J. Harrison and L. Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of LPAR'93, pages 351--353, 1993. Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... reasoning problems and practical considerations in designing and interacting with the system, we have seen a rapid move towards integrative frameworks combining various external reasoners [ Denzinger, 1993; Benzm uller et al. 1997; Dahn, 1997 ] and computation systems [ Clarke and Zhao, 1992; Harrison and Th ery, 1993; Ballarin et al. 1995; Kerber et al. 1998 ] Ideally, the reasoning modules in the mega system interact with each other to complete open subgoals during the development of a proof. This can be initiated and supervised on line by the user. This can be also guided by the mega system itself, ....

.... The same problem arises in other approaches concerned with the integration of two or several theorems provers (cf. Felty and Howe, 1997; Slind et al. 1998; Benzm uller and Sorge, 1998 ] or theorem provers with decision procedures or Computer Algebra systems (cf. Clarke and Zhao, 1992; Harrison and Th ery, 1993; Ballarin et al. 1995; Kerber et al. 1998 ] that generally do not follow a common paradigm, i.e. a similar input output speci cation. Their solutions do heavily depend on the integrated systems. The question how di erent theorem provers can be easily combined in a single environment that ....

J. Harrison and L. Thery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), volume 698 of LNAI, pp. 351-353. Springer, Berlin, 1993.

.... reasoning problems and practical considerations in designing and interacting with the system, we have seen a rapid move towards integrative frameworks combining various external reasoners [ Denzinger, 1993; Benzmuller et al. 1997; Dahn, 1997 ] and computation systems [ Clarke and Zhao, 1992; Harrison and Th ery, 1993; Ballarin et al. 1995; Kerber et al. 1998 ] Ideally, the reasoning modules in the Omega mega system interact with each other to complete open subgoals during the development of a proof. This can be initiated and supervised on line by the user. This can be also guided by the Omega mega ....

.... The same problem arises in other approaches concerned with the integration of two or several theorems provers (cf. Felty and Howe, 1997; Slind et al. 1998; Benzmuller and Sorge, 1998 ] or theorem provers with decision procedures or Computer Algebra systems (cf. Clarke and Zhao, 1992; Harrison and Th ery, 1993; Ballarin et al. 1995; Kerber et al. 1998 ] that generally do not follow a common paradigm, i.e. a similar input output specification. Their solutions do heavily depend on the integrated systems. The question how different theorem provers can be easily combined in a single environment that ....

J. Harrison and L. Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), volume 698 of LNAI, pp. 351--353. Springer, Berlin, 1993.

....of existentially quantified variables. Operator appl cond PLANNER SAPPER Maple CAS CAS expand with PDS compute with Maple result proof plan initialize reflect plan LINEQ tell ask Figure 2: Integration of Proof Planning with External Reasoners systems (similar to approaches of [1, 8, 5]) and thus sapper works as simple bridge between the planner and the CAS. On the other hand, sapper also has the ability to use a CAS as a proof planner itself. That is, if the CAS can provide additional information on its computations, this information is recorded by sapper and translated into a ....

John Harrison and Laurent Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), volume 698 of LNAI, pages 351--353, St. Petersburg, Russia, July 1993. Springer Verlag, Berlin, Germany.

....user interface. Driven by the complexity of real world reasoning problems and practical considerations in designing and interacting with the system, we have seen a rapid move towards integrative frameworks combining various external reasoners [Den93, HKK 94, Dah97] and computation systems [HT93b, BHC95, HT93a, KKS98] Ideally, the reasoning modules in the Omega mega system interact with each other to complete open subgoals during the development of a proof. This can be initiated and supervised on line by the user. This can be also guided by the Omega mega system itself, for instance ....

John Harrison and Laurent Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), Volume698 of LNAI, pages 351--353, St. Petersburg, Russia, Juli 1993. Springer Verlag, Berlin.

....and percolate to the client. ffl Often there will be an external source of information (call it an oracle) that can solve a problem raised inside a theorem prover. How should this information be accessed and treated An interesting example of this is interacting with a computer algebra system [HT93] At times, the theorem prover will want to use a result from an oracle as a theorem, but simple acceptance of such results means that the correctness of the theorem prover is dependent on the correctness of the oracle (which we hold to be an unsatisfactory state of affairs) We know of two ways ....

.... of the theorem prover is dependent on the correctness of the oracle (which we hold to be an unsatisfactory state of affairs) We know of two ways to handle this: Check that the result from the oracle is in fact a theorem, by proving it inside the logic (in many cases this can be automated[HT93, Sli93] Tag the result and propagate the tag to every theorem derived from the result. In case the oracle is flawed (as is often the case) a false theorem might get proved in the proof system, but the tag would show which oracle(s) were at fault. This idea is due to Mike Gordon, who found ....

John Harrison and Laurent Thery. Reasoning about the reals: The marriage of HOL and Maple. In LPAR 93 (LNAI 698), St. Petersburg, Russia, 1993.

....algebra systems (CAS) apparently have different objectives. Their integration is, however, highly desirable, since both different tasks, proving and calculating, have to be performed in many formal proofs. Consequently several concepts of combining these systems have recently been developed, see [CZ92, HT93, BHC95] for examples. However using CAS for term rewriting leads to proofs that are no longer completely within the ND calculus and thus no longer verifiable by a simple proof checker. Furthermore we might obtain incorrect proofs if there are any computational errors in an algorithm 1 . The ....

J. Harrison and L. Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), volume 698 of LNAI, pages 351--353, St. Petersburg, Russia, July 1993. Springer Verlag.

....equations, factorizing polynomials and finding integrals, require complicated methods, but the answers can be checked quite easily, so it is quite feasible to do only this part in the theorem prover. These possibilities are explored, using the example of integration, in our forthcoming paper [13]. 9.4 Hybrid Systems Hybrid systems are those which involve both analogue and digital components, or both discrete and continuous models. These are of course very important when computers are used in real world applications such as chemical plant controllers. Various formalisms for dealing with ....

J. R. Harrison, L. Th'ery, Reasoning About the Reals: The Marriage of HOL and Maple, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR 93), Springer Lecture Notes in Artificial Intelligence vol. 698, pp. 351--353, 1993.

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J. Harrison and L. Th'ery. Reasoning About the Reals: The Marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of LPAR'93, pages 351--353, 1993. Springer.

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Harrison, J., and Th ery, L. Reasoning about the reals: the marriage of HOL and Maple. In Logic Programming and Automated Reasoning (1993), A.Voronkov, Ed., no. 698 in Lecture Notes in Arti cial Intelligence, LPAR'93, Springer-Verlag, pp. 351-359.

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HT93b. J. Harrison and L. Th'ery. Reasoning about the reals: The marriage of HOL and Maple. In A. Voronkov, editor, Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning (LPAR'93), pages 351--353, St. Petersburg, Russia, 1993. Springer Verlag, LNAI 698.

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