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SRL is a Lisp-based language for representing discrete-time signals as abstract objects whose properties reflect those of the represented signals. The basic concepts and facilities of SRL are motivated by a number of elementary observations about the mathematics of signals and the mathematical notations commonly employed to describe them. The fundamental activity in SRL programming is the implementation of signal types. A signal type is a representation for a class of signals which share a common procedure for computing the value of a sample. Instances of a signal type are created by fixing the values of the free variables of this procedure. The basic observable properties of a signal are the dimensions of its domain and the values of its samples. Signal objects are immutable so that the properties of a signal remain fixed after the signal is created.