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We reformulate the Korf-Eppstein method for automatic inversion of first-order functional programs using a structural operational semantics and compare it with the program inversion method described by Gries. We analyze the method and suggest possible extensions. The method is noteworthy in that it was used to construct the first automatic program inverter described in the literature. The key features of the Korf-Eppstein method are the simultaneous inversion of an injective system of functions, an equation-oriented transformation, and the use of postcondition inference heuristics.

Abstract. We present a method for automatic program inversion in a first-order functional programming language. We formalize the transformation and illustrate it with several examples including the automatic derivation of a program for run-length decoding from a program for runlength encoding. This derivation is not possible with other automatic program inversion methods. One of our key observations is that the duplication of values and testing of their equality are two sides of the same coin in program inversion. This leads us to the design of a new self-inverse primitive function that considerably simplifies the automatic inversion of programs.

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