# First-Order Terms

 Title: First-Order Terms Authors: Christian Sternagel (c /dot/ sternagel /at/ gmail /dot/ com) and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at) Submission date: 2018-02-06 Abstract: We formalize basic results on first-order terms, including matching and a first-order unification algorithm, as well as well-foundedness of the subsumption order. This entry is part of the Isabelle Formalization of Rewriting IsaFoR, where first-order terms are omni-present: the unification algorithm is used to certify several confluence and termination techniques, like critical-pair computation and dependency graph approximations; and the subsumption order is a crucial ingredient for completion. BibTeX: @article{First_Order_Terms-AFP, author = {Christian Sternagel and René Thiemann}, title = {First-Order Terms}, journal = {Archive of Formal Proofs}, month = feb, year = 2018, note = {\url{https://isa-afp.org/entries/First_Order_Terms.html}, Formal proof development}, ISSN = {2150-914x}, } License: GNU Lesser General Public License (LGPL) Depends on: Abstract-Rewriting Used by: Functional_Ordered_Resolution_Prover, Knuth_Bendix_Order, Resolution_FOL, Saturation_Framework_Extensions, Stateful_Protocol_Composition_and_Typing