Technical Correspondence Techniques for Automatic Memoization with Applications to Context-Free Parsing

It is shown that a process similar to Earley's algorithm can be generated by a simple top-down backtracking parser, when augmented by automatic memoization. The memoized parser has the same complexity as Earley's algorithm, but parses constituents in a different order. Techniques for deriving memo functions are described, with a complete implementation in Common Lisp, and an outline of a macro-based approach for other languages. 1. Memoization The term memoization was coined by Donald Michie (1968) to refer to the process by which a function is made to automatically remember the results of previous compu-tations. The idea has become more popular in recent years with the rise of functional languages; Field and Harrison (1988) devote a whole chapter to it. The basic idea is just to keep a table of previously computed input/result pairs. In Common Lisp one could write: 1 (defun memo (fn) "Return a memo-function of fn.&quot