From Reduction-based to Reduction-free Normalization


We present a systematic construction of a reduction-free normalization function. Starting from a reduction-based normalization function, i.e., the transitive closure of a one-step reduction function, we successively subject it to refocusing (i.e., deforestation of the intermediate reduced terms), simplification (i.e., fusing auxiliary functions), refunctionalization (i.e., Church encoding), and direct-style transformation (i.e., the converse of the CPS transformation). We consider two simple examples and treat them in detail: for the first one, arithmetic expressions, we construct an evaluation function; for the second one, terms in the free monoid, we construct an accumulator-based flatten function. The resulting two functions are traditional reduction-free normalization functions. The construction builds on previous work on refocusing and on a functional correspondence between evaluators and abstract machines. It is also reversible.

DOI: 10.1016/j.entcs.2005.01.007

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@article{Danvy2005FromRT, title={From Reduction-based to Reduction-free Normalization}, author={Olivier Danvy}, journal={Electr. Notes Theor. Comput. Sci.}, year={2005}, volume={124}, pages={79-100} }