Common Strengths
Polyhedral frameworks are designed to support compilers techniques for analysis and transformation of codes with nested loops, producing exact results for loop nests with affine loop bounds and subscripts ("Static Control Parts" of programs). They can be used to represent and reason about executions (iterations) of statements, rather than treating a statement as a single object representing properties of all executions of that statement. Polyhedral frameworks typically also allow the use of symbolic expressions.
Polyhedral frameworks can be used for dependence analysis for arrays, including both traditional alias analysis and more advanced techniques such as the analysis of data flow in arrays or identification of conditional dependencies. They can also be used to represent code transformation, and provide features to generate the transformed code in a high-level language. The transformation and generation systems can typically handle imperfectly nested loops.
Read more about this topic: Frameworks Supporting The Polyhedral Model
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