Unification and anti-unification in the calculus of constructions

Algorithms for unification and anti-unification in the calculus of constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higher-order patterns, are presented. Most general unifiers and least common anti-instances are shown to exist and are unique up to a simple equivalence. The unification algorithm is used for logic program execution and type and term reconstruction in the current implementation of Elf and has shown itself to be practical.<
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