Linear higher-order matching is NP-complete
Résumé
We consider the problem of higher-order matching restricted to the set of linear lambda-terms (i.e., lambda-terms where each abstraction (lambda x. M) is such that there is exactly one free occurrence of x in M). We prove that this problem is decidable by showing that it belongs to NP. Then we prove that this problem is in fact NP-complete. Finally, we discuss some heuristics for a practical algorithm.