Telescoping languages is a strategy to automatically generate highly-optimized domain-specific libraries. The key idea is to create specialized variants of library procedures through extensive offline processing. This paper describes a telescoping system, called ARGen, which generates high-performance Fortran or C libraries from prototype Matlab code for the linear algebra library, ARPACK. ARGen uses variable types to guide procedure specializations on possible calling contexts. We show that type-based specializations of generated libraries can lead to more than 50% speedup. ARGen needs to infer Matlab types in order to speculate on the possible variants of library procedures, as well as to generate code. This paper develops an approach combining static and dynamic type inference that includes a graph-theoretic algorithm that is shown to be efficient under a set of conditions that are easily met for most practical cases. The ideas developed here provide a basis for building a more general telescoping system for Matlab.