Higher-order unification

Question

I\'m working on a higher-order theorem prover, of which unification seems to be the most difficult subproblem.

If Huet\'s algorithm is still considered state-of-the-

Answer 1

There is also Tobias Nipkow's 1993 paper Functional Unification of Higher-Order Patterns (only 11 pages, 4 of which are bibliography and code appendix). The abstract:

The complete development of a unification algorithm for so-called higher-order patterns, a subclass of $\lambda$-terms, is presented. The starting point is a formulation of unification by transformation, the result a directly executable functional program. In a final development step the result is adapted to $\lambda$-terms in de Bruijn's notation. The algorithms work for both simply typed and untyped terms.