On Dec 30, 2011, at 10:19 AM, Conal Elliott wrote:

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.

Two questions trouble me:

How can we know whether this claim is true or not?

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.)

-Gregg