Abstract
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale V, which covers the cases of (in)equations and (ultra)metric equations among others. Our main result is the introduction of a V-equational deductive system for linear ?-calculus together with a proof that it is sound and complete (in fact, an internal language) for a class of enriched autonomous categories. In the case of inequations, we get an internal language for autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an internal language for autonomous categories enriched over (ultra)metric spaces. We use our results to obtain examples of inequational and metric equational systems for higher-order programs that contain real-time and probabilistic behaviour.

Abstract
The prevalence and availability of cloud infrastructures has made them the de facto solution for storing and archiving data, both for organizations and individual users. Nonetheless, the cloud's wide spread adoption is still hindered by dependability and security concerns, particularly in applications with large data collections where efficient search and retrieval services are also major requirements. This leads to an increased tension between security, efficiency, and search expressiveness. In this article we tackle this tension by proposing BISEN, a new provably-secure boolean searchable symmetric encryption scheme that improves these three complementary dimensions by exploring the design space of isolation guarantees offered by novel commodity hardware such as Intel SGX, abstracted as Isolated Execution Environments (IEEs). BISEN is the first scheme to support multiple users and enable highly expressive and arbitrarily complex boolean queries, with minimal information leakage regarding performed queries and accessed data, and verifiability regarding fully malicious adversaries. Furthermore, BISEN extends the traditional SSE model to support filter functions on search results based on generic metadata created by the users. Experimental validation and comparison with the state of art shows that BISEN provides better performance with enriched search semantics and security properties.

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Deductive verification has gained paramount attention from both academia and industry. Although intensive research in this direction covers almost all mainstream languages, the research community has paid little attention to the verification of database applications. This paper proposes a comprehensive set of Verification Conditions (VCs) generation techniques from database programs, adapting Symbolic Execution, Conditional Normal Form, and Weakest Precondition. The validity checking of the generated VCs for a database program determines its correctness w.r.t. the annotated database properties. The developed prototype DBverify based on our theoretical foundation allows us to instantiate VC generation from PL/SQL codes, yielding to detailed performance analysis of the three approaches under different circumstances. With respect to the literature, the proposed approach shows its competence to support crucial SQL features (aggregate functions, nested queries, NULL values, and set operations) and the embedding of SQL codes within a host imperative language. For the chosen set of benchmark PL/SQL codes annotated with relevant properties of interest, our experiment shows that only 38% of procedures are correct, while 62% violate either all or part of the annotated properties. The primary cause for the latter case is mostly due to the acceptance of runtime inputs in SQL statements without proper checking.