Third Order Matching is Decidable
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The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed λ-calculus, i.e. to solve the equation a = b where a and b are simply typed λ-terms and b is ground. The decidability of this problem is still open. We prove the decidability of the particular case in which the variables occurring in the problem are at most third order.
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