The role the YC plays in this case is hiding the memoization. The memoizing Y combinator is the same as the Y combinator, except it doesn't re-compute inputs i

The role the YC plays in this case is hiding the memoization. The memoizing Y combinator is the same as the Y combinator, except it doesn't re-compute inputs it's already seen. Writing recursive functions in "Y-combinator style" is a way to expose internal recursive call sites to external inspection and manipulation. The Y combinator version still grows the stack.