Non-exhaustive pattern matches only because I left off `otherwise =`?

Question

I wrote a simple program in Haskell that plays the guessing game described in The Rust Programming Language book:

Here’s how it works: the program will generate a random integer between 1 and 100. It will then prompt the player to enter a guess. After entering a guess, it will indicate whether the guess is too low or too high. If the guess is correct, the game will print congratulations and exit.

Here is what I wrote:

import Control.Monad (when)
import System.Random (randomRIO)

-- | Check if the guess is correct, otherwise provide a hint
respond :: Int -> Int -> String
respond correct guess
  | guess > correct = "Smaller than " ++ show guess
  | guess < correct = "Larger than " ++ show guess
  | guess == correct = "Correct! " ++ show correct

-- | Main game loop; prompt for input and repeat until guessed correctly
play :: Int -> IO ()
play x = do
  putStr "Guess: "
  guess <- read <$> getLine
  putStrLn $ respond x guess
  when (guess /= x) $ play x

-- | Start the game with a random number between 1 and 100
main :: IO ()
main = play =<< randomRIO (1, 100)

The code works, but GHC gives me a warning that "Pattern match(es) are non exhaustive. In an equation for 'respond': Patterns not matched: _ _"

I take those two underscores to represent the two Ints I have as arguments to the respond function. What I don't understand is which case I haven't covered. Those aren't Maybe Ints or anything special — the function requires two valid Ints, so I only need to deal with integers — and I don't think there is any number that cannot be deemed greater than, less than, or equal to another?

Is this just GHC assuming I have not covered all cases because I didn't add a final otherwise = guard? Even though it logically covers all cases.

---

Also, if you have any tips on how to write more idiomatic Haskell, I'd appreciate them. I'm still learning the basics.

Answer 1

GHC simply doesn't know that one of a > b, a < b, or a == b must evaluate to True. (Indeed, it is possible to write an Ord instance that violates this assumption -- though most programmers would not consider doing so, and certainly the one for Int will behave nicely in this regard.)

You can make it patently obvious to GHC that you've covered all the cases by using a complete pattern match instead, e.g.

respond correct guess = case compare guess correct of
    GT -> ...
    LT -> ...
    EQ -> ...

GHC also has a special case in its exhaustiveness checker for the guards otherwise and True, so you may add (or replace) one of the guards with this as an alternative solution.

respond correct guess
    | guess > correct = ...
    | guess < correct = ...
    | otherwise = ...

Answer 2

The compiler does only a static semantic analysis. This is unable to see that the three cases cover all possible inputs because the meaning of the operators are determined at run-time.

Your code is provably correct. If you want to avoid the warning from GHC, you can change the final condition to otherwise.