This paper presents an incrementalapproach to automatic algorithm design, which can be described byalgebraic specifications precisely and conveniently. The definitions ofselection operator and extension operator which can be defined bystrategy relations and transformations are given in order to model theprocess of finding the solution of a problem. Also discussed is itsobject-oriented implementation. The functional specification and thedesign specification for an algorithm are given in one framework so thatthe correctness of the algorithm can be easily proved.