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In 1972, Reynolds outlined a general method for eliminating functional arguments known as dejunctionalization. The idea underlying defunctionahzation is encoding a functional value as first-order data, and then realizing the applications of the encoded function via an apply function. Although this process is simple enough, problems arise when defunctionalization is used in a polymorphic language. In such a language, a functional argument of a higher-order function can take different type instances in different applications. As a consequence, its associated apply function can be untypable in the source language. In the paper we present a defrmctionalization transformat ion which preserves typability. Moreover, the transformation imposes no restriction on functional arguments of recursive functions, and it handles functions as results as well as functions encapsulated in constructors. The key to thk success is the use of type information in the defunctionaliiation transformation. Run-time characteristics are preserved by defunctionalization; hence, there is no performance improvement coming from the transformation itself. However closures need not be implemented to compile the transformed program.

The B method has been successfully used to specify many industrial applications by refinement. Previously, we proposed enriching the B event systems by formulating its dynamic properties in LT L. This enables us to combine model-checking with theorem-proving verification technologies. The model-checking of LT L formulae necessitates that the B event system semantics is a transition system. In this paper, we express the refinement relation by a relationship between transition systems. A result of our study shows that this relation is a special kind of simulation allowing us to exploit the partition of the reachable state space for a modular verification of LT L formulae. The results of the paper allow us to build a bridge between the above view of the refinement and the notions of observability characterized as simulation relations by Milner, van Glabbeek, Bloom and others. The refinement relation we define in the paper is a ready-simulation generalization which is similar to the refusal simulation of Ulidowsky. The way the relation is defined allows us to obtain a compositionality result w.r.t. parallel composition operation. For complex systems, it is important in practice to associate a design by refinement with a design by a parallel composition of their components. This refinement relation has two main applications: it allows the splitting of the refined transition system into modules; it allows the construction of complex systems by a parallel composition of components. It makes sense to qualify the refinement relation as being modular.

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