I/O, Yay!!

module LectureIO where

Um, yeah. OK. Maybe I/O is not that scary in most languages. To be honest, though, it’s pretty messy in most languages. How lovely really is java.util.Scanner, std::cin, scanf, etc.?

1 What are Monads?

A monad in Haskell is an instance m of the Monad type class. The type class says that m must be a type constructor of one argument (like ProVal or list) with two operations:

return :: a -> m a

This “injects” a value into the monad in some trivial way. If we think of the monad as a “container” (like a Proval Double is a container for a Double along with some provenance commentary or a [Double] is a container for many doubles arranged in an order), then this constructs a container capapble of holding as, with nothing inside but its argument.

So, for ProVal, return x might make a new ProVal with x inside and no commentary. For lists, return x makes the list [x].

(>>=) :: m a -> (a -> m b) -> m b

Also known as “bind”, this lets us build a new container (an m b) by taking an original container (m a) and a function that tells us what m b to “splice in” as a replacement for each a in the container. It makes a new container representing the result of that splicing.¹

1.1 You Can Check Out Anytime You Like, But You Can Never Leave²

If you take a close look at the signatures of return :: a -> m a and (>>=) :: m a -> (a -> m b) -> m b, you’ll notice:

1. It’s easy to “get a value out” of m and do something with it. You can use ma >>= f. Now, f can access the (or every) a inside the ma “container” and act on it.

   We can even define a new function using return and >>=:

   fmap :: Monad m => (a -> b) -> (m a -> m b)
   fmap f ma = ma >>= (\a -> return (f a))

   fmap f lets us use any normal function f that we want as a function that operates on values in any monad instead!

   (So, we can “check out” of the m monad anytime we want to and get at the regular values inside.)

2. However, the result types of return and >>= make it so that in the end, anytime we operate on a value in an m container, the result ends up in an m container as well!

   (So, we can never really leave the monad, at least note with the Monad type class’s operations.)

Haskell defines a huge number of operations and functions (and even special syntax³) we can now use to manipulate anything that instantiates Monad, and we can take advantage of all of them if we make a Monad instance.

Here’s one simple one. >> is just like >>= except that when we “splice in” a m b, it’s always the same m b. It ignores the a it’s replacing:

(>>) :: Monad m => m a -> m b -> m b
ma >> mb   = ma >>= (\_ -> mb)
-- (\_ -> mb) is a little lambda function that
-- takes an argument, ignores it, and returns mb.

1.2 Our First Monad Instance

TODO: continue from here on Wednesday

Here’s an updated version of ProVal:

data ProVal a = ProVal a [String]
  deriving (Eq, Ord, Show, Read)

Rather than a single String for comments, it has a list of Strings. That also means that a “plain” value x can simply have no comments: ProVal x [].

Let’s make it an instance of Monad! return will make the simplest ProVal we can. pa >>= f will take the a value from pa, feed it to f, get the ProVal b it produces, and finally prepend all of pa’s comments onto the ProVal b’s comments. (So, we end up with the b value, but we carry all the provenance comments along, in the correct order.)

instance Monad ProVal where
  ...

Here are our three solutions from class using a plain helper (commented out), a local helper with where (commented out), and a case expression:

-- assembleNewProVal :: [String] -> ProVal b -> ProVal b
-- assembleNewProVal aComments (ProVal b bComments) = ProVal b (aComments ++ bComments)

instance Monad ProVal where
  return :: a -> ProVal a
  return x = ProVal x []
  
--   (>>=) :: ProVal a -> (a -> ProVal b) -> ProVal b
--   (ProVal a aComments) >>= f = helper (f a)
--     where helper (ProVal b bComments) = ProVal b (aComments ++ bComments)
    
  (>>=) :: ProVal a -> (a -> ProVal b) -> ProVal b
  (ProVal a aComments) >>= f = case f a of
                                 ProVal b bComments -> ProVal b (aComments ++ bComments)

(Two exercises.)

2 Why Would You Bother, or, What’s So Scary About I/O?

The trouble with I/O (and side effects in general) in Haskell are (1) they aren’t functional and (2) lazy evaluation means we don’t even know when (or if) they happen.

But, what if we made a new monad called IO? An IO a as a container is “an action, possibly with side effects that, when run, produces an a value”.

For the IO monad, return x makes a “fake” action that just produces x when run.

ioa >>= f makes a new action that, when run:

• runs ioa first,
• gets the a it produces,
• feeds it to f,
• runs the action that f returns second, and
• produces as its final value whatever that second action produced.

Did you see the trick there? >>= solves our two problems above: (1) It produces an action value without actually performing the action. No side effects! (2) But that value represents an action that does what we want in the correct order.

Now, we can build up actions like “read in the user’s name >>= given string s, say hello to s”, which produces an action that, when run, first reads in the user’s name and then feeds that name into code that says hello to them.

-- | An action to read in the user's name.
-- Remember that ioa >> iob produces an action that
-- performs ioa and then performs iob, producing iob's
-- result. (So, like >>=, but ignoring ioa's value.)
readName :: IO String
readName = putStrLn "What is your name?" >> getLine

-- | An action to say hello to s.
-- () is a special type with only one value in it: ()
-- It is similar in a sense to the void type in Java.
-- (The type is called "unit" when you read it aloud.)
sayHello :: String -> IO ()
sayHello s = putStrLn ("Hello, " ++ s ++ "!")

Now, let’s make this file a program that reads a user’s name and greets them, using readName and sayHello above and >>=:

-- | When you run a program in Haskell, it is `main` 
-- that is run. Its `IO ()` action is created and then
-- ACTUALLY RUN, which is magical and beyond the scope
-- of normal Haskell.
--
-- In ghci, any `IO a` we evaluate at the prompt is also run.
main :: IO ()
main = greet

-- | Get a user's name and greet them.
-- We can use our helpers above to write this.
greet :: IO ()
greet = readName >>= sayHelloForever
  where sayHelloForever name = sayHello name >> sayHelloForever name

We’ll just run it in ghci.⁴

(Four exercises.)

3 Our Game(s) With IO

We should really make a version of our game(s) with a user interface. For lack of time, we’re just going to give it to you for you to look through rather than go through it step-by-step. Try it out and investigate the code!

Here’s a playable game (minus one piece we suggest as an exercise for you!).

4 Function Composition: The Period at the End of Haskell’s Sentence.

There is one last Haskell operator we’re going to learn. It does function composition:

(.) :: (b -> c) -> (a -> b) -> (a -> c)
(f . g) x = f (g x)

I intentionally wrote its type with parentheses around a -> c at the end, even though those aren’t necessary. We think of . as an operator that takes two functions and “chains them together” to form a single function.

Since we often break a Haskell problem down into a series of functions operating one after another to produce an eventual value, . is incredibly handy to define new functions!

Here’s hasMSWin that determines if a list of numbers contains any three that sum to 15:

hasMSWin :: [Int] -> Bool
hasMSWin ns = not (null (filter (== 15) (map sum (all3Lists ns))))

Let’s write hasMSWin' = ..., where we use function composition to create a chain of functions on the right side:

hasMSWin' :: [Int] -> Bool
hasMSWin' = not . null . filter (== 15) . map sum . all3Lists

The new version means the same thing. Is is easier to read? Is it clearer?

Let’s practice describing functions as “chains” of other functions!

(Two exercises.)

Note: hasMSWin needs these to work, but we won’t review them:

allSubLists :: Int -> ([a] -> [[a]])
allSubLists 0 _ = [[]]
allSubLists _ [] = []
allSubLists n (a:as) | n < 0 = []
                     | otherwise = map (a:) (allSubLists (n-1) as) ++ allSubLists n as

all3Lists :: [a] -> [[a]]
all3Lists = allSubLists 3

5 Appendix

Here are some extra notes on I/O in Haskell.

5.1 The Trouble with I/O

Simon Peyton Jones ruefully and authoritatively describes the trouble with I/O in Tackling the Awkward Squad: “A purely functional program implements a function; it has no side effect. Yet the ultimate purpose of running a program is invariably to cause some side effect: a changed file, some new pixels on the screen, a message sent, or whatever. Indeed it’s a bit cheeky to call input/output”awkward” at all. I/O is the raison d’être of every program — a program that had no observable effect whatsoever (no input, no output) would not be very useful.”

5.2 The Bad Old Days

We discussed (and Peyton Jones points out) lazy evaluation makes the I/O problem even worse. We don’t know when the side effects (like I/O) will actually happen, or even if they will happen!

Laziness also presents one potential solution: Just model the input to the program as a potentially-infinite list of “input objects” from the world and output by the program as a potentially-infinite list of “output objects”. An output could be requesting some information, which will hopefully eventually come back in on the input.

Haskell used to use this solution.. but it has lots of problems resolved by monads!