Sparse computations are important in scientific computing. Many scientific applications compute on sparse data. These computations are considered irregular because they introduce programming patterns not suited for regular compiler optimization techniques. Sparse formats make use of auxiliary arrays to store non-zeros, as a result, the contents of auxiliary arrays are not known until run-time. The Inspector/Executor (I/E) paradigm enables the use of run-time information for compiler optimizations. An inspector computes information at run-time to drive transformations. The executor-a compile-time transformation of the original code- uses information computed by the inspector. The sparse polyhedral framework (SPF) encompasses a series of tools to support I/E run-time transformations. This work proposes a unified framework that wraps relevant SPF tool-chains while providing a holistic view of a computation as an intermediate representation (IR). This work also proposes a method to automatically synthesize inspectors for transforming between sparse formats. This work proposes improvements to the sparse polyhedral framework to explore performance of irregular applications, and introduces techniques for automatic generation of inspectors.