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The compositional interchange format for hybrid systems (CIF) supports inter-operability of a wide range of tools by means of model transformations to and from the CIF. Work on the CIF takes place in the FP7 Multiform project, and in several other European projects. The CIF consists of an abstract and a concrete format, used for defining a formal semantics and for modeling, respectively. This paper discusses the results of a redesign of the abstract format as previously published, leading to the following main changes: variables are introduced using scoping operators; the abstract language is made more orthogonal by providing an operator for each concept in the language; parallel composition has been defined in such a way that compositional verification (assume/guarantee reasoning) is supported; and the concept of urgent actions has been properly defined. As a result, the expressivity and semantics of the …