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In this section of the course we study a powerful theory for representing and evaluating loop transformations. This promises:

efficient algorithms which guarantee to extract parallelism if it is present.

efficient algorithms for optimising load balance and locality.

The theory is not all-powerful:

it does not handle tiling/blocking entirely elegantly, and

It needs to be extended substantially to handle real programs (e.g. imperfectly-nested and triangular loops).