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....the untimed model is used to express the system requirements. A normal form for the timed program is used to obtain an untimed program that can be verified to meet its requirements. The framework makes use of a meta method for formal method integration based on heterogenous notations [11, 12, 13]. The meta method describes an informal approach to integration, via combining notations and relating processes. The use of the method consists in selecting a base methods which is to be complemented by the other methods. The invasive methods are chosen to complement the base method. A ....

....for formal methods integration was presented in [12] The methods was used to integrate a subset of UML with a predicative programming design calculus [13] The metamethod describes an informal approach to intergate, via combining notations and relating processes. The method, as presented by Paige [12, 13, 11], can be summerized in the following steps ffl Fix the base method. A base method provides the basic notation for the main processes that will be combined with the other (invasive) methods. At this point integrators have a clear understanding of the role of each method in the integrated ....

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R. Paige. Formal method integration via heterogeneous notations, 1997.

....has two main goals. The first is to present an integration involving the program design calculus of predicative programming [8] and a representative objectoriented method that uses a core subset of the Unified Modelling Language (UML) 9] The integration is carried out using the meta method of [10] and is presented so as to show how to make a program design calculus and more generally, any formal method more appropriate for largescale software development, by combining it with an objectoriented method. The integration will allow the design calculus and its refinement techniques to be ....

....and structures produced by a method, as well as the process phases and their temporal ordering [7] A meta model is used to admit well formed specifications and to reject illformed ones. Formal method integration is method integration involving at least one and possibly several formal methods [10]. It is suggested in [6] that constructing heterogeneous notations can be a first step in integrating formal methods with other methods. Informally, integration can occur by formalizing the meaning of compositions of partial specifications written in the notations of interest; this also requires ....

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Paige, R. F. (1997) Formal Method Integration via Heterogeneous Notations. PhD Dissertation, University of Toronto, November.

.... of Computer Science, University of Toronto, Toronto, Ontario, M5S 3G4, Canada paige cs.toronto.edu February 7, 1997 Abstract We combine a formal specification technique with an object oriented method using a meta method for formal method integration based on heterogeneous notations [18, 19]. We discuss the integrated method, and then apply it to an example. 1 Introduction It is generally accepted that a single method for software development is insufficient for all situations [11, 5] This is due to the complexity of the problems being solved, the diversity of expertise, and the ....

....accepted that a single method for software development is insufficient for all situations [11, 5] This is due to the complexity of the problems being solved, the diversity of expertise, and the limitations of a single set of notations and procedures, among other reasons. Method integration [13, 18] is a technique that can be used to abet multiple method use, and solve some of the problems associated with using a single technique. Method integration has been studied in at least two settings: in the context of integrating particular methods [20, 22] and, in a setting where systematic and ....

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Paige, R.F. (1997) Formal Method Integration via Heterogeneous Notations, PhD Dissertation, University of Toronto, expected.

....the remainder can be found in [Pai99] Other translations can be constructed by composition. In presenting the translations, we assume that all notations use the unprimedprimed convention of Z [Spi89] to distinguish pre and poststate. Different notations, such as CSP and Larch, are considered in [Pa97a, Pa97b]. 2.1. Predicative programming and specification statements Predicative specifications [Heh93] can come in two forms: the first makes no mention of timing or termination; the second explicitly talks about time through use of the time variables t and t 0 . Such variables can provide constraints ....

.... with one notation (and in most cases, can express strictly less) Though we have taken an intersection approach to semantics in this paper, the general approach to PFMI that we present permits use of other approaches to giving a semantics to heterogeneous specifications (examples are discussed in [Pa97a]) We use only intersection techniques in the work summarized herein. 6 R. F. Paige 3. Generalizing Algorithm Refinement The heterogeneous basis of Section 2 provides translations that are used to supply heterogeneous specifications with a formal semantics. Such a semantics can be used to ....

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R.F. Paige.: Formal Method Integration via Heterogeneous Notations, PhD dissertation, University of Toronto, November 1997.

....because one method possesses tool support for a specific task, while a second does not. For example, Z possesses support of tools, e.g. for proof or syntax and semantic checking, while predicative programming does not. A specific example of such a complementarity used in practice is in [21], where Larch and predicative programming were combined: Larch tools, e.g. LP, were used behind the scenes to prove assertions about an abstract data type that was used in the predicative specifications. Such an integration was carried out so as to acquire use of tools without having to build ....

....for classifying methods in terms of their complementarity. The next step to take should be to further formalize and clarify this framework, in part by providing clear examples of complementary methods under each of the categories described previously. Work on semantic expressiveness, e.g. [13,21] can be applied for this purpose, as can efforts on theory unification [16] and classification of formalizations of semiformalisms, such as with Structured Analysis [2] Very useful, in this respect, will be Jackson s notion of problem frame [17] Jackson states that a method is associated with a ....

Paige, R.F., Formal Method Integration via Heterogeneous Notations, PhD dissertation (University of Toronto, November 1997).

....that defines the meaning of the initial specification. We depict the translations in Fig. 1. In Fig. 1, the arrows represent translations that will explicitly be written down; other translations can be constructed by composition. Further notations, e.g. CSP and Larch, are considered in [Pa97a, Pa97b]. The notations in Fig. 1 are all quite similar to begin with. Each makes use of first order logic or Zermelo Frankel set theory for types, and each has a similar model of state transitions. This similarity suggests that we should expect the notations to combine in a straightforward manner, and ....

....w . Notice that Z cannot express infeasible specifications; furthermore, SSToZ is not one to one since both abort and magic map to schemas with false for a property. We use the translations that we have presented here in the transformation rules and examples described later (and in the references [Pa97a, Pa97b]) However, alternative translations could certainly be devised and used to carry out PFMI, if they were determined to be necessary for a specific task. 3.5. Expressiveness We catalogue the differences in notation expressiveness among the formal notations of the heterogeneous basis. For each ....

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R.F. Paige.: Formal Method Integration via Heterogeneous Notations, PhD dissertation, University of Toronto, November 1997.

....Meta Method for Formal Method Integration Richard F. Paige Department of Computer Science, University of Toronto, Toronto, Ontario, M5S 3G4, Canada. paige cs.toronto.edu Abstract. We describe a meta method for formal method integration [Pai97]. The approach is applied to combining formal methods with other formal and semiformal methods. We discuss the theory behind formal method integration, present two example combinations, and use an integrated method in solving a small problem. 1 Introduction Method integration involves defining ....

....involves defining relationships between different methods so that they may be productively used together to solve problems. In a software engineering context, method integration has seen recent research on combining specific methods [LKP91, SFD92] and on the formulation of systematic techniques [Kro93, Pai97]. In this paper, we follow the latter theme and describe a meta method for formal method integration based on heterogeneous notations [Pai97] We commence with a brief overview of method integration and the general means we take to accomplishing it. Our approach is based on heterogeneous ....

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R.F. Paige. Formal Method Integration via Heterogeneous Notations, PhD Dissertation, July 1997.

....languages) by allowing specifications to be constructed from parts written in several different languages. Definition 1. A heterogeneous notation is syntactically and semantically composed from two or more notations. In this paper, we consider only compositions involving formal notations. In [Pai97], we provide a wider perspective and also consider semiformalisms. Specifications written using more than one notation will be called heterogeneous. Definition 2. A specification is heterogeneous if it is a composition of partial specifications written in two or more notations. A number of ....

....role. Compositions between notations are not always possible. A reasonable requirement is that the notations being composed have the same or can be given the same underlying model. We consider only notations that are compatible in this sense herein; compatibility is examined in more detail in [Pai97]. 1.3. Heterogeneous Notations for Method Integration Heterogeneous notations are a technique that can be used to combine languages. We are interested in heterogeneous notations as a means to carry out method integration; with notations combined, method integration becomes procedure ....

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R.F. Paige.: Formal Method Integration via Heterogeneous Notations, PhD dissertation, expected 1997.

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Paige, R.F. (1997) Formal Method Integration via Heterogeneous Notations. PhD Dissertation, University of Toronto, November 1997.

....IN USING A META METHOD FOR FORMAL METHOD INTEGRATION Richard F. Paige Department of Computer Science, University of Toronto, Toronto, ON, Canada, M5S 3G4. paige cs.toronto.edu Abstract. We summarize the results of several experiments in applying a metamethod for formal method integration [18, 19]. We provide a small example of using an instance of integrated formal methods, and discuss properties and difficulties associated with applying the meta method to combining and using several formal and semiformal methods. 1 Introduction Method integration involves defining relationships between ....

....1 Introduction Method integration involves defining relationships between different methods so that they may be cooperatively used together. In software engineering, method integration has seen recent research on combining specific methods [15, 25] and on the formulation of systematic techniques [14, 18, 19]. In this paper, we follow the latter theme and describe several case studies in the application (and use of the products) of a metamethod for formal method integration [18, 19] We commence with a very brief overview of method integration and the means we take to accomplishing it. Our lightweight ....

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R.F. Paige. Formal Method Integration via Heterogeneous Notations, PhD Dissertation, November 1997.

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