Abstract
Platforms to support novices learning to program are often accompanied by automated next-step hints that guide them towards correct solutions. Many of those approaches are data-driven, building on historical data to generate higher quality hints. Formal specifications are increasingly relevant in software engineering activities, but very little support exists to help novices while learning. Alloy is a formal specification language often used in courses on formal software development methods, and a platform-Alloy4Fun-has been proposed to support autonomous learning. While non-data-driven specification repair techniques have been proposed for Alloy that could be leveraged to generate next-step hints, no data-driven hint generation approach has been proposed so far. This paper presents the first data-driven hint generation technique for Alloy and its implementation as an extension to Alloy4Fun, being based on the data collected by that platform. This historical data is processed into graphs that capture past students' progress while solving specification challenges. Hint generation can be customized with policies that take into consideration diverse factors, such as the popularity of paths in those graphs successfully traversed by previous students. Our evaluation shows that the performance of this new technique is competitive with non-data-driven repair techniques. To assess the quality of the hints, and help select the most appropriate hint generation policy, we conducted a survey with experienced Alloy instructors.

Abstract
A key feature of model finding techniques allows users to enumerate and explore alternative solutions. However, it is challenging to guarantee that the generated instances are relevant to the user, representing effectively different scenarios. This challenge is exacerbated in quantitative modelling, where one must consider both the qualitative, structural part of a model, and the quantitative data on top of it. This results in a search space of possibly infinite candidate solutions, often infinitesimally similar to one another. Thus, research on instance enumeration in qualitative model finding is not directly applicable to the quantitative context, which requires more sophisticated methods to navigate the solution space effectively. The main goal of this paper is to explore a generic approach for navigating quantitative solution spaces and showcase different iteration operations, aiming to generate instances that differ considerably from those previously seen and promote a larger coverage of the search space. Such operations are implemented in QAlloy – a quantitative extension to Alloy – on top of Max-SMT solvers, and are evaluated against several examples ranging, in particular, over the integer and fuzzy domains. © 2025 Elsevier B.V., All rights reserved.