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Abstract:
In current implementations of higher-order logics higher-orderunification is used to lift the resolution principle from the first-order case to the higher-order case. Higher-order matching is the core of implementations of
higher-order rewriting systems and some systems for program transformation.
In this paper I argue that Church's original lambda calculus, called non-forgetful lambda calculus, is an appropriate basis for higher-order matching. I provide two correct and complete algorithms for unification in the non-forgetful lambda calculus. Finally, I show how these unification algorithms can be used for matching in the non-forgetful lambda calculus.
