Function Totality with IO

Question

After reading over Prof. Yorgey's lecture on IO, is the following function considered to be total?

Prelude> let f x = return $ error "44" :: IO Int

I understand that a total function terminates and returns a value for every input.

However, since Haskell separates the evaluation and execution of IO, I'm not sure how totality applies to f.

Answer 1

The function f is indeed total. It returns, for any input, a value. Specifically, it produces every time the same value.

The value happens to be an IO action, that, when executed, will probably terminate the program, unless run in a context that can deal with the error. But this doesn't play a role, since merely applying f does not run the IO action.

Here is an example program that uses f :

main = putStrLn $ show $ length $ map (f$) [1,2,3]

and it should print

3