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In this paper we show that mathematical functions and logical expressions can very well be used as, partial, specifications. Reactive systems can be modelled by powerful extended state transition systems, that can be nondeterministic and can handle parameterized and infinite types for the inputs, outputs and states. These specifications can very concisely and directly be stated in a modern functional programming language. The test tool Gast is able to generate test data based on these specifications, execute the associated tests, and make a verdict fully automatically. Test data can be generated fully automatically, but can also be tailored in various high level ways, if that is desired. Advantages of this approach are that one specifies properties instead of instances of these properties, test data are automatically derived instead of manually, the tests performed are always up to date with the current specification, and testing is automatic (and hence fast and accurate).