Is Haskell truly pure (is any language that deals with input and output outside the system)?

Question

After touching on Monads in respect to functional programming, does the feature actually make a language pure, or is it just another \"get out of jail free card\" for reason

Answer 1

I think of it like this: Programs have to do something with the outside world to be useful. What's happening (or should be happening) when you write code (in any language) is that you strive to write as much pure, side-effect-free code as possible and corral the IO into specific places.

What we have in Haskell is that you're pushed more in this direction of writing to tightly control effects. In the core and in many libraries there is an enormous amount of pure code as well. Haskell is really all about this. Monads in Haskell are useful for a lot of things. And one thing they've been used for is containment around code that deals with impurity.

This way of designing together with a language that greatly facilitates it has an overall effect of helping us to produce more reliable work, requiring less unit testing to be clear on how it behaves, and allowing more re-use through composition.

If I understand what you're saying correctly, I don't see this as a something fake or only in our minds, like a "get out of jail free card." The benefits here are very real.

Answer 2

What does it mean to reason about computer systems "outside of blackboard maths"? What kind of reasoning would that be? Dead reckoning?

Side-effects and pure functions are a matter of point of view. If we view a nominally side-effecting function as a function taking us from one state of the world to another, it's pure again.

We can make every side-effecting function pure by giving it a second argument, a world, and requiring that it pass us a new world when it is done. I don't know C++ at all anymore but say read has a signature like this:

vector<char> read(filepath_t)

In our new "pure style", we handle it like this:

pair<vector<char>, world_t> read(world_t, filepath_t)

This is in fact how every Haskell IO action works.

So now we've got a pure model of IO. Thank goodness. If we couldn't do that then maybe Lambda Calculus and Turing Machines are not equivalent formalisms and then we'd have some explaining to do. We're not quite done but the two problems left to us are easy:

• What goes in the world_t structure? A description of every grain of sand, blade of grass, broken heart and golden sunset?

• We have an informal rule that we use a world only once -- after every IO operation, we throw away the world we used with it. With all these worlds floating around, though, we are bound to get them mixed up.

The first problem is easy enough. As long as we do not allow inspection of the world, it turns out we needn't trouble ourselves about storing anything in it. We just need to ensure that a new world is not equal to any previous world (lest the compiler deviously optimize some world-producing operations away, like it sometimes does in C++). There are many ways to handle this.

As for the worlds getting mixed up, we'd like to hide the world passing inside a library so that there's no way to get at the worlds and thus no way to mix them up. Turns out, monads are a great way to hide a "side-channel" in a computation. Enter the IO monad.

Some time ago, a question like yours was asked on the Haskell mailing list and there I went in to the "side-channel" in more detail. Here's the Reddit thread (which links to my original email):

http://www.reddit.com/r/haskell/comments/8bhir/why_the_io_monad_isnt_a_dirty_hack/