A system for compiling programs for execution thereof using a hierarchical processing system having two or more levels of memory hierarchy can perform memory-level-specific optimizations, without exceeding a specified maximum compilation time. To this end, the compiler system employs a polyhedral model and limits the dimensions of a polyhedral program representation that is processed by the compiler at each level using a focalization operator that temporarily reduces one or more dimensions of the polyhedral representation. Semantic correctness is provided via a defocalization operator that can restore all polyhedral dimensions that had been temporarily removed.