Abstract
Higher-order patterns, together with higher-order matching, enable concise specification of program transformation, and have been implemented in several program transformation systems. However,higher-order matching in general is nondeterministic, and the matching algorithm is so expensive that even second-order matching is NP-complete. It is orthodox to impose constraint on the form of patterns to obtain the desirable matches satisfying certain properties such as decidability and finiteness. In the context of unification, Miller’s higher-order patterns have a single most general unifier. We relax the restrictions in his patterns without changing determinism within the context of matching instead of unification. As a consequence, the new class of patterns covers a wide class of useful patterns for program transformation. The time-complexity of the matching algorithm is linear for the size of a term for a fixed pattern.
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