Specification and Implementation

This chapter considers the need to understand the relation between specification and implementation of computing systems, and to clarify the problem of miscomputation.

Constructive Galois Connections

Galois connections are a foundational tool for structuring abstraction in semantics, and their use lies at the heart of the theory of abstract interpretation. Yet, mechanization of Galois connections using proof assistants remains limited to restricted modes of use, preventing their general application in mechanized metatheory and certified programming. This paper presents constructive Galois connections, a variant of Galois connections that is effective both on paper and in proof assistants; is complete with respect to a large subset of classical Galois connections; and enables more general reasoning principles, including the “calculational” style advocated by Cousot. To design constructive Galois connections, we identify a restricted mode of use of classical ones which is both general and amenable to mechanization in dependently typed functional programming languages. Crucial to our metatheory is the addition of monadic structure to Galois connections to control a “specification effect.” Effectful calculations may reason classically, while pure calculations have extractable computational content. Explicitly moving between the worlds of specification and implementation is enabled by our metatheory. To validate our approach, we provide two case studies in mechanizing existing proofs from the literature: the first uses calculational abstract interpretation to design a static analyzer, and the second forms a semantic basis for gradual typing. Both mechanized proofs closely follow their original paper-and-pencil counterparts, employ reasoning principles not captured by previous mechanization approaches, support the extraction of verified algorithms, and are novel.

Managing Large Amounts of Data Generated by a Smart City Internet of Things Deployment

The Smart City concept is being developed from a lot of different axes encompassing multiple areas of social and technical sciences. However, something that is common to all these approaches is the central role that the capacity of sharing information has. Hence, Information and Communication Technologies (ICT) are seen as key enablers for the transformation of urban regions into Smart Cities. Two of these technologies, namely Internet of Things and Big Data, have a predominant position among them. The capacity to “sense the city” and access all this information and provide added-value services based on knowledge derived from it are critical to achieving the Smart City vision. This paper reports on the specification and implementation of a software platform enabling the management and exposure of the large amount of information that is continuously generated by the IoT deployment in the city of Santander.