In what sense is the IO Monad pure?

Question

I\'ve had the IO monad described to me as a State monad where the state is \"the real world\". The proponents of this approach to IO argue that this makes IO operations pure

Answer 1

Suppose we have something like:

animatePowBoomWhenHearNoiseInMicrophone :: TimeDiff -> Sample -> IO ()
animatePowBoomWhenHearNoiseInMicrophone
    levelWeightedAverageHalfLife levelThreshord = ...

programA :: IO ()
programA = animatePowBoomWhenHearNoiseInMicrophone 3 10000

programB :: IO ()
programB = animatePowBoomWhenHearNoiseInMicrophone 3 10000

Here's a point of view:

animatePowBoomWhenHearNoiseInMicrophone is a pure function in the sense that its results for same input, programA and programB, are exactly the same. You can do main = programA or main = programB and it would be exactly the same.

animatePowBoomWhenHearNoiseInMicrophone is a function receiving two arguments and resulting in a description of a program. The Haskell runtime can execute this description if you set main to it or otherwise include it in main via binding.

What is IO? IO is a DSL for describing imperative programs, encoded in "pure-haskell" data structures and functions.

"complete-haskell" aka GHC is an implementation of both "pure-haskell", and an imperative implementation of an IO decoder/executer.