Linear Higher-Order Matching Is NP-Complete
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Journal of Functional Programming
Towards abstract categorial grammars
ACL '01 Proceedings of the 39th Annual Meeting on Association for Computational Linguistics
On the complexity of higher-order matching in the linear λ-calculus
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Higher-order matching in the linear lambda calculus in the absence of constants is NP-complete
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A note on the complexity of abstract categorial grammars
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
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We introduce syntactic descriptions, an extended type system for the linear λ-calculus. With this type system checking that a linear λ-term normalizes to another one reduces to type-checking. As a consequence this type system can be seen as a formal tool to design matching algorithms. In that respect, solving matching equations becomes a combination of type inference and proof search. We present such an algorithm for linear matching equations.In the case of second order equations, this algorithm stresses the similarities between linear matching in the linear λ-calculus and linear context matching. It uses tabular techniques and is a practical alternative to Huet's algorithm for those equations.