People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.
"When are two algorithms the same?." Bull. Symbolic Logic 15 (2) 145 - 168, June 2009. https://doi.org/10.2178/bsl/1243948484