Reasoning about UML/OCL class diagrams using constraint logic programming and formula

Highlights

• Reasoning about CD/OCL models based on CLP using the tool Formula as model-finder.

• Translation of CD to Formula following a MOF-like proposal.

• Identified an expressive fragment of OCL and provided its translation to Formula.

• Provided an experimental MDA-based implementation of our CD-to-Formula proposal.

• Model design reasoning by checking correctness properties and generating model instances automatically.

Abstract

Model Driven Engineering promotes the use of models as the main artifacts in software and system development. Verification and validation of models are key activities to ensure the quality of the system under development. This paper presents a framework to reason about the satisfiability of class models described using the Unified Modeling Language (UML). The proposed framework allows us to identify possible design flaws as early as possible in the software development cycle. More specifically, we focus on UML Class Diagrams annotated with Object Constraint Language (OCL) invariants, which are considered to be the main artifacts in Object-Oriented analysis and design for representing the static structure of a system. We use the Constraint Logic programming (CLP) paradigm to reason about UML Class Diagrams modeling foundations. In particular, we use Formula as a model-finding and design space exploration tool. We also present an experimental Eclipse plug-in, which implements our UML model to Formula translation proposal following a Model Driven Architecture (MDA) approach. The proposed framework can be used to reason, validate, and verify UML Class Diagram software designs by checking correctness properties and generating model instances using the model exploration tool Formula.

Introduction

Model Driven Engineering (MDE) [1] promotes models as cornerstone components in software development. Verification and validation of models become important activities to ensure the quality of a system. Effective model verification and validation methods can reduce time to market and decrease development costs. In the context of MDE, the Unified Modeling Language (UML) and the Object Constraint Language (OCL) constitute two of the most commonly used modeling languages. UML [2] has been widely accepted as the de-facto standard object-oriented software modeling language. OCL [3] is an integral part of UML which has been introduced into UML as a declarative language to express integrity constraints that UML diagrams cannot convey by themselves.

Software models, as any other software artifact, may contain defects. Unfortunately, in some occasions, possible design flaws are not detected until the later implementation stages, thus increasing the cost of development [4], [5]. This situation requires a wide adoption of formal methods as well as verification and validation approaches. In this line, there have been remarkable efforts to formalize UML semantics, and to address and solve ambiguity, uncertainty, and underspecification issues detected in UML semantics. In particular, the formalization and analysis of specific UML artifacts can be done by carrying out a translation to another language that preserves the semantics [4], [5], [6], [7], [8], [9]. The resulting translation can be used for several purposes, such as to reason about implicit properties in UML models and about particular model instances.

In this paper we propose an overall framework to reason about specific UML Class Diagram (CDs) based on the Constraint Logic programming (CLP) paradigm. More specifically, we focus on UML Class Diagrams, annotated with OCL constraints, which are considered to be the mainstay of object-oriented analysis and design representing the static structure of a system, and whose formalization and analysis have motivated a significant number of proposals [4], [10], [11]. As reasoning tool, we use a model-finding and design space exploration tool called Formula [12], which presents distinctive strength properties compared to other similar tools, including more expressivity [13], [14]. More specifically, Formula is based on algebraic data types and CLP, and relies on the Formula solver Z3 as underlying engine to reason about models where proof goals are encoded as CLP satisfiability problem. Formula utilizes a bounded verification approach by means of which the reasoning process is carried out by establishing finite bounds for the number of instances of the model to be considered during the verification process. In the case that Z3 finds a solution that satisfies all encoded constraints, Formula will reconstruct a complete model from this information derived of known facts.

Our approach can be used for several different purposes. It can be used to rigorously reason about a UML design, by checking predefined correctness properties about the original model, such as satisfiability or the lack of redundant constraints [5]. Additionally, our proposal can be used to inspect models of complex system development contexts, to search for conforming object models and to choose those that better fit domain needs. Overall, our proposal can contribute to software design validation and verification.

The results presented in this paper are based on the work published by the authors of this paper in [15], [16]. In this paper we provide a revised and extended version of those works, focusing mainly on the conceptual definition of our framework, constituting the first paper that includes a complete description of our proposal. Additionally, in this paper we provide extra material regarding the reasoning process to follow when using our approach and a more detailed explanation about the comparison among our proposal and others.

The paper is structured as follows. Next, we motivate and present an overview of our approach, introducing the case study we use throughout the paper. Section 3 provides a brief introduction to Formula. Section 4 presents the translation of a UML class diagram to Formula, while Section 5 describes the OCL fragment we consider in our proposal and its representation into Formula. Section 6 describes the CD2Formula tool we have developed to implement our Class diagram to Formula translation proposal, and illustrates the usefulness of our overall approach by applying it to the case study. Section 7 summarizes the strengths and weaknesses of our approach and discusses related work. Finally, Section 8 contains our main conclusions.