Parsing As Tree Traversal

This paper presents a unified approach to parsing, in which top-down, bot tomup and left-corner parsers m:e related to preorder, postorder and inorder tree traversals. It is shown that the simplest bo t tom-up and left-corner parsers are left recursive and must be converted using an extended Greibach normal form. With further partial execution, the bo t tom-up and left-corner parsers collapse togethe~ as in the I]IJP parser of Matsumoto . 1 I N T R O D U C T I O N In this paper , I present a unified approach to parsing, in which top-down, bo t tom-up and left-corner parsers are related to preorder, postorder and inorder tree traversals. To some extent , this connection is already clear since for each parsing strategy the nodes of the parse tree are constructed according to the corresponding tree traversal. It is somewhat trickier though, to actually use a tree traversa.l program as a parser since the resulting pa.rser may be left recursive. This left recursion can *The research presented in this paper was partially sponsored by Teilprojekt Bd "Constraints on Grammar for Efficient Generation" of the Sonderforschungsbereich 340 of the Deutsche Forschungsgemeinschaft. I wouhl also like to thank Guido Minnen and Dieter Martini for helpflfl comments. All mistakes are of course my own. ?KI. Wilhelmstr. 113, D-72074 T(ibingen, Germany, [email protected]. be el iminated, however, by employing a version of Greibach Normal Form which is extended to handle argument instantiations in definite clause grammars . The resulting parsers resemble the s tandard Prolog versions of versions of such parsers. One can then go one step further and partially execute the parser with respect to a part icular g rammaras is normally done with definite clause gra,,nn~a,'s (Per(,ir~ ~ Warren [JO]). a surprising result of this partial execution is l.ha.t the bo t tom-up and leftcorner parsers become identical when they are 1)oth partially executed. This may explain why the BUP parser of ~/lil.tSllll]OtO e t a ] . [6] [71 was ,'eferre.d tO as a bottona-u I) parser even though i t c lear ly fol lows a le f t -corner strategy. T R E E T R A V E R S A L