D. Kapur, D.R. Musser, and X. Nie. An Overview of the Tecton Proof System. Theoretical Computer Science, Vol. 133, October 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....procedure for a combination of T 1 and T 2 . The most successful and well known method for combining decision procedures was invented in 1979 by Nelson and Oppen [NO79] This method is at the heart of the verification systems cvc [SBD02] esc [DLNS98] eves [CKM 91] sdvs [LFMM92] and tecton [KNM94] among others. The Nelson Oppen method allows us to decide the satisfiability of quantifierfree formulae in a combination T of a theory T 1 and a theory T 2 , using as black boxes a decision procedure for the satisfiability of quantifier free formulae in T 1 and a decision procedure for the ....

Deepak Kapur, Xumin Nie, and David R. Musser. An overview of the Tecton proof system. Theoretical Computer Science, 133(2):307-- 339, 1994.

....congruence closure algorithm [7] for ground equalities with uninterpreted function symbols, Sh. Secondly, an extended version of Fourier Motzkin s linear arithmetic decision procedure capable of deducing implicit equalities [6] FM. Thirdly, we implemented a combination of Sh and FM following [4], ShFM. If X is one of the decision procedures above, then X 7 denotes X with augmentation enabled. This allowed us to readily obtain ve instances of CCR(X) in RDL: i) CCR(Sh) inspired to [5] ii) CCR(Sh 7 ) iii) CCR(FM) iv) CCR(FM 7 ) both inspired to [3] and (v) CCR(ShFM 7 ....

....one of the decision procedures above, then X 7 denotes X with augmentation enabled. This allowed us to readily obtain ve instances of CCR(X) in RDL: i) CCR(Sh) inspired to [5] ii) CCR(Sh 7 ) iii) CCR(FM) iv) CCR(FM 7 ) both inspired to [3] and (v) CCR(ShFM 7 ) inspired to [4]. The last step was to implement the proof engine of RDL, i.e. a strategy that given a c : e e (where c and e are ground expressions and e is a Prolog variable) tries to instantiate e to a normal form of e by searching through the available rules and performing the transitive and re exive ....

D. Kapur, D.R. Musser, and X. Nie. An Overview of the Tecton Proof System. Theoretical Computer Science, Vol. 133, October 1994.

....some conclusions are drawn in Section 6. 2 Contextual Rewriting Contextual rewriting is an extended form of conditional rewriting whereby information contained in the context of the expression being rewritten is used by 1 To our knowledge if we exclude nqthm and its descendant ACL2 [15] Tecton [13] is the only prover based on the Boyer Moore s original ideas. 2 the rewriting activity. To illustrate, let us consider the problem of rewriting the literal p occurring in the clause fpg [ E via a set of conditional rewrite rules, say R. The key idea of contextual rewriting is that while ....

D. Kapur, D.R. Musser, and X. Nie. An Overview of the Tecton Proof System. Theoretical Computer Science, Vol. 133, October 1994.

....This has allowed us to easily fast prototype and validate the integration schemas described in this paper. 1 Introduction We are interested in the problem of integrating decision procedures with rewriting as in many state of the art veri cation systems such as nqthm [4] pvs [13] Tecton [9] and STeP [7] The key factors in the success of such systems are (a) a tight integration schema for the cooperation of decision procedures, and (b) a carefully designed integration schema between the decision procedures and rewriting. While abstract accounts of (a) can be found in the literature ....

.... 615, rue du Jardin Botanique, BP 101 54602 Villers les Nancy Cedex France, armando loria.fr z Viale Causa 13 16145 Genova Italia, silvio dist.unige.it both contextual rewriting and two sophisticated integration schemas: the simpli er of nqthm [3] and the simpli er of Tecton [9]. Furthermore, we identify the set of the interface functionalities that the decision procedure must provide for the integration to be e ective. The rule based speci cation of CCR given in this paper contrasts the practice of describing the integration by examples or in informal ways with ....

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D. Kapur, D.R. Musser, and X. Nie. An Overview of the Tecton Proof System. Theoretical Computer Science, Vol. 133, October 1994.

....systems. The 8 automata of Manna and Pnueli [13] are a third graphical formalism for specifying temporal properties of systems. Most of these notations are oriented toward the depiction of states and state transitions, rather than toward depiction of the evolution of properties in time. Tecton [10] is a formal verification system that uses visual techniques such as tables, graphics and hypertext. Graphical interfaces to traditional theorem proving systems are considered in [22] As opposed to GIL, however, these systems are based on textual logics and the visualization serves to facilitate ....

Kapur, D., Musser, D. R. and Nie, X., "An overview of the Tecton proof system," Proc. of the Workshop on Formal Methods in Databases and Software Engineering, Montreal, Quebec, Canada, May 1992.

....in A if and only if it satisfies all of the requirements in R. This definition is derived in part from formal concept analysis [35, 36] in which, however, the abstractions are usually merely names or simple descriptions of objects. Another source is the Tecton concept description language ([13, 14]; see also [21] in which the abstractions are more complex: they are algebras or other similar abstract objects such as abstract data types. An informal but widely known example of this understanding of concepts is the documentation of the C Standard Template Library developed at SGI [2] ....

D. Kapur, D. R. Musser, and X. Nie. An overview of the Tecton proof system. Theoretical Computer Science, 133:307--339, October 24 1994.

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D. Kapur, D. R. Musser, and X. Nie, "An overview of the Tecton Proof System," Proc. of a Workshop on Formal Methods in Databases and Software Engineering, Concordia University, Montreal, May 15-16, 1992.

....of how a proof can be attempted. The Tecton system also provides a nice visualization of proof attempts and support for hyper links among parts of proofs that are dependent upon each other, including multiple proof attempts, which can help when an automatic proof attempt does not succeed; see [24] for more details. Since most proofs about circuit descriptions are done in this paper using induction, we briefly review below the cover set induction method. 2.1 Cover Set Induction The cover set method for mechanizing well founded induction was proposed in [37] and has been successfully used ....

D. Kapur, D.R. Musser, and X. Nie, "An Overview of the Tecton Proof System," Theoretical Computer Science Journal, special issue on Formal Methods in Databases and Software Engineering, (ed. V. Alagar), Vol. 133, October, 1994, 307-339.

....Kapur and Krishnamoorthy [13, 12] introduced a cover set method for designing induction schemes for automating proofs by induction from equations. This method has been implemented in the theorem prover Rewrite Rule Laboratory (RRL) 10] and a proof management system Tecton built on top of RRL [7], and has been used to prove many nontrivial theorems and reason about sequential as well as parallel programs. The cover set method is based on the assumption that a function symbol is defined using a finite set of terminating (conditional or unconditional) rewrite rules. The termination ordering ....

D. Kapur, D.R. Musser, and X. Nie, "An Overview of the Tecton Proof System," Theoretical Computer Science Journal, special issue on Formal Methods in Databases and Software Engineering, (ed. V. Alagar), Vol. 133, October, 1994, 307-339.

....hand sides of type T and left hand sides of type U. For example, int a[100] double b[100] code to initialize array a Call 1: copy all of array a to array b: copy( a[0] a[100] b[0] Call 2: shift a[1] a[99] left one position: copy( a[1] a[100] a[0] Call 3: shift b[10], b[19] left ten positions: copy( b[10] b[20] b[0] Call 4: copy a[0] a[9] to a[10] a[19] copy( a[0] a[10] a[10] Based on these calls three different instances of the copy algorithm are created by the C compiler, with type signatures double copy(int , int , double ) ....

....of type U. For example, int a[100] double b[100] code to initialize array a Call 1: copy all of array a to array b: copy( a[0] a[100] b[0] Call 2: shift a[1] a[99] left one position: copy( a[1] a[100] a[0] Call 3: shift b[10] b[19] left ten positions: copy( b[10], b[20] b[0] Call 4: copy a[0] a[9] to a[10] a[19] copy( a[0] a[10] a[10] Based on these calls three different instances of the copy algorithm are created by the C compiler, with type signatures double copy(int , int , double ) int copy(int , int , int ) double ....

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D. Kapur, D. R. Musser, and X. Nie, "An Overview of the Tecton Proof System," Theoretical Computer Science 133 (1994) 307--339.

....the end of the sequence being partitioned. We plan to report on this example in a separate paper. We are also experimenting with partial automation of proofs about generic algorithms, using the PVS specification language [12] and prover [13] and the Tecton language [4, 5] and proof system [6]. Even if such proofs require extensive human direction and attention to detail, the fact that the algorithms are generic means that the necessary investments of effort can be amortized over the many subsequent uses of the algorithms. These efforts will be the subject of future papers. ....

D. Kapur, D. R. Musser, and X. Nie, "An Overview of the Tecton Proof System," Theoretical Computer Science 133 (1994) 307--339.

....abstraction and specialization as the key structuring mechanisms. In Tecton abstraction and specialization are expressed using concept descriptions. It is planned that concept descriptions will be supported by syntactic and semantic checking in an extension to the current Tecton Proof System [18]. In this paper we define the syntax and semantics for concept descriptions and develop a number of small examples and one extended example, a behavioral and structural description of a carrylookahead adder circuit. A separate working paper [15] contains additional examples of concept ....

....essential no matter how much abstraction is used. There must continue to be strong research efforts to develop theorem proving support for the above mentioned languages and others, including packaging it in a way that non experts can use it productively. This is a goal for the Tecton Proof System [18], in which, for example, considerable attention is being devoted to development of a good human interface. 18] contains a discussion of the Tecton notion of proofs as forests of proof trees and how the system constructs and displays such proof trees in a graphical format. See also [24] for a ....

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D. Kapur, D. R. Musser, and X. Nie, "An overview of the Tecton Proof System," Proc. of a Workshop on Formal Methods in Databases and Software Engineering, Concordia University, Montreal, May 15-16, 1992.

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D. Kapur, D.R. Musser, and X. Nie. An Overview of the Tecton Proof System. Theoretical Computer Science, Vol. 133, October 1994.

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