Uwe Wolter

Uwe Wolter

Reflecting our experiences in areas, like Algebraic Specifications, Abstract Model Theory, Graph Transformations, and Model Driven Software Engineering (MDSE), we present a general, category independent approach to Logics of First-Order Constraints (LFOC). Traditional First-Order Logic, Description Logic and the sketch framework are discussed as examples. We use the concept of institution [Diaconescu08,GoguenBurstall92] as a guideline to describe LFOC's. The main result states that any choice of the six parameters, we are going to describe, gives us a corresponding "institution of constraints" at hand. The "presentations" for an institution of constraints can be characterized as "first-order sketches". As a corresponding variant of the "sketch-entailments" in [Makkai97], we finally introduce "sketch rules" to equip LFOC's with the necessary expressive power.

Uwe Wolter, Fernando Macías, Adrian Rutle

Multilevel modeling extends traditional modeling techniques with a potentially unlimited number of abstraction levels. Multilevel models can be formally represented by multilevel typed graphs whose manipulation and transformation are carried out by multilevel typed graph transformation rules. These rules are cospans of three graphs and two inclusion graph homomorphisms where the three graphs are multilevel typed over a common typing chain. In this paper, we show that typed graph transformations can be appropriately generalized to multilevel typed graph transformations improving preciseness, flexibility and reusability of transformation rules. We identify type compatibility conditions, for rules and their matches, formulated as equations and inequations, respectively, between composed partial typing morphisms. These conditions are crucial presuppositions for the application of a rule for a match---based on a pushout and a final pullback complement construction for the underlying graphs in the category Graph---to always provide a well-defined canonical result in the multilevel typed setting. Moreover, to formalize and analyze multilevel typing as well as to prove the necessary results, in a systematic way, we introduce the category Chain of typing chains and typing chain morphisms.

Fernando Macías, Uwe Wolter, Adrian Rutle et al.

The use of Domain-Specific Languages (DSLs) is a promising field for the development of tools tailored to specific problem spaces, effectively diminishing the complexity of hand-made software. With the goal of making models as precise, simple and reusable as possible, we augment DSLs with concepts from multilevel modelling, where the number of abstraction levels are not limited. This is particularly useful for DSL definitions with behaviour, whose concepts inherently belong to different levels of abstraction. Here, models can represent the state of the modelled system and evolve using model transformations. These transformations can benefit from a multilevel setting, becoming a precise and reusable definition of the semantics for behavioural modelling languages. We present in this paper the concept of Multilevel Coupled Model Transformations, together with examples, formal definitions and tools to assess their conceptual soundness and practical value.