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Subtree replacement systems: A unifying theory for recursive equations, LISP, lucid and combinatory logic

Recent work on computation of functions defined by sets of recursive equations by Cadiou [Ca72], Vuillemin [Vu74] and Downey and Sethi [DS76] depends on semantic interpretations of such equations. A purely syntactic, combinatory approach yields similar results for a much wider class of sets of equations, including sets of defining equations for LISP, Lucid and the combinator calculus. The application to LISP proves several conjectures of Henderson and Morris [HM76].