This chapter addresses the semantical aspects of the Signal language. It presents two kinds of semantics: an operational semantics in Sect. 7.1 and a denotational semantics in Sect. 7.2. In the operational approach to semantics, the meaning of a program is described in terms of its execution steps on an abstract machine. Thus, operational semantics assigns to a program, a computation structure (a graph), representing all possible executions of a program on an abstract machine. In his seminal note, Plotkin (Journal of Logic and Algebraic Programming 60–61:3–15, 2004) proposed a structural view on the operational semantics. This view has now become the de facto standard for giving operational semantics to languages. The denotational semantics of programming languages was originally studied by Scott and Strachey (in Proceedings of the Symposium on Computers and Automata, Polytechnic Institute of Brooklyn, pp. 19–46, 1971). It aims at describing how the meaning (also referred to as the denotation) of a valid program is interpreted as a function from its inputs to its outputs. The two semantics of Signal presented in this chapter were originally proposed by Benveniste et al. (Science of Computer Programming 16:103–149, 1991) and Le Guernic et al. (Journal for Circuits, Systems and Computers 12:261–304, 2003). For each semantics, some preliminary notions are first defined. Then, they are used to describe properly the semantics of the basic constructs of the language.
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