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Certified CYK parsing of context-free languages. (English) Zbl 1371.68137
Summary: We report a work on certified parsing for context-free grammars. In our development we implement the Cocke-Younger-Kasami parsing algorithm and prove it correct using the Agda dependently typed programming language.

MSC:
 68Q42 Grammars and rewriting systems 68N15 Theory of programming languages 68Q45 Formal languages and automata
Agda; TRX
Full Text:
References:
 [1] Firsov, D.; Uustalu, T., Certified parsing of regular languages, (Gonthier, G.; Norrish, M., Proc. of 3rd Int. Conf. on Certified Programs and Proofs, CPP 2013, Lect. Notes Comput. Sci., vol. 8307, (2013), Springer Berlin), 98-113 · Zbl 1303.68077 [2] Norell, U., Towards a practical programming language based on dependent type theory, (2007), Chalmers University of Technology Göteborg, Ph.D. thesis [3] Norell, U., Dependently typed programming in agda, (Koopman, P.; Plasmeijer, R.; Swierstra, S. D., Revised Lectures from 6th Int. School on Advanced Functional Programming, AFP 2009, Lect. Notes Comput. Sci., vol. 5832, (2009), Springer Berlin), 230-266 · Zbl 1263.68038 [4] Younger, D., Recognition and parsing of context-free languages in time $$O(n^3)$$, Inf. Comput., 10, 2, 189-208, (1967) · Zbl 0149.24803 [5] Valiant, L. G., General context-free recognition in less than cubic time, J. Comput. Syst. Sci., 10, 2, 308-314, (1975) · Zbl 0312.68042 [6] Nordström, B., Terminating general recursion, BIT Numer. Math., 28, 3, 605-619, (1988) · Zbl 0659.68020 [7] Wadler, P., Comprehending monads, (Proc. of 1990 ACM Conf. on LISP and Functional Programming, LFP ’90, (1990), ACM New York), 61-78 [8] Barthwal, A.; Norrish, M., Verified, executable parsing, (Castagna, G., Proc. of 18th Europ. Symp. on Programming Languages and Systems, ESOP ’09, Lect. Notes Comput. Sci., vol. 5502, (2009), Springer Berlin), 160-174 · Zbl 1234.68359 [9] Koprowski, A.; Binsztok, H., TRX: a formally verified parser interpreter, Log. Methods Comput. Sci., 7, 2, (2011), art. no. 18 · Zbl 1260.68194 [10] Jourdan, J.-H.; Pottier, F.; Leroy, X., Validating LR(1) parsers, (Seidl, H., Proc. of 21st Europ. Symp. on Programming, ESOP 2012, Lect. Notes Comput. Sci., vol. 7211, (2012), Springer Berlin), 397-416 · Zbl 1352.68131 [11] Danielsson, N. A., Total parser combinators, (Proc. of 15th ACM SIGPLAN Int. Conf. on Functional Programming, ICFP ’10, (2010), ACM New York), 285-296 · Zbl 1323.68330 [12] Sjöblom, T. B., An agda proof of the correctness of Valiant’s algorithm for context free parsing, (2013), Chalmers University of Technology Göteborg, Master’s thesis [13] Ridge, T., Simple, functional, sound and complete parsing for all context-free grammars, (Jouannaud, J.-P.; Shao, Z., Proc. of 1st Int. Conf. on Certified Programs and Proofs, CPP 2011, Lect. Notes Comput. Sci., vol. 7086, (2011), Springer Berlin), 103-118 · Zbl 1350.68164
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