Abstract
In this extended abstract we report on an investigation of Higher-Order E-Unification, which consists of unifying typed lambda terms in the context of a first-order set of equations E. This problem subsumes both higher-order unification and general E-unification, and provides a theoretical background for reasoning systems which incorporate both algebraic and higher-order logic. The problem and its properties are discussed, a set of transformations (inference rules) extending those of Martelli-Montanari for standard unification is given, and then we prove the completeness of this non-deterministic algorithm. The completeness of restrictions of these rules for higher-order pre-E-unification and higher-order narrowing are corollaries of these results. Finally, we connect these results with previous work, and conclude with future directions and open problems. The major result is a set of inference rules for higher-order E-unification and a proof of its soundness and completeness (wrt complete sets of unifiers).
This research was partially supported by NSF Grant No. CCR-8910268.
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Snyder, W. (1990). Higher order E-unification. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_115
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DOI: https://doi.org/10.1007/3-540-52885-7_115
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