On Fri, Dec 30, 2011 at 12:49 AM, Heinrich Apfelmus <apfelmus@quantentunnel.de> wrote:

The function

 f :: Int -> IO Int

 f x = getAnIntFromTheUser >>= \i -> return (i+x)

is pure according to the common definition of "pure" in the context of purely functional programming. That's because

 f 42 = f (43-1) = etc.

Put differently, the function always returns the same IO action, i.e. the same value (of type  IO Int) when given the same parameter.

time t:  f 42   (computational process implementing func application begins…)

t+1:   <keystroke> = 1

t+2:  43   (… and ends)

time t+3:  f 42

t+4:  <keystroke> = 2

t+5:  44

Conclusion:  f 42 != f 42

(This seems so extraordinarily obvious that maybe Heinrich has something else in mind.)