Download Automated Mathematical Induction by Francois Bronsard, Uday S. Reddy, Robert W. Hasker (auth.), PDF

By Francois Bronsard, Uday S. Reddy, Robert W. Hasker (auth.), Hantao Zhang (eds.)

It has been proven how the typical constitution that defines a relatives of proofs might be expressed as an evidence plan [5]. This universal constitution should be exploited within the look for specific proofs. an explanation plan has complementary parts: an explanation procedure and an evidence tactic. by way of prescribing the constitution of an evidence on the point of primitive inferences, a tactic [11] offers the warrantly a part of the facts. against this, a mode presents a extra declarative rationalization of the facts by way of preconditions. each one strategy has linked results. The execution of the consequences simulates the appliance of the corresponding tactic. Theorem proving within the facts making plans framework is a two-phase technique: 1. Tactic development is through a strategy of process composition: Given a target, an appropriate procedure is chosen. The applicability of a mode depends on comparing the method's preconditions. the strategy results are then used to calculate subgoals. This approach is utilized recursively till not more subgoals stay. as a result of the one-to-one correspondence among tools and strategies, the output from this approach is a composite tactic adapted to the given objective. 2. Tactic execution generates an evidence within the object-level common sense. observe that no seek is interested by the execution of the strategy. all of the seek is handled in the course of the making plans approach. the genuine advantages of getting separate making plans and execution stages develop into appar­ ent while an evidence try fails.

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INDUCTION USING TERM ORDERS 37 29. edu electronic bulletin board, 1990. 30. Musser, D. : On proving inductive properties of abstract data types, in ACM Symp. on Prine. of Program. , ACM, 1980, pp. 154-162. 31. Reddy, U. : Term rewriting induction, in M. ), 10th CADE Conj, LNAI 449, Springer-Verlag, 1990, pp. 162-177. 32. : Etude des Systemes de Reecriture Conditionnels et Applications aux Types Abstraits Algebriques, Th. Etat, INPL, Nancy (France), 1982. 33. Robinson, G. A. and Wos, L. : Paramodulation and first-order theorem proving, in B.

Kaplan and M. Okada (eds), Proc. 2nd CTRS Workshop, LNCS 516, Springer-Verlag, 1991, pp. 2-13. 9. Bronsard, F. and Reddy, U. : Reduction techniques for first-order reasoning, in M. Rusinowitch and J. L. Remy (eds), Proc. 3rd CTRS Workshop, LNCS 656, Springer-Verlag, 1992, pp. 242-256. 10. , Reddy, U. ), Proc. , LNAI 814, Springer-Verlag, 1994, pp. 102-117. 11. : A rational reconstruction and extension of recursion analysis, in IlCAI, 1989. 12. : Completion and its applications, in Resolution of Equations in Algebraic Structures, Vol.

In order to keep the presentation simple, the algorithm is given assuming the definition of f to be constructor based and that there are no relations on constructors (E is empty). The algorithm can be generalized to consider an arbitrary E if syntactic unification (unification modulo the empty theory) below is replaced by = E unification. Of course, = E unification must be decidable and finitary, and each of the most general unifiers (mgus) in Steps 2(a) is used to generate an induction case, and every mgu in Step 2(b) is used to generate an induction hypothesis.

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