Certified Derivative-Based Parsing of Regular Expressions

Lopes, Raul; Ribeiro, Rodrigo; Camarão, Carlos

doi:10.1007/978-3-319-45279-1_7

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…Hardin [11] uses the HOL4 theorem prover to verify an implementation of Brzozowski's regex-to-DFA algorithm, which is incorporated into a lexer. Lopes et al [16] present a regex matcher based on Brzozowski derivatives. The matcher takes a regular expression e and a string s as input; if s matches e, the tool produces a proof of the match.…”

Section: Related Workmentioning

confidence: 99%

Verbatim++: verified, optimized, and semantically rich lexing with derivatives

Egolf

Lasser

Fisher

2022

Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs

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Lexers and parsers are attractive targets for attackers because they often sit at the boundary between a software system's internals and the outside world. Formally verified lexers can reduce the attack surface of these systems, thus making them more secure.One recent step in this direction is the development of Verbatim, a verified lexer based on the concept of Brzozowski derivatives. Two limitations restrict the tool's usefulness. First, its running time is quadratic in the length of its input string. Second, the lexer produces tokens with a simple łtag and stringž representation, which limits the tool's ability to integrate with parsers that operate on more expressive token representations.In this work, we present a suite of extensions to Verbatim that overcomes these limitations while preserving the tool's original correctness guarantees. The lexer achieves effectively linear performance on a JSON benchmark through a combination of optimizations that, to our knowledge, has not been previously verified. The enhanced version of Verbatim also enables users to augment their lexical specifications with custom semantic actions, and it uses these actions to produce semantically rich tokensÐi.e., tokens that carry values with arbitrary, user-defined types. All extensions were implemented and verified with the Coq Proof Assistant.

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Section: Related Workmentioning

confidence: 99%

Verbatim++: verified, optimized, and semantically rich lexing with derivatives

Egolf

Lasser

Fisher

2022

Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs

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“…al. [28] describe an Idris formalization of a RE parsing tool using Brzozowski's derivatives. Like our work, they proved both soundness and completeness lemmas for the derivative operation and used data-types for denoting prefixes and substrings proofs for a given input RE and string.…”

Section: Related Workmentioning

confidence: 99%

“…al. [28] also mention that they use natural numbers in Peano notation to represent alphabet symbols as their respective ASCII codes, instead of using Idris type for characters. According to the authors, the reason for this design choice is due to the way that Idris deals with propositional equality for primitive types, like Char.…”

Section: Related Workmentioning

confidence: 99%

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The Design of a Verified Derivative-Based Parsing Tool for Regular Expressions

Cardoso¹,

Amaro²,

Feitosa³

et al. 2021

CLEIej

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We describe the formalization of Brzozowski and Antimirov derivative based algorithms for regular expression parsing, in the dependently typed language Agda. The formalization produces a proof that either an input string matches a given regular expression or that no matching exists. A tool for regular expression based search in the style of the well known GNU grep has been developed with the certified algorithms. Practical experiments conducted with this tool are reported.

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“…In subsequent work, Tan and Morrisett [24] certified encoder/decoder pairs are constructed from bidirectional grammars. Lopes, Ribeiro, and Camarão [19] have also verified a regular expression parser using Idris [5]. Bernardy and Jansson [3] have formalized Valiant's algorithm for parsing context-free languages in Agda [4].…”

Section: Introductionmentioning

confidence: 99%

A verified packrat parser interpreter for parsing expression grammars

Blaudeau

Shankar

2020

Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

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Parsing expression grammars (PEGs) offer a natural opportunity for building verified parser interpreters based on higherorder parsing combinators. PEGs are expressive, unambiguous, and efficient to parse in a top-down recursive descent style. We use the rich type system of the PVS specification language and verification system to formalize the metatheory of PEGs and define a reference implementation of a recursive parser interpreter for PEGs. In order to ensure termination of parsing, we define a notion of a well-formed grammar. Rather than relying on an inductive definition of parsing, we use abstract syntax trees that represent the computational trace of the parser to provide an effective proof certificate for correct parsing and ensure that parsing properties including soundness and completeness are maintained. The correctness properties are embedded in the types of the operations so that the proofs can be easily constructed from local proof obligations. Building on the reference parser interpreter, we define a packrat parser interpreter as well as an extension that is capable of semantic interpretation. Both these parser interpreters are proved equivalent to the reference one. All of the parsers are executable. The proofs are formalized in mathematical terms so that similar parser interpreters can * be defined in any specification language with a type system similar to PVS.

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Certified Derivative-Based Parsing of Regular Expressions

Cited by 7 publications

References 24 publications

Verbatim++: verified, optimized, and semantically rich lexing with derivatives

Verbatim++: verified, optimized, and semantically rich lexing with derivatives

The Design of a Verified Derivative-Based Parsing Tool for Regular Expressions

A verified packrat parser interpreter for parsing expression grammars

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