GCLA is a new programming language, which increases expressiveness compared with traditional logic programming languages and functional programming languages. The basis for the language is a generalization of the concept inductive definitions, called partial inductive definitions. The program defines a logic, which is used to make inferences to prove if a query holds or not. This report first presents a short introduction to these ideas. Then, an abstract machine, called GAM, for GCLA is presented; the instructions as well as an introduction to the compiling schema is given together with some examples. The main idea is to extend the Warren Abstract Machine (WAM), which is an abstract machine for the language Prolog.