Scientists want to encode their applications in domain languages with high-level operators that reflect the way they conceptualize computations in their domains. Telescoping languages calls for automatically generating optimizing compilers for these languages by pre-compiling the underlying libraries that define them to generate multiple variants optimized for use in different possible contexts, including different argument types. The resulting compiler replaces calls to the high-level constructs with calls to the optimized variants. This approach aims to automatically derive high-performance executables from programs written in high-level domain-specific languages. TeleGen is a prototype telescoping-languages compiler that performs type-based specializations. For the purposes of this dissertation, types include any set of variable properties such as intrinsic type, size and array sparsity pattern. Type inference and specialization are cornerstones of the telescoping-languages strategy. Because optimization of library routines must occur before their full calling contexts are available, type inference gives critical information needed to determine which specialized variants to generate as well as how to best optimize each variant to achieve the highest performance. To build the prototype compiler, we developed a precise type-inference algorithm that infers all legal type tuples, or type configurations, for the program variables, including routine arguments, for all legal calling contexts. We use the type information inferred by our algorithm to drive specialization and optimization. We demonstrate the practical value of our type-inference algorithm and the type-based specialization strategy in TeleGen.