Unification of Deterministic Higher-Order Patterns

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Abstract
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure can be seen as a special case of full higher-order unification where flex-flex pairs can be solved in a most general way. Moreover, our method generalizes Libal and Miller’s recent functions-as-constructors higher-order unification (FCU) by dropping their global restriction on variable arguments, thereby losing the property that every solvable problem has a most general unifier. In fact, minimal complete sets of unifiers of deterministic higher-order patterns may be infinite, so decidability of the unification problem remains an open question.

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