Abstract : We prove that linear second-order matching in the linear $\lambda$-calculus with linear occurrences of the unknowns is NP-complete. This result shows that context matching and second-order matching in the linear $\lambda$-calculus are, in fact, two different problems.
Sylvain Salvati, Philippe de Groote. On the complexity of higher-order matching in the linear $\lambda$-calculus. International Conference on Rewriting Techniques and Applications - RTA'2003, Jun 2003, Valencia, Spain, pp.234-245. ⟨inria-00099593⟩