D. J. Howe. Importing mathematics from hol into Nuprl. In J. Von Wright, J. Grundy, and J. Harrison, editors, Ninth International Conference on Theorem Proving in Higher Order Logics TPHOL, volume 1125 of LNCS, pages 267--282. Springer-Verlag, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....using different provers. The bigger these libraries become the more obvious it is that translating formal results from one system into another may be less time consuming than re proving almost identical theorems from scratch. One of the first works in this area has been done by Howe in [8] and [7]. He developed semantical foundations and semiautomated procedure for importing Mathematics from HOL [6] into NuPRL [4] Later, in a joint work with Felty [5] he used this translation to conduct proofs in a hybrid HOL NuPRL system. This paper presents an attempt to develop a general methodology ....

....can be manually adjusted to different object logics. At the present moment the converter works with Isabelle Meta Logic and Isabelle Higher Order Logic. We expect that the same methodology can be applied to the majority of other Isabelle object logics. The major difference between our work and [7], besides the use of different source systems, is the way the logical soundness of the interpretation is proven. While Howe is using Set Theory semantics for NuPRL, we will give direct syntactical proof. The syntactical approach seems to be easier and more straightforward. Just like Howe [7] we ....

[Article contains additional citation context not shown here]

D.J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--282, Berlin, 1996. Springer-Verlag.

....concepts, and an extendable library of verified knowledge from various domains. Since its first release in 1984 it has been used in increasingly large applications in mathematics and programming, such as verifications of a logic synthesis tool [AL93] and of the SCI cache coherency protocol [How96] as well as the verification and optimization of group communication systems [KHH98,Kre99,L 99] Over the years it has turned out that the rapidly growing demands for formal knowledge and tools cannot be met by a single closed system anymore. Automatic tools such as decision procedures, fully ....

....structures cooperate through a common knowledge base that can store all these informations. It is obvious that translations between di#erent formalisms need to be developed to make such a cooperation possible and that several theoretical issues need to be addressed for each of them (see e.g. How96,FH97] 172 But the Nuprl LPE provides the necessary infrastructure for these translations. They only have to operate on the formal knowledge stored in the library and can be provided as independent external processes that are invoked as necessary. Translations can also be used in a transitive ....

D. Howe. Importing mathematics from HOL into NuPRL. Theorem Proving in Higher Order Logics, LNCS 1125, pp. 267--282. Springer, 1996.

....using different provers. The bigger these libraries become the more obvious it is that translating formal results from one system into another may be less time consuming than re proving almost identical theorems from scratch. One of the first works in this area has been done by Howe in [8] and [7]. He developed semantical foundations and semiautomated procedure for importing Mathematics from HOL [6] into NuPRL [4] Later, in joint work with Felty [5] he used this translation to conduct proofs in a hybrid HOL NuPRL system. This paper presents an attempt to develop a general methodology ....

....develop a universal converter from Isabelle into NuPRL that will be able to handle all possible object logics. In this work we mainly focus on interpreting Isabelle Higher Order Logic in NuPRL. Most of other theories can be handled in a similar fashion. The major difference between our work and [7], besides the use of different source systems, is the way the logical soundness of the interpretation is proven. While Howe is using Set Theory semantics for NuPRL, we will give direct syntactical proof. Syntactical approach seems to be easier and more straightforward. Just like Howe [7] we ....

[Article contains additional citation context not shown here]

D.J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--282, Berlin, 1996. Springer-Verlag.

....logic) and Gandalf [7] a tableaux system for rst order logic) However these 10 systems operate on a xed logic and hence their Plug Ins do not need to be extensible. ACL2 and Hol both support theory de nition, and so ACL2 is in this respect more similar to the Nuprl Hol connection [6] and the Hol CLAM system, which work with arbitrary theory descriptions. The ACL2PII system is entirely focussed on using Hol as a client. The PROSPER Plug In framework also allows Hol to be used as a server, and so it may be possible to feed results from Hol theories to ACL2. Aspects of this ....

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Proceedings of TPHOLs'96: The 9th International Conference on Theorem Proving in Higher Order Logics, volume 1125 of LNCS. SpringerVerlag, 1996.

....of the Deductive Tableau are avoided and the methodology becomes richer. 1 Recent work of Howe has shown how to provide a classical semantics for certain constructive type theories that permits classical reasoning; however, the programs synthesized may contain oracles that cannot be executed (Howe, 1996; Howe, 1997) A. Ayari and D. Basin We would like to close with two areas where we see a need for further work. The first concerns the specialization of generic theorem provers for program synthesis. In this paper we have shown some of the advantages of implementing program development ....

Howe, D. J. (1996). Importing mathematics from HOL into Nuprl. In von Wright, J., Grundy, J., Harrison, J., editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--281, Berlin. Springer-Verlag.

....to formalize Chapters 1 9 with our four person team in about eighteen months. The collaboration methods we have learned would extend to larger teams. It would be especially interesting to collaborate with other theorem proving systems as Howe and his colleagues are doing with HOL and Nuprl [19, 18]. Much of a classical treatment of languages can easily be re interpreted constructively. It would be especially fruitful to collaborate with other constructive provers such as Alf, Coq and Lego or with Isabelle which has formalized Martin L of type theory. Although these provers are based on ....

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125, of LNCS, pages 267--282. Springer-Verlag, Berlin, 1996.

....to formalize Chapters 1 9 with our four person team in about eighteen months. The collaboration methods we have learned would extend to larger teams. It would be especially interesting to collaborate with other theorem proving systems as Howe and his colleagues are doing with HOL and Nuprl [19, 18]. Much of a classical treatment of languages can easily be re interpreted constructively. It would be especially fruitful to collaborate with teams using other constructive provers such as Alf, Coq, Lego, or Isabelle with its Martin Lof type theory object logic. Although these provers are based on ....

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125, of LNCS, pages 267--282. SpringerVerlag, Berlin, 1996.

....discrete mathematics. The work is part of a research program to explore the foundations of computational mathematics. An attempt to formalize the undecidability results of Hopcroft and Ullman s Chapter 3 in classical set theory (say as in Mizar [46] or in classical type theory (say HOL [34, 43, 42] or PVS [60] would encounter severe difficulties. It could not remain close to the style of the book. It could not capture the computational intuitions that motivate and permeate the whole account. But in constructive set theory the Hopcroft and Ullman account can be followed essentially ....

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125, of Lecture Notes in Computer Science, pages 267--282. Springer-Verlag, Berlin, 1996.

....Classical Set Theoretic Model of Polymorphic Extensional Type Theory Douglas J. Howe Bell Labs, Lucent Technologies 600 Mountain Ave. Room 2B 438 Murray Hill, NJ 07974, USA. Abstract. We give a new semantic foundation for type theories in the lineage of Martin Lof s polymorphic extensional type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. ....

....cartesian product. This means that the set theoretic meaning of each U i has to be closed under the corresponding set constructors. This requires the use of inaccessible cardinals. These are defined in many set theory texts, and the reason for their use in this context is explained further in (Howe, 1991) We choose the ordinal oe 0 in the definition of W to be the limit of a countable sequence 1 2 : of inaccessible cardinals. For each i 1, let fl i = V Z i . We do not explicitly give the entire set of operators (with arities) for the language for Nuprl. We complete the definition of the set K of canonical ....

Howe, D. J. (1996a). Importing mathematics from HOL into Nuprl. In von Wright, J., Grundy, J., and Harrison, J., editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--281, Berlin. Springer-Verlag.

....of effort since these basic facts tend to be similar across systems. To avoid doing this ourselves, we import some basic mathematics from HOL [5] a system that has, over the years, accumulated a large corpus of mathematics of the kind useful for software hardware verification. The paper [7] gives the basic design of the connection between HOL and Nuprl, and [4] gives an extension to it and an application to a moderately difficult problem in metamathematics. Our work, though just a first step, establishes that sharing mathematics can be useful in software hardware verification. Type ....

D. J. Howe. Importing mathematics from HOL into Nuprl. In Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--281. Springer-Verlag, 1996.

....In [10] we gave a new semantics for Nuprl that justifies an extension in which HOL s classical type theory (and other classical set type theories) can be directly embedded. The extended logic is classical, but proofs that use only constructive reasoning still yield executable programs. In [9] we described the basic mechanism for importing an HOL theory into Nuprl and imported a few theories by hand as illustration. The current work extends [9] as follows. We have added automated support for interpreting theories and updating Nuprl s automated reasoners to use the imported ....

....can be directly embedded. The extended logic is classical, but proofs that use only constructive reasoning still yield executable programs. In [9] we described the basic mechanism for importing an HOL theory into Nuprl and imported a few theories by hand as illustration. The current work extends [9] as follows. We have added automated support for interpreting theories and updating Nuprl s automated reasoners to use the imported theories. The core of HOL90 s standard library (i.e. the theory HOL and all of its ancestors) was imported, as well as an extensive theory of lists ....

[Article contains additional citation context not shown here]

D. J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267--282, Berlin, 1996. Springer-Verlag.

No context found.

D. J. Howe. Importing mathematics from hol into Nuprl. In J. Von Wright, J. Grundy, and J. Harrison, editors, Ninth International Conference on Theorem Proving in Higher Order Logics TPHOL, volume 1125 of LNCS, pages 267--282. Springer-Verlag, 1996.

No context found.

D. J. Howe. Importing mathematics from hol into Nuprl. In J. Von Wright, J. Grundy, and J. Harrison, editors, Ninth International Conference on Theorem Proving in Higher Order Logics TPHOL, volume 1125 of LNCS, pages 267-282. Springer-Verlag, 1996.

No context found.

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125, of Lecture Notes in Computer Science, pages 267--282. Springer-Verlag, Berlin, 1996.

No context found.

D. J. Howe. Importing mathematics from hol into Nuprl. In J. Von Wright et al., editors, Theorem Proving in Higher Order Logics (TPHOLs 1996.

No context found.

D. J. Howe. Importing mathematics from hol into Nuprl. In J. Von Wright et al., editors, Theorem Proving in Higher Order Logics (TPHOLs 1996), volume 1125 of LNCS, pages 267-282. Springer-Verlag, 1996.

No context found.

D. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of LNCS, pages 267-282, Berlin, 1996. Springer-Verlag.

No context found.

Douglas J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125, of Lecture Notes in Computer Science, pages 267--282. Springer-Verlag, Berlin, 1996.

No context found.

J. Howe Douglas. Importing mathematics from HOL into Nuprl. In Proceedings of The 1996 International Conference on Theorem Proving in Higher Order Logics, 1996. To appear.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC