This thesis develops telescoping-language technology for automatically generating high performance libraries from development code written in high-level languages, like Matlab. The generated library subroutines have pre-optimized variants based on possible uses of the library. Specifically, a specialized variant is generated for each possible type configuration on inputs to the library. This thesis develops an efficient graph-theoretical, constraint-based algorithm for inferring types in Matlab needed for translation into lower-level languages, optimization, and determination of which specialized variants to generate. The algorithm computes type jump functions, which allows it to infer types inter procedurally. To illustrate the power of the technology, this thesis develops ARGen, a system which generates code equivalent to ARPACK, a Fortran linear algebra library, from its Matlab development code. By accomplishing the type inferencing algorithm and ARGen, which uses it, this thesis provides a basis for a general system for telescoping languages.