In simple cases (for example a function UInt8 -> Something) it might be reasonable to expect the optimiser to know how to memoise automatically. But how about functions of the form (Integer -> Something), which have an essentially infinite domain? How much space is the memoization allowed to use? What kind of data structure should be used for the lookup? This could be very hard for the application programmer to communicate to the compiler.

Memoising a function f in Haskell can be done like this: create some lazy map where the keys are arguments, and the associated value is f(argument). The function f will only be evaluated once you actually try to use the values of the map.

I thought the first example in this blog post on TH was an interesting idea: https://www.parsonsmatt.org/2015/11/15/template_haskell.html

Best case scenario would be the optimizer does it for you. Less optimal would be compiler hints saying 'please memoize this function'.