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The inspector/executor paradigm permits using runtime information in concert with compiler optimization. An inspector collects information that is only available at runtime; this information is used by an optimized executor that was created at compile time. Inspectors are widely used in optimizing irregular computations, where information about data dependences, loop bounds, data structures, and memory access pa erns are collected at runtime and used to guide code transformation, parallelization, and data layout. Most research that uses inspectors relies on instantiating inspector templates, invoking inspector library code, or manually writing inspectors. is paper describes abstractions for generating inspectors for loop and data transformations for sparse matrix computations using the Sparse Polyhedral Framework (SPF). SPF is an extension of the polyhedral framework for transformation and code generation. SPF extends the polyhedral framework to represent runtime information with uninterpreted functions and inspector computations that explicitly realize such functions at runtime. It has previously been used to derive inspectors for data and iteration space reordering. is paper introduces data transformations into SPF, such as conversions between sparse matrix formats, and show how prior work can be supported by SPF. We also discuss possible extensions to support inspector composition and incorporate other optimizations. is work represents a step towards creating composable inspectors in keeping with the composability of a ne transformations on the executors.more » « less