G. Dowek, T. Hardin and C. Kirchner. Hol-lambda-sigma: an intentional first-order expression of higher-order logic. Mathematical Structures in Computer Science, 11:1--25, 2001.

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From Higher-Order to First-Order Rewriting - Bonelli, Kesner, Ríos   (Correct)

....different first order calculi for the calculus [1, 4, 17, 15, 6, 22] which is the paradigmatic example of a higher order (term) rewriting system. Other examples are the translations of higher order unification to first order unification modulo [11] higher order logic to first order logic modulo [12], higher order theorem proving to first order theorem proving modulo [9] etc. All these translations have a theoretical interest because the expressive power of higher and first order formalisms is put in evidence, but another practical issue arises, that of the possibility of transferring ....

G. Dowek, T. Hardin and C. Kirchner. Hol-lambda-sigma: an intentional first-order expression of higher-order logic. Mathematical Structures in Computer Science, 11:1--25, 2001.

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