Generating parsers for affix grammars

ABSTRACT

Affix grammars are two-level grammars which are similar to van Wijngaarden's two-level grammars used in the definition of Algol 68. Affix grammars are shown by Koster to be equal in power to van Wijngaarden grammars. They are much more suited to parsing than are the latter, however. Koster, the inventor of affix grammars, suggests a top-down scheme for parsing them, based on recursive procedures. This paper presents a bottom-up scheme for parsing them, based on an extension of Floyd Production Language (FPL). Included is an algorithm, similar to that of DeRemer's, for converting a large class of affix grammars into FPL. The paper concludes by discussing briefly the applicabilities of the conversion algorithm and affix grammars in general, and some possible extensions to Koster's definition of affix grammars.

REFERENCES

• 1: DeRemer, F.L. Generating parsers for BNF grammars. Proc. AFIPS 1969 SJCC, Vol. 34, AFIPS Press, Montvale, N.J., pp. 795-799.
• 2: Robert W. Floyd, A Descriptive Language for Symbol Manipulation, Journal of the ACM (JACM), v.8 n.4, p.579-584, Oct. 1961 [doi>10.1145/321088.321096]
• 3: Koster, C.H.A. Affix grammars. In ALGOL 68 Implementation, North-Holland Pub. Co., Amsterdam, 1971, p. 95.
• 4: Koster, C.H.A. Two-level Grammars. Seminar on Automata and Mathematical Linguistics, Mathematisch Instituut, Budapest, May 1970.
• 5: Koster, C.H.A. Syntax-directed parsing of ALGOL 68 programs. Proc. Informal Conf. on ALGOL 68 Implementation, U. of British Columbia, Vancouver, Aug. 1969.

INDEX TERMS

Keywords:
Floyd Production Language, algorithmic language processing, bottom-up parsing, parsing, syntax directed compiling, translator writing systems, two-level grammars