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Order-sorted equational unification

Abstract : Order-sorted equational unification is studied from an algebraic point of view. We show how order-sorted equational unification algorithms can be built when the order-sorted signature is regular (i.e. every term has a unique least sort) and the equational specification is sort-preserving (i.e. any A-equal terms have the same least sort). Under these conditions the transformations rules allowing to build unification algorithms in the unsorted framework can be extended to the order-sorted one. This allows us to generalize the known results to order-sorted equational unification, in particular when there exist overloaded symbols with different properties. An important application is order-sorted associative-commutative unification for which no direct algorithm was given until now.
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Reports (Research report)
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Submitted on : Wednesday, May 24, 2006 - 6:35:18 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:49 AM
Long-term archiving on: : Friday, May 13, 2011 - 1:31:17 PM


  • HAL Id : inria-00075605, version 1



Claude Kirchner. Order-sorted equational unification. [Research Report] RR-0954, INRIA. 1988. ⟨inria-00075605⟩



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