Type system in programming languages

Type system provides a precise description of a programming language. This is a prerequisite for the implementation and use of language. It also conducts mechanical and transparent type-checking on programs to prevent the occurrence of execution error during the running of programs. So, it can be said that, on the one hand, type system works as a formal tool to do mathematical analysis of language; on the other hand, it is a formal method for rigorously and precisely designing and implementing language. In this paper, some basic concepts of type system are discussed first. And then, the implementation of a graph-rewriting-based functional language - SClean's type system is given in details. It is hoped that the proposed method of using and implementing type system is of practical usefulness.