Formal Reasoning Using an Iterative Approach with an Integrated Web IDE

This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE designed for the purpose. Our experience in using such an IDE, supported by a 'push-button' verifying compiler in a classroom setting, reveals the highly iterative process learners use to arrive at suitably specified, automatically provable code. We explain how the IDE facilitates reasoning at each step of this process by providing human readable verification conditions (VCs) and feedback from an integrated prover that clearly indicates unprovable VCs to help identify obstacles to completing proofs. The paper discusses the IDE's usage in verified software development using several examples drawn from actual classroom lectures and student assignments to illustrate principles of design-by-contract and the iterative process of creating and subsequently refining assertions, such as loop invariants in object-based code.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338

Energetics and local spin magnetic moment of single 3,4d impurities encapsulated in an icosahedral Au12 cage

The energetics and local spin magnetic moment of a single 3,4d impurity (Sc-Ni, Y-Pd) encapsulated in an icosahedral Au12 cage have been studied theoretically by using a real-space first-principles cluster method with generalized gradient approximation for exchange-correlation functional. The relativistic effect is considered by scalar relativistic pseudopotentials. All doped clusters show unexpected large relative binding energies compared with icosahedral Au13cluster. The smallest and the largest values appear at Pd and Zr, 2.186 and 7.791eV per cluster, respectively, indicating doping could stabilize the icosahedral Au12 cage and promote the formation of a new binary alloy cluster. Comparatively large magnetic moments are observed for 3d elements Cr, Mn, Fe, Co, and Ni (2.265, 3.512, 3.064, 1.947, and 0.943μB), and 4d elements Tc, Ru, and Rh (0.758, 1.137, and 0.893μB). The density of states and the relativistic effects on electronic structure are discussed