Abstract
This paper considers AC unification of higher-order patterns (short: patterns), which are simply typed λ-terms in long β-normal form where the arguments of a free variable are always η-equal to distinct bound variables. A pattern is called pure if it can be written as λx 1 ... λx k.s1+...+s n, where + is an AC function symbol and each s i is either a bound variable or a subterm starting with a free variable. As the main part of the paper, we propose an AC unification algorithm for pure patterns, which is parameterized by a first-order AC1 unification algorithm. The algorithm for pure patterns is terminating and complete whenever the parameterizing AC1 unification algorithm is. A terminating and complete AC unification algorithm for all patterns is obtained by combining the algorithm for pure patterns and an AC unification algorithm for free patterns. Theoretically, the result presented here implies the decidability of AC unification of patterns. Practically, our algorithm can be used to extend higher-order logic programming and proof systems with AC operators.
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Qian, Z., Wang, K. (1994). Modular AC unification of higher-order patterns. In: Jouannaud, JP. (eds) Constraints in Computational Logics. CCL 1994. Lecture Notes in Computer Science, vol 845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016847
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DOI: https://doi.org/10.1007/BFb0016847
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