The pattern matching facility of MACSYMA, an algebraic manipulation system, is described in this paper. By taking advantage of the special semantic properties of algebraic expressions, diverse expressions are recognized as occurrences of the same pattern. For example, a semantic pattern for “quadratic in x” matches both 3*x**2+4 and (x+1)*(x+6).
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Richard J. Fateman (1971) studied this question.