Giving Alloy a family

Abstract

Lightweight formal methods ought to provide to the end user the rigorousness of mathematics, without compromising simplicity and intuitiveness. ALLOY is a powerful tool, particularly successful on this mission. Limitations on the verification side, however, are known to prevent its wider use in the development of safety or mission critical applications. A number of researchers proposed ways to connect Alloy to other tools in order to meet such challenges. This paper's proposal, however, is not establishing a link from ALLOY to another single tool, but rather to "plunge" it into the HETS network of logics, logic translators and provers. This makes possible for Alloy specifications to "borrow" the power of several, non dedicated proof systems. Semantical foundations for this integration are discussed in detail.

Proof theory for hybrid(ised) logics

“…In order be able to hybridise Alloy specifications, to capture reconfigurable systems, but also, in a wider perspective, to 'connect' it to a vast network of logics and provers [33]-Neves et al [34,28] introduced an institution for Alloy along with suitable translations to (variants of) first-order and second-order logics. This makes possible not only to hybridise Alloy but also to verify the corresponding specifications in powerful provers such as SPASS [35] and LEO-II [36].…”

An Institution for Alloy and Its Translation to Second-Order Logic

“…In [17] the authors discussed the integration of Alloy [9] in Hets platform of logics, logic translators and provers, by scketching its formalisation as an institution [7,6] and defining its encoding into Casl [14], an extension of multisorted first order logic with partiality and free types. The motivation was clear: to offer a systematic way to connect Alloy to a huge network of logics and logical systems in order to complement the model finder strategies of the former with suitable theorem provers already linked into the latter.…”

“…There is a number of results on connecting Alloy to specific theorem provers. The perspective taken in [17], however, and complemented in this paper goes a step further by "plugging" Alloy into the Hets network, providing a number of effective and sound connections to several logical systems and tools at once. Currently, Hets integrates several world-class reasoners, namely Isabelle [18], LEO-II [4], SPASS [21], Vampire [19], Darwin [2], among many others.…”

“…The present paper addresses this challenge by developing in full detail the semantical foundations for this integration, including a formalisation of Alloy as an institution, and introducing a new, more general translation of it to secondorder logic (SOL) [12]. This new translation allows a more natural embedding of Alloy, when compared to the previous, essentially first-order translation to Casl introduced in [17]. Moreover, this translation establishes a connection between Alloy and higher-order provers, such as LEO-II and Isabelle, using the logic THF [3] which integrates second-order features.…”

“…Moreover, this translation establishes a connection between Alloy and higher-order provers, such as LEO-II and Isabelle, using the logic THF [3] which integrates second-order features. The original translation to Casl, presented in [17], is re-framed in this context, because, in practice, it opens doors to a broad number of theorem provers, namely for first-order systems. Both translations are depicted in Fig.…”