Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Completion of rewrite systems with membership constraints. Part I: deduction rules
Journal of Symbolic Computation - Special issue: order-sorted rewriting
A decision algorithm for distributive unification
Theoretical Computer Science - Special issue on rewriting techniques and applications
Higher order unification via explicit substitutions
Information and Computation
On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
On the Exponent of Periodicity of Minimal Solutions of Context Equation
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Context Unification and Traversal Equations
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
An Algorithm for Distributive Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Solvability of Context Equations with Two Context Variables is Decidable
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the relation between Context and Sequence Unification
Journal of Symbolic Computation
Sequence unification through currying
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Stratified context unification is NP-complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Bounded second-order unification is NP-complete
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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The Curry form of a term, like f(a, b), allows us to write it, using just a single binary function symbol, as @(@(f, a), b). Using this technique we prove that the signature is not relevant in second-order unification, and conclude that one binary symbol is enough. By currying variable applications, like X(a), as @(X, a), we can transform second-order terms into first-order terms, but we have to add beta-reduction as a theory. This is roughly what it is done in explicit unification. We prove that by currying only constant applications we can reduce second-order unification to second-order unification with just one binary function symbol. Both problems are already known to be undecidable, but applying the same idea to context unification, for which decidability is still unknown, we reduce the problem to context unification with just one binary function symbol.We also discuss about the difficulties ofapplying the same ideas to third or higher order unification.