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Backtracking techniques which are often used to extend recursive descent (RD) parsers can have explosive run-times and cannot deal with grammars with left recursion. GLL parsers are fully general, worst-case cubic parsers which have the recursive descent-like property that they are easy to write and to use for grammar debugging. They have the direct relationship with the grammar that an RD parser has. In this paper we give an algorithm for generating GLL parsers which build an SPPF representation of the derivations of the input, complementing our existing GLL recognition algorithm, and we show that such parsers and recognisers are worst-case cubic.