Type systems for programming languages

Many programming languages rely on the use of a system of types to distinguish between different kinds of value. This in turn is used to identify two classes of program; those which are well-typed and accepted by the type system, and those that it rejects. Many different kinds of type system have been considered but, in each case, the principal benefits are the same:

• The ability to detect program errors at compile time: A type discipline can often help to detect simple program errors such as passing an inappropriate number of parameters to a function.

• Improved performance: If, by means of the type system, it is possible to ensure that the result of a particular calculation will always be of a certain type, then it is possible to omit the corresponding runtime checks that would otherwise be needed before using that value. The resulting program will typically be slightly shorter and faster.

• Documentation: The types of the values defined in a program are often useful as a simple form of documentation. Indeed, in some situations, just knowing the type of an object can be enough to deduce properties about its behaviour (Wadler, 1989).

The main disadvantage is that no effective type system is complete; there will always be programs that are rejected by the type system, even though they would have produced welldefined results if executed without consideration of the types of the terms involved.