Download Tests and Proofs: First International Conference, TAP 2007, by Yannis Smaragdakis, Christoph Csallner (auth.), Yuri PDF

By Yannis Smaragdakis, Christoph Csallner (auth.), Yuri Gurevich, Bertrand Meyer (eds.)

This booklet constitutes the completely refereed post-proceedings of the 1st foreign convention on try out and Proofs, faucet 2007, held in Zurich, Switzerland in February 2007.

The 12 revised complete papers provided have been conscientiously reviewed and chosen for inclusion within the booklet. The papers are dedicated to the convergence of software program proofing and checking out and have present learn paintings that mixes principles from either side to foster software program caliber. themes addressed are iteration of attempt situations or oracles via theorem proving, constraint common sense programming, version checking, or symbolic execution; software proving by using trying out innovations; computerized instruments; case reports; formal frameworks; in addition to verification options combining proofs and tests.

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Extra info for Tests and Proofs: First International Conference, TAP 2007, Zurich, Switzerland, February 12-13, 2007. Revised Papers

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4. For the example in Fig. 3, the “solutions” of the left branch could be enumerated as [ P ≡ 2 ], [ P ≡ 1 ], [ P ≡ 0 ], [ P ≡ −1 ], . . , and the solutions of the right branch as [ P ≡ 0 ], [ P ≡ 1 ], [ P ≡ 2 ], . . In this case, we would observe that, for instance, the substitution represented by [ P ≡ 0 ] closes the whole proof. Generally, the conjunction of the constraints for the different branches describes the substitution that allows to close a proof (provided that it is consistent). , pre-state) has to be found that simultaneously satisfies the pre-conditions, violates the post-conditions in one (or multiple) proof branches and invalidates the branch predicates of all remaining proof branches.

2. Advantages. Compared to backtracking, the main benefits of the constraint approach are that duplicated rule applications (due to removed parts of the proof tree that might have to be re-constructed) are avoided, and that it is possible to search for different solutions in parallel. Because large parts of the proofs in question—the parts that involve symbolic execution—can be constructed algorithmically and do not require search, the first point is particularly significant here. The second point holds because the proof search does never commit to one particular (partial) solution by applying a substitution.

In our experiments, we also used breadth-first exploration of the execution tree of programs, which simply corresponds to a fair selection of proof branches and formulae that rules are applied to. For formula (5), the method could find the same solution (7) as the backtracking approach of Sect. 2. Advantages. Compared to backtracking, the main benefits of the constraint approach are that duplicated rule applications (due to removed parts of the proof tree that might have to be re-constructed) are avoided, and that it is possible to search for different solutions in parallel.

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