known semantics of resolution-based languages such as logic programming and Prolog. Other semantics can be derived similarly, for instance for modelling infinite computations by combining inductive and co-inductive semantics [50] and for modelling different forms of negation [27].…”

Section: Resultsmentioning

confidence: 99%

“…In the following we use the grammar LALR-based notation in [35] for sets of clauses. We let stacks ∈ S K + for a program P ∈ P be nonempty sequences of control states κ ∈ K C ∪ M which are either a clause state in C {[i:A ← B B ] | i:A ← B B ∈ P} specifying the control state of the derivation (B has been derived while B is still to be derived) or a marker…”

Section: Stacksmentioning

confidence: 99%

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Abstract interpretation of resolution-based semantics

Cousot

Giacobazzi

2009

Theoretical Computer Science

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a b s t r a c tWe extend the abstract interpretation point of view on context-free grammars by Cousot and Cousot to resolution-based logic programs and proof systems. Starting from a transition-based small-step operational semantics of Prolog programs (akin to the Warren Machine), we consider maximal finite derivations for the transition system from most general goals. This semantics is abstracted by instantiation to terms and furthermore to ground terms, following the so-called c-and s-semantics approach. Orthogonally, these sets of derivations can be abstracted to SLD-trees, call patterns and models, as well as interpreters providing effective implementations (such as Prolog). These semantics can be presented in bottom-up fixpoint form. This abstract interpretation-based construction leads to classical bottom-up semantics (such as the s-semantics of computed answers, the c-semantics of correct answers of Keith Clark, and the minimal-model semantics of logical consequences of Maarten van Emden and Robert Kowalski). The approach is general and can be applied to infinite and top-down semantics in a straightforward way.

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Section: Resultsmentioning

confidence: 99%

Section: Stacksmentioning

confidence: 99%

Abstract interpretation of resolution-based semantics

Cousot

Giacobazzi

2009

Theoretical Computer Science

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“…Let F be an overapproximation of α(post * N (m 0 )) and let B be an overapproximation α( pre * N (S)). The following lemma which easily follows from the results of [7] shows the usefulness of such approximations.…”

Section: Abstract Semanticsmentioning

confidence: 93%

From Many Places to Few: Automatic Abstraction Refinement for Petri Nets

Ganty

Raskin

Begin

2007

Petri Nets and Other Models of Concurrency – ICATPN 2007

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Abstract. Current algorithms for the automatic verification of Petri nets suffer from the explosion caused by the high dimensionality of the state spaces of practical examples. In this paper, we develop an abstract interpretation based analysis that reduces the dimensionality of state spaces that are explored during verification. In our approach, the dimensionality is reduced by trying to gather places that may not be important for the property to establish. If the abstraction that is obtained is too coarse, an automatic refinement is performed and a more precise abstraction is obtained. The refinement is computed by taking into account information about the inconclusive analysis. The process is iterated until the property is proved to be true or false.

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“…Bottom-up methods compute the leaves of the parse tree first, and grow toward the root. Yet, derivative-based parsing differs from bottom-up methods too, including abstract interpretation [4,5], operator-precedence parsing [11,16], simple precedence parsing [8], bounded context parsing [12], SLR parsing [7], LALR parsing [6], LR(k) parsing [14], GLR parsing [17], CYK parsing [10,20,3], and Earley parsing [9]. Derivative-based parsing shares full coverage of all context-free grammars with GLR, CYK and Earley.…”

Section: Related Workmentioning

confidence: 99%

Yacc is dead

Might,

Darais

2010

Preprint

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We present two novel approaches to parsing context-free languages. The first approach is based on an extension of Brzozowski's derivative from regular expressions to context-free grammars. The second approach is based on a generalization of the derivative to parser combinators. The payoff of these techniques is a small (less than 250 lines of code), easy-to-implement parsing library capable of parsing arbitrary context-free grammars into lazy parse forests. Implementations for both Scala and Haskell are provided. Preliminary experiments with S-Expressions parsed millions of tokens per second, which suggests this technique is efficient enough for use in practice.1 Top-down motivation: End cargo cult parsing "Cargo cult parsing" is a plague upon computing. 1 Cargo cult parsing refers to the use of "magic" regular expressions-often cut and pasted directly from Google search results-to parse languages which ought to be parsed with contextfree grammars. Such parsing has two outcomes. In the first case, the programmer produces a parser that works "most of the time" because the underlying language is fundamentally ir regular. In the second case, some domain-specific language ends up with a mulish syntax, because the programmer has squeezed the language through the regular bottleneck. There are two reasons why regular expressions are so abused while context-free languages remain foresaken: (1) regular expression libraries are available in almost every language, while parsing libraries and toolkits are not, and (2) regular expressions are "WYSIWYG"-the language described is the language that gets matched-whereas parser-generators are WYSIWYGIYULR(k)-"what you see is what you get if you understand LR(k)." To end cargo-cult parsing, we need a new approach to parsing that:1. handles arbitrary context-free grammars; 2. parses efficiently on average; and 3. can be implemented as a library with little effort.The end goals of the three conditions are simplicity, feasibility and ubiquity. The "arbitrary context-free grammar" condition is necessary because programmers will be less inclined to use a tool that forces them to learn or think about LL/LR arcana. It is hard for compiler experts to imagine, but the constraints on LL/LR 1 The term "cargo cult parsing" is due to Larry Wall, 19 June 2008, Google Tech Talk.

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Grammar Analysis and Parsing by Abstract Interpretation

Cited by 9 publications

References 17 publications

Abstract interpretation of resolution-based semantics

Abstract interpretation of resolution-based semantics

From Many Places to Few: Automatic Abstraction Refinement for Petri Nets

Yacc is dead

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