# Haskell/Control structures

Haskell offers several ways of expressing a choice between different values. We explored some of them in the Haskell Basics chapters. This section will bring together what we have seen thus far, discuss some finer points, and introduce a new control structure.

`if` and guards revisited

edit
We have already met these constructs. The syntax for `if`

expressions is:

```
if <condition> then <true-value> else <false-value>
```

`<condition>` is an expression which evaluates to a boolean. If the `<condition>` is `True` then the `<true-value>` is returned, otherwise the `<false-value>` is returned. Note that in Haskell `if` is an expression (which is converted to a value) and not a statement (which is executed) as in many imperative languages.^{[1]} As a consequence, the `else` is *mandatory* in Haskell. Since `if` is an expression, it must evaluate to a result whether the condition is true or false, and the `else` ensures this. Furthermore, `<true-value>` and `<false-value>` must evaluate to the same type, which will be the type of the whole if expression.

When `if`

expressions are split across multiple lines, they are usually indented by aligning `else`

s with `then`

s, rather than with `if`

s. A common style looks like this:

```
describeLetter :: Char -> String
describeLetter c =
if c >= 'a' && c <= 'z'
then "Lower case"
else if c >= 'A' && c <= 'Z'
then "Upper case"
else "Not an ASCII letter"
```

Guards and top-level `if`

expressions are mostly interchangeable. With guards, the example above is a little neater:

```
describeLetter :: Char -> String
describeLetter c
| c >= 'a' && c <= 'z' = "Lower case"
| c >= 'A' && c <= 'Z' = "Upper case"
| otherwise = "Not an ASCII letter"
```

Remember that `otherwise`

is just an alias to `True`

, and thus the last guard is a catch-all, playing the role of the final `else`

of the `if`

expression.

Guards are evaluated in the order they appear. Consider a set up like the following:

```
f (pattern1) | predicate1 = w
| predicate2 = x
f (pattern2) | predicate3 = y
| predicate4 = z
```

Here, the argument of `f`

will be pattern-matched against pattern1. If it succeeds, then we proceed to the first set of guards: if predicate1 evaluates to `True`

, then `w`

is returned. If not, then predicate2 is evaluated; and if it is true `x`

is returned. Again, if not, then we proceed to the next case and try to match the argument against pattern2, repeating the guards procedure with predicate3 and predicate4. (Of course, if neither pattern matches or neither predicate is true for the matching pattern there will be a runtime error. Regardless of the chosen control structure, it is important to ensure all cases are covered.)

### Embedding `if` expressions

edit
A handy consequence of `if`

constructs being *expressions* is that they can be placed anywhere a Haskell expression could be, allowing us to write code like this:

```
g x y = (if x == 0 then 1 else sin x / x) * y
```

Note that we wrote the `if`

expression without line breaks for maximum terseness. Unlike `if`

expressions, guard blocks are not expressions; and so a `let`

or a `where`

definition is the closest we can get to this style when using them. Needless to say, more complicated one-line `if`

expressions would be hard to read, making `let`

and `where`

attractive options in such cases.

## Short-circuit operators

editThe `||`

and `&&`

operators mentioned before are in fact control structures: they evaluate the first argument and then the second argument only if needed.

### Avoiding excessive effort

editFor instance, suppose a large number n is to be checked to determine if it is a prime number and a function isPrime is available, but alas, it requires a lot of computation to evaluate. Using the function `\n -> n == 2 || (n `mod` 2 /= 0 && isPrime n)`

will help if there are to be many evaluations with even values of n.

### Avoidance of error conditions

edit`&&`

can be used to avoid signalling a run-time error, such as divide-by-zero or index-out-of-bounds, etc. For instance, the following locates the last non-zero element of a list:

```
lastNonZero a = go a (length a-1)
where
go a l | l >= 0 && a !! l == 0 = go a (l-1)
| l < 0 = Nothing
| otherwise = Just (a !! l)
```

Should all elements of the list be zero, the loop will work down to `l = -1`

, and in this case the condition in the first guard will be evaluated without attempting to dereference element -1, which does not exist.

`case` expressions

edit
One control structure we haven't talked about yet is `case`

expressions. They are to piece-wise function definitions what `if`

expressions are to guards. Take this simple piece-wise definition:

```
f 0 = 18
f 1 = 15
f 2 = 12
f x = 12 - x
```

It is equivalent to - and, indeed, syntactic sugar for:

```
f x =
case x of
0 -> 18
1 -> 15
2 -> 12
_ -> 12 - x
```

Whatever definition we pick, the same happens when `f`

is called: The argument `x`

is matched against all of the patterns in order, and on the first match the expression on the right-hand side of the corresponding equal sign (in the piece-wise version) or arrow (in the `case`

version) is evaluated. Note that in this `case`

expression there is no need to write `x`

in the pattern; the wildcard pattern `_`

gives the same effect.^{[2]}

Indentation is important when using `case`

. The cases must be indented further to the right than the beginning of the line containing the `of`

keyword, and all cases must have the same indentation. For the sake of illustration, here are two other valid layouts for a `case`

expression:

```
f x = case x of
0 -> 18
1 -> 15
2 -> 12
_ -> 12 - x
```

```
f x = case x of 0 -> 18
1 -> 15
2 -> 12
_ -> 12 - x
```

Since the left hand side of any case branch is just a pattern, it can also be used for binding, exactly like in piece-wise function definitions:^{[3]}

```
describeString :: String -> String
describeString str =
case str of
(x:xs) -> "The first character of the string is: " ++ [x] ++ "; and " ++
"there are " ++ show (length xs) ++ " more characters in it."
[] -> "This is an empty string."
```

This function describes some properties of `str` using a human-readable string. Using case syntax to bind variables to the head and tail of our list is convenient here, but you could also do this with an if-expression (with a condition of `null str`

to pick the empty string case).

Finally, just like `if`

expressions (and unlike piece-wise definitions), `case`

expressions can be embedded anywhere another expression would fit:

```
data Colour = Black | White | RGB Int Int Int
describeBlackOrWhite :: Colour -> String
describeBlackOrWhite c =
"This colour is"
++ case c of
Black -> " black"
White -> " white"
RGB 0 0 0 -> " black"
RGB 255 255 255 -> " white"
_ -> "... uh... something else"
++ ", yeah?"
```

The case block above fits in as any string would. Writing `describeBlackOrWhite`

this way makes `let`

/`where`

unnecessary (although the resulting definition is not as readable).

Exercises |
---|

Use a `case` expression to implement a `fakeIf` function which could be used as a replacement to the familiar `if` expressions. |

## Controlling actions, revisited

editIn the final part of this chapter, we will introduce a few extra points about control structures while revisiting the discussions in the "Simple input and output" chapter. There, in the Controlling actions section, we used the following function to show how to execute actions conditionally within a `do`

block using `if`

expressions:

```
doGuessing num = do
putStrLn "Enter your guess:"
guess <- getLine
if (read guess) < num
then do putStrLn "Too low!"
doGuessing num
else if (read guess) > num
then do putStrLn "Too high!"
doGuessing num
else putStrLn "You Win!"
```

We can write the same `doGuessing`

function using a ` case`
expression. To do this, we first introduce the Prelude function

`compare`

which takes two values of the same type (in the `Ord`

class) and returns a value of type `Ordering`

— namely one of
`GT`

, `LT`

, `EQ`

, depending on
whether the first is greater than, less than, or equal to the second.
```
doGuessing num = do
putStrLn "Enter your guess:"
guess <- getLine
case compare (read guess) num of
LT -> do putStrLn "Too low!"
doGuessing num
GT -> do putStrLn "Too high!"
doGuessing num
EQ -> putStrLn "You Win!"
```

The ` do`s after the

`->`

s are necessary on the
first two options, because we are sequencing actions within each case.
### A note about `return`

edit
Now, we are going to dispel a possible source of confusion. In a typical imperative
language (C, for example) an implementation of `doGuessing`

might look like the following
(if you don't know C, don't worry with the details, just follow the if-else chain):

```
void doGuessing(int num) {
printf("Enter your guess:");
int guess = atoi(readLine());
if (guess == num) {
printf("You win!\n");
return;
}
// we won't get here if guess == num
if (guess < num) {
printf("Too low!\n");
doGuessing(num);
} else {
printf("Too high!\n");
doGuessing(num);
}
}
```

This `doGuessing`

first tests the equality case, which does not lead to
a new call of `doGuessing`

, and the `if`

has no accompanying
`else`

. If the guess was right, a `return`

statement is used to
exit the function at once, skipping the other cases. Now, going back to Haskell, action
sequencing in `do`

blocks looks a lot like imperative code, and furthermore
there actually *is* a `return`

in Prelude. Then, knowing that `case`

expressions (unlike `if`

expressions) do not force us to cover all cases, one
might be tempted to write a literal translation of the C code above (try running it if
you are curious)...

```
doGuessing num = do
putStrLn "Enter your guess:"
guess <- getLine
case compare (read guess) num of
EQ -> do putStrLn "You win!"
return ()
-- we don't expect to get here if guess == num
if (read guess < num)
then do putStrLn "Too low!"
doGuessing num
else do putStrLn "Too high!"
doGuessing num
```

... but it won't work! If you guess correctly, the function
will first print "You win!," but it *will not exit* at the `return ()`

.
Instead, the program will continue to the `if`

expression and check whether
`guess`

is less than `num`

. Of course it is
not, so the else branch is taken, and it will print "Too high!" and
then ask you to guess again. Things aren't any better with an incorrect guess:
it will try to evaluate the case expression and get either `LT`

or
`GT`

as the result of the `compare`

. In either case,
it won't have a pattern that matches, and the program will fail immediately
with an exception (as usual, the incomplete `case`

alone should be
enough to raise suspicion).

The problem here is that `return`

is not at all equivalent to the
C (or Java etc.) statement with the same name. For our immediate purposes,
we can say that `return`

is a *function*.^{[4]}
The `return ()`

in particular evaluates to an action which does nothing.
`return`

*does not affect the control flow at all*. In the correct guess
case, the case expression evaluates to `return ()`

, an action of type
`IO ()`

, and execution just follows along normally.

The bottom line is that while actions and `do`

blocks resemble imperative
code, they must be dealt with on their own terms - Haskell terms.

Exercises |
---|

- Redo the "Haskell greeting" exercise in Simple input and output/Controlling actions, this time using a
`case` expression. - What does the following program print out? And why?
```
main =
do x <- getX
putStrLn x
getX =
do return "My Shangri-La"
return "beneath"
return "the summer moon"
return "I will"
return "return"
return "again"
``` |

## Notes

- ↑ If you have programmed in C or Java, you will recognize Haskell's if/then/else as an equivalent to the ternary conditional operator
`?:`

. - ↑ To see why this is so, consider our discussion of matching and binding in the Pattern matching section
- ↑ Thus,
`case`

expressions are a lot more versatile than most of the superficially similar switch/case statements in imperative languages which are typically restricted to equality tests on integral primitive types. - ↑
*Superfluous note*: somewhat closer to a proper explanation, we might say`return`

is a function which takes a value and makes it into an action which, when evaluated, gives the original value. A`return "strawberry"`

within one of the`do`

blocks we are dealing with would have type`IO String`

- the same type as`getLine`

. Do not worry if that doesn't make sense for now; you will understand what`return`

really does when we*actually*start discussing monads further ahead on the book.