Maybe Another Way of Error Handling ...

Errors!

Throw exceptions!

That seems simple, but is it? Let’s define a simple function with some boundary conditions. For example, division is undefined if the denominator is 0.

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// calculate a/b
double safeDiv(double a, double b) {
    if (b == 0.0) {
        throw runtime_error("Exception: Denominator Cannot be 0.")
    }
    return a / b;
}

What’s wrong with this function? At the very first line, we defined safeDiv as a mapping take takes two double and returns a double. But when the function throw a runtime error, does it return a double? Then, out function header is lying to us!

As a careful programmer, we always want out function to be honest. In a program, the type of a function should indicate what the function does.

Maybe it Returns a …

Let’s stay on the example of safeDiv. Since the denominator cannot be 0 if we get a 0 for the denominator but cannot throw an exception, what should we do? In this case, the return value cannot be a double neither.

Actually, we say the safe division maybe returns a double, or nothing.

  • if the denominator is 0, safeDiv returns Nothing,
  • otherwise, it returns just the division.

That is,

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safeDiv :: Double -> Double -> Maybe Double
safeDiv _ 0 = Nothing
safeDiv a b = Just (a / b)

it returns

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*Main> safeDiv 1 4
Just 0.25
*Main> safeDiv 3 0
Nothing

which is exactly what the type signature tells us!

This idea words on more generic function too. For example, when we want the head of an empty list, there would be an error

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Prelude> head []
*** Exception: Prelude.head: empty list

We can define a safeHead function to solve this problem,

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safeHead :: [a] -> Maybe a
safeHead [] = Nothing
safeHead (x : _) = Just x

our we can just use the Prelude head

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safeHead :: [a] -> Maybe a
safeHead [] = Nothing
safeHead xs = Just (head xs)

this will give us 

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*Main> safeHead [1..5]
Just 1
*Main> safeHead []
Nothing

Composition with Error

Function composition is the highest call in functional programming. For example, if we want to convert a division result to string

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*Main> show (5/3)
"1.6666666666666667"
*Main> show (5/0)
"Infinity"

The type signature of show is

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show :: Show a => a -> String

and if we compose it with show with our safeDiv

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*Main> show $ safeDiv 5 0
"Nothing"
*Main> show $ safeDiv 5 3
"Just 1.6666666666666667"

we will need another parser to extract the division result.

In a simple way, we may define a safeShow to solve this problem.

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safeShow :: Maybe Double -> String
safeShow Nothing = ""
safeShow (Just a) = show a
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*Main> safeShow $ safeDiv 5 3
"1.6666666666666667"
*Main> safeShow $ safeDiv 5 0
""

But our safeShow only handles the Maybe Double type. We cannot compose it with other type functions, which contradicts the idea of function reusability.

Ideally, we want to keep show‘s generic type in our safeShow, while extracting the result easily and quickly.

To solve these two problems, we may define safeShow as

  • if safeShow receives nothing, it returns nothing
  • otherwise it returns just the show of the value

We introduce the >>= bind operator. Let’s see how it works. First, we can define the safeShow as we want: it takes any showable type and the return type maybe is string.

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safeShow :: Show a => a -> Maybe String
safeShow = Just . show

Then we can try in ghci

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*Main> safeDiv 5 1 >>= safeShow
Just "5.0"
*Main> safeDiv 5 0 >>= safeShow
Nothing
*Main> safeHead [1..5] >>= safeShow
Just "1"
*Main> safeHead [] >>= safeShow
Nothing

>>= is the composition operator of functions that return a Maybe type! What’s its type in this case?

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

This function takes two inputs

  • Maybe a as the output of our other safe* functions;
  • a function that map a to Maybe b type.

The actual type of >>= is

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

You may wonder what is Monad m, and as mentioned before in type signature of show, Show a.We said Show a means “showable” type.In fact, the keywords Monad and Show are type class.Visit blog post “Types! What are They?”.

We said >>= is a composition operator,but why it does not take two functions?If you are interested in that,visit blog post “Object Oriented Mathematics !?”.

For more information,visit A Fistful of Monads.