In computer science, the Tak function is a recursive function, named after Ikuo Takeuchi [ja]. It is defined as follows:

$${\displaystyle \tau (x,y,z)={\begin{cases}\tau (\tau (x-1,y,z),\tau (y-1,z,x),\tau (z-1,x,y))&{\text{if }}y<x\\z&{\text{otherwise}}\end{cases}}}$$

This function is often used as a benchmark for languages with optimization for recursion.

The original definition by Takeuchi was as follows:

tarai is short for たらい回し (tarai mawashi, "to pass around") in Japanese.

John McCarthy named this function tak() after Takeuchi.

However, in certain later references, the y somehow got turned into the z. This is a small, but significant difference because the original version benefits significantly from lazy evaluation.

Though written in exactly the same manner as others, the Haskell code below runs much faster.