By Thomas Kropf (auth.), Yves Bertot, Gilles Dowek, Laurent Théry, André Hirschowitz, Christine Paulin (eds.)

This booklet constitutes the refereed complaints of the twelfth overseas convention on Theorem Proving in greater Order Logics, TPHOLs '99, held in great, France, in September 1999. The 20 revised complete papers offered including 3 invited contributions have been conscientiously reviewed and chosen from 35 papers submitted. All present elements of upper order theorem proving, formal verification, and specification are mentioned. one of the theorem provers evaluated are COQ, HOL, Isabelle, Isabelle/ZF, and OpenMath.

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Extra resources for Theorem Proving in Higher Order Logics: 12th International Conference, TPHOLs’ 99 Nice, France, September 14–17, 1999 Proceedings

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Objec -orien ed veri ca ion based on record sub yping in higher-order logic. In J. Grundy and M. Newey, edi ors, Theorem Provin in Hi her Order Lo ics, volume 1479 of LNCS. Springer, 1998. [14] T. Nipkow and D. von Oheimb. Java i ht is ype-safe de ni ely. In Proc. 25th ACM Symp. Principles of Pro rammin Lan ua es. ACM Press, New York, 1998. [15] S. Owre, S. Rajan, J. M. Rushby, N. Shankar, and M. Srivas. PVS: combining speci ca ion, proof checking, and model checking. In R. Alur and T. A. Henzinger, edi ors, Computer Aided Veri cation, volume 1102 of LNCS.

Type classes and overloading in higher-order logic. In 10th International Conference on Theorem Provin in Hi her Order Lo ics, TPHOLs’97, volume 1275 of LNCS. Springer, 1997. de Abstract. We present a theory of isomorphisms between typed sets in Isabelle/ HOL. Those isomorphisms can serve to link a shallow embedding with a theory that defines certain concepts directly in HOL. Thus, it becomes possible to use the advantage of a shallow embedding that it allows for efficient proofs about concrete terms of the embedded formalism with the advantage of a deeper theory that establishes general abstract propositions about the key concepts of the embedded formalism as theorems in HOL.

If more ypes would occur non-recursively, he rs argumen would be he sum of hese ypes. Since Induc ive Da a ypes in HOL 29 here is no nes ed recursion involving func ion ypes, he second argumen of dtree is jus he dummy ype unit. 3 in roduces he abs rac ion and represen a ion func ions Abs-list :: ( unit)dtree list Rep-list :: list ( unit)dtree as well as he axioms Rep-list-inverse, Abs-list-inverse and Rep-list. Using hese func ions, we can now de ne he cons ruc ors Nil and Cons: Nil Cons x xs Abs-list Nil-rep Abs-list (Cons-rep x (Rep-list xs)) Freeness We can now prove ha Nil and Cons are dis inc and ha Cons is x = x xs = xs .

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