Let's start off with a very simple problem. We want to let a user input his/her
birth year, and tell him/her his/her age in the year 2020.
Using the function `read`, this is really simple:
```active haskell
main = do
putStrLn "Please enter your birth year"
year <- getLine
putStrLn $ "In 2020, you will be: " ++ show (2020 - read year)
```
If you run that program and type in a valid year, you'll get the right result.
However, what happens when you enter something invalid?
```
Please enter your birth year
hello
main.hs: Prelude.read: no parse
```
The problem is that the user input is coming in as a `String`, and `read` is
trying to parse it into an `Integer`. But not all `String`s are valid
`Integer`s. `read` is what we call a __partial function__, meaning that under
some circumstances it will return an error instead of a valid result.
A more resilient way to write our code is to use the `readMay` function, which
will return a `Maybe Integer` value. This makes it clear with the types
themselves that the parse may succeed or fail. To test this out, try running
the following code:
```active haskell
import Safe (readMay)
main = do
-- We use explicit types to tell the compiler how to try and parse the
-- string.
print (readMay "1980" :: Maybe Integer)
print (readMay "hello" :: Maybe Integer)
print (readMay "2000" :: Maybe Integer)
print (readMay "two-thousand" :: Maybe Integer)
```
So how can we use this to solve our original problem? We need to now determine
if the result of `readMay` was successful (as `Just`) or failed (a `Nothing`).
One way to do this is with pattern matching:
```active haskell
import Safe (readMay)
main = do
putStrLn "Please enter your birth year"
yearString <- getLine
case readMay yearString of
Nothing -> putStrLn "You provided an invalid year"
Just year -> putStrLn $ "In 2020, you will be: " ++ show (2020 - year)
```
## Decoupling code
This code is a bit coupled; let's split it up to have a separate function for
displaying the output to the user, and another separate function for
calculating the age.
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided an invalid year"
Just age -> putStrLn $ "In 2020, you will be: " ++ show age
yearToAge year = 2020 - year
main = do
putStrLn "Please enter your birth year"
yearString <- getLine
let maybeAge =
case readMay yearString of
Nothing -> Nothing
Just year -> Just (yearToAge year)
displayAge maybeAge
```
This code does exactly the same thing as our previous version. But the
definition of `maybeAge` in the `main` function looks pretty repetitive to me.
We check if the parse year is `Nothing`. If it's `Nothing`, we return
`Nothing`. If it's `Just`, we return `Just`, after applying the function
`yearToAge`. That seems like a lot of line noise to do something simple. All we
want is to conditionally apply `yearToAge`.
## Functors
Fortunately, we have a helper function to do just that. `fmap`, or __functor
mapping__, will apply some function over the value contained by a __functor__.
`Maybe` is one example of a functor, another common one is a list. In the case
of `Maybe`, `fmap` does precisely what we described above. So we can replace
our code with:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided an invalid year"
Just age -> putStrLn $ "In 2020, you will be: " ++ show age
yearToAge year = 2020 - year
main = do
putStrLn "Please enter your birth year"
yearString <- getLine
let maybeAge = fmap yearToAge (readMay yearString)
displayAge maybeAge
```
Our code definitely got shorter, and hopefully a bit clearer as well. Now it's
obvious that all we're doing is applying the `yearToAge` function over the
contents of the `Maybe` value.
So what *is* a functor? It's some kind of container of values. In `Maybe`, our
container holds zero or one values. With lists, we have a container for zero or
more values. Some containers are even more exotic; the `IO` functor is actually
providing an action to perform in order to retrieve a value. The only thing
functors share is that they provide some `fmap` function which lets you modify
their contents.
## do-notation
We have another option as well: we can use do-notation. This is the same way
we've been writing our `main` function in so far. That's because- as we
mentioned in the previous paragraph- `IO` is a functor as well. Let's see how
we can change our code to not use `fmap`:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided an invalid year"
Just age -> putStrLn $ "In 2020, you will be: " ++ show age
yearToAge year = 2020 - year
main = do
putStrLn "Please enter your birth year"
yearString <- getLine
let maybeAge = do
yearInteger <- readMay yearString
return $ yearToAge yearInteger
displayAge maybeAge
```
Inside the `do-`block, we have the __slurp operator__ <-. This
operator is special for do-notation, and is used to pull a value out of its
wrapper (in this case, `Maybe`). Once we've extracted the value, we can
manipulate it with normal functions, like `yearToAge`. When we complete our
do-block, we have to return a value wrapped up in that container again. That's
what the `return` function does.
do-notation isn't available for all `Functor`s; it's a special feature reserved
only for `Monad`s. `Monad`s are an extension of `Functor`s that provide a
little extra power. We're not really taking advantage of any of that extra
power here; we'll need to make our program more complicated to demonstrate
it.
## Dealing with two variables
It's kind of limiting that we have a hard-coded year to compare against. Let's
fix that by allowing the user to specify the "future year." We'll start off
with a simple implementation using pattern matching and then move back to do
notation.
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge =
case readMay birthYearString of
Nothing -> Nothing
Just birthYear ->
case readMay futureYearString of
Nothing -> Nothing
Just futureYear -> Just (futureYear - birthYear)
displayAge maybeAge
```
OK, it gets the job done... but it's very tedious. Fortunately, do-notation makes this kind of code really simple:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
birthYear <- readMay birthYearString
futureYear <- readMay futureYearString
return $ yearDiff futureYear birthYear
displayAge maybeAge
```
This is very convenient: we've now slurped our two values in our do-notation.
If either parse returns `Nothing`, then the entire do-block will return
`Nothing`. This demonstrates an important property about `Maybe`: it provides
__short circuiting__.
Without resorting to other helper functions or pattern matching, there's no way
to write this code using just `fmap`. So we've found an example of code that
requires more power than `Functor`s provide, and `Monad`s provide that power.
## Partial application
But maybe there's something else that provides enough power to write our
two-variable code without the full power of `Monad`. To see what this might be,
let's look more carefully at our types.
We're working with two values: `readMay birthYearString` and `readMay
futureYearString`. Both of these values have the type `Maybe Integer`. And we
want to apply the function `yearDiff`, which has the type `Integer -> Integer
-> Integer`.
If we go back to trying to use `fmap`, we'll seemingly run into a bit of a
problem. The type of `fmap`- specialized for `Maybe` and `Integer`- is
`(Integer -> a) -> Maybe Integer -> Maybe a`. In other words, it takes a
function that takes a single argument (an `Integer`) and returns a value of
some type `a`, takes a second argument of a `Maybe Integer`, and gives back a
value of type `Maybe a`. But our function- `yearDiff`- actually takes two
arguments, not one. So `fmap` can't be used at all, right?
Not true actually. This is where one of Haskell's very powerful features comes
into play. Any time we have a function of two arguments, we can also look at is
as a function of one argument which returns a __function__. We can make this
more clear with parentheses:
```haskell
yearDiff :: Integer -> Integer -> Integer
yearDiff :: Integer -> (Integer -> Integer)
```
So how does that help us? We can look at the `fmap` function as:
```haskell
fmap :: (Integer -> (Integer -> Integer))
-> Maybe Integer -> Maybe (Integer -> Integer)
```
Then when we apply `fmap` to `yearDiff`, we end up with:
```haskell
fmap yearDiff :: Maybe Integer -> Maybe (Integer -> Integer)
```
That's pretty cool. We can apply *this* to our `readMay futureYearString` and
end up with:
```haskell
fmap yearDiff (readMay futureYearString) :: Maybe (Integer -> Integer)
```
That's certainly very interesting, but it doesn't help us. We need to somehow
apply this value of type `Maybe (Integer -> Integer)` to our `readMay
birthYearString` of type `Maybe Integer`. We can do this with do-notation:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
yearToAge <- fmap yearDiff (readMay futureYearString)
birthYear <- readMay birthYearString
return $ yearToAge birthYear
displayAge maybeAge
```
We can even use `fmap` twice and avoid the second slurp:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
yearToAge <- fmap yearDiff (readMay futureYearString)
fmap yearToAge (readMay birthYearString)
displayAge maybeAge
```
But we don't have a way to apply our `Maybe (Integer -> Integer)` function to
our `Maybe Integer` directly.
## Applicative functors
And now we get to our final concept: applicative functors. The idea is simple:
we want to be able to apply a function which is *inside* a functor to a value
inside a functor. The magic operator for this is <*>. Let's
see how it works in our example:
```active haskell
import Safe (readMay)
import Control.Applicative ((<*>))
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge =
fmap yearDiff (readMay futureYearString)
<*> readMay birthYearString
displayAge maybeAge
```
In fact, the combination of `fmap` and `<*>` is so common that we have a
special operator, `<$>`, which is a synonym for `fmap`. That means we can make
our code just a little prettier:
```active haskell
import Safe (readMay)
import Control.Applicative ((<$>), (<*>))
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
-- show
let maybeAge = yearDiff
<$> readMay futureYearString
<*> readMay birthYearString
-- /show
displayAge maybeAge
```
Notice the distinction between `<$>` and `<*>`. The former uses a function
which is *not* wrapped in a functor, while the latter applies a function which
is wrapped up.
## So we don't need Monads?
So if we can do such great stuff with functors and applicative functors, why do
we need monads at all? The terse answer is __context sensitivity__: with a
monad, you can make decisions on which processing path to follow based on
previous results. With applicative functors, you have to always apply the same
functions.
Let's give a contrived example: if the future year is less than the birth year,
we'll assume that the user just got confused and entered the values in reverse,
so we'll automatically fix it by reversing the arguments to `yearDiff`. With
do-notation and an if statement, it's easy:
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
futureYear <- readMay futureYearString
birthYear <- readMay birthYearString
return $
if futureYear < birthYear
then yearDiff birthYear futureYear
else yearDiff futureYear birthYear
displayAge maybeAge
```
## Exercises
1. Implement `fmap` using `<*>` and `return`.
```active haskell
import Control.Applicative ((<*>), Applicative)
import Prelude (return, Monad)
import qualified Prelude
fmap :: (Applicative m, Monad m) => (a -> b) -> (m a -> m b)
-- show
fmap ... ... = FIXME
-- /show
main =
case fmap (Prelude.+ 1) (Prelude.Just 2) of
Prelude.Just 3 -> Prelude.putStrLn "Good job!"
_ -> Prelude.putStrLn "Try again"
```
@@@SHOW SOLUTION
```active haskell
import Control.Applicative ((<*>))
-- show
myFmap function wrappedValue = return function <*> wrappedValue
main = print $ myFmap (+ 1) $ Just 5
-- /show
```
@@@
2. How is `return` implemented for the `Maybe` monad? Try replacing `return`
with its implementation in the code above.
```haskell active
-- show
returnMaybe = FIXME
-- /show
main
| returnMaybe "Hello" == Just "Hello" = putStrLn "Correct!"
| otherwise = putStrLn "Incorrect, please try again"
```
@@@SHOW SOLUTION
`return` is simply the `Just` constructor. This gets defined as:
```haskell
instance Monad Maybe where
return = Just
```
@@@
3. `yearDiff` is really just subtraction. Try to replace the calls to
`yearDiff` with explicit usage of the `-` operator.
```haskell active
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
futureYear <- readMay futureYearString
birthYear <- readMay birthYearString
return $
-- show
if futureYear < birthYear
then yearDiff birthYear futureYear
else yearDiff futureYear birthYear
-- /show
displayAge maybeAge
```
@@@SHOW SOLUTION
```haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
futureYear <- readMay futureYearString
birthYear <- readMay birthYearString
return $
-- show
if futureYear < birthYear
then birthYear - futureYear
else futureYear - birthYear
-- /show
displayAge maybeAge
```
@@@
4. It's possible to write an applicative functor version of the
auto-reverse-arguments code by modifying the `yearDiff` function. Try to do
so.
```active haskell
import Safe (readMay)
import Control.Applicative ((<$>), (<*>))
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
-- show
yearDiff futureYear birthYear = FIXME
-- /show
main
| yearDiff 5 6 == 1 = putStrLn "Correct!"
| otherwise = putStrLn "Please try again"
```
@@@ SHOW SOLUTION
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
-- show
yearDiff futureYear birthYear
| futureYear > birthYear = futureYear - birthYear
| otherwise = birthYear - futureYear
-- /show
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
futureYear <- readMay futureYearString
birthYear <- readMay birthYearString
return $
if futureYear < birthYear
then yearDiff birthYear futureYear
else yearDiff futureYear birthYear
displayAge maybeAge
```
@@@
* Now try to do it without modifying `yearDiff` directly, but by using a
helper function which is applied to `yearDiff`.
```active haskell
import Safe (readMay)
import Control.Applicative ((<$>), (<*>))
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
-- show
yourHelperFunction f ...
-- /show
main
| yourHelperFunction yearDiff 5 6 == 1 = putStrLn "Correct!"
| otherwise = putStrLn "Please try again"
```
@@@ SHOW SOLUTION
```active haskell
import Safe (readMay)
displayAge maybeAge =
case maybeAge of
Nothing -> putStrLn "You provided invalid input"
Just age -> putStrLn $ "In that year, you will be: " ++ show age
yearDiff futureYear birthYear = futureYear - birthYear
main = do
putStrLn "Please enter your birth year"
birthYearString <- getLine
putStrLn "Please enter some year in the future"
futureYearString <- getLine
let maybeAge = do
futureYear <- readMay futureYearString
birthYear <- readMay birthYearString
return $
if futureYear < birthYear
then yourHelperFunction yearDiff birthYear futureYear
else yourHelperFunction yearDiff futureYear birthYear
displayAge maybeAge
-- show
yourHelperFunction f x y
| x > y = f x y
| otherwise = f y x
-- /show
```
@@@