A Heuristic Program That Solves Symbolic Integration Problems in Freshman Calculus, Symbolic Automatic Integrator (Saint)

摘要

Some ideas about problem solving by a machine were tried out on the nontrivial problem domain of elementary symbolic integration. To this end, the author programmed a large, high speed, general-purpose digital computer (I. B. M. 7090) to use these ideas to solve some symbolic integration problems. The computer so programmed is called 'SAINT', an acronym for 'symbolic automatic integrator'. SAINT performs symbolic integration which includes indefinite integration. It also performs definite and multiple integration when these are trivial extensions of indefinite integration. SAINT solves symbolic integration problems approximately at the level of a good college freshman and, in fact, uses many of the same methods (including heuristics) used by a freshman. Taking an average of two minutes per problem, SAINT solved fifty-two (ninety-sicx per cent) of the attempted fifty-four M.I.T. freshman calculus final examination problems. The author draws many conclusions from this and other experiments with SAINT and makes suggestions for future work in the field of Artificial Intelligence. (Author)