Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda
Artikel i vetenskaplig tidskrift, 2016

Valiant (1975) has developed an algorithm for recognition of context free languages. As of today, it remains the algorithm with the best asymptotic complexity for this purpose. In this paper, we present an algebraic specification, implementation, and proof of correctness of a generalisation of Valiant’s algorithm. The generalisation can be used for recognition, parsing or generic calculation of the transitive closure of upper triangular matrices. The proof is certified by the Agda proof assistant. The certification is representative of state-of-the-art methods for specification and proofs in proof assistants based on type-theory. As such, this paper can be read as a tutorial for the Agda system.

Proof

Context-Free Parsing

Valiant’s algorithm

Agda.

Författare

Jean-Philippe Bernardy

Chalmers, Data- och informationsteknik, Programvaruteknik

Patrik Jansson

Chalmers, Data- och informationsteknik, Programvaruteknik

Logical Methods in Computer Science

1860-5974 (ISSN)

Vol. 12 28-

Ämneskategorier

Algebra och logik

Programvaruteknik

Datavetenskap (datalogi)

Styrkeområden

Informations- och kommunikationsteknik

Fundament

Grundläggande vetenskaper

DOI

10.2168/LMCS-12(2