Array processing languages such as APL, Matlab and Octave rely on dynamic typechecking by the interpreter rather than static typechecking and are designed for user convenience with a syntax close to mathematical notation. Functions and operators are highly overloaded. The price to be paid for this flexibility is computational performance, since the run-time system is responsible for type checking, array shape determination, function call dispatching, and handling possible run-time errors. In order to produce effecient code, an Octave compiler should address those issues at compile-time as much as possible. In particular, static type and shape inferencing can improve the quality of the generated code. In this paper we discuss how overloading in dynamically typed Octave programs can be resolved by program specialization. We discuss the typing issues in compilation of Octave programs and give an overview of the implementation of the specializer in the transformation language Stratego.