Why Functions Are Values
The first great Haskell idea: functions can be named, stored, passed around and composed like any other value.
In many languages, a function first appears as a named block of instructions. Haskell invites a more powerful picture: a function is a value. It can be passed to another function, returned as a result and placed inside a data structure.
A higher-order function accepts another function as an argument, returns one as its result, or does both.
A small transformation
double :: Int -> Int
double x = x * 2
numbers :: [Int]
numbers = [1, 2, 3, 4]
result :: [Int]
result = map double numbersThe expression map double numbers does not call double just once. It hands the function itself to map, which applies it to every element.
Anonymous functions
When a transformation is tiny, we can write it directly as a lambda expression.
map (\x -> x * 2) [1, 2, 3, 4]
-- [2, 4, 6, 8]The backslash resembles the Greek letter λ. Lambda calculus uses λ to mean “construct a function.”
Composition
shout :: String -> String
shout = (++ "!")
announceLength :: String -> String
announceLength = shout . show . length
announceLength "Haskell"
-- "7!"Composition lets the output of one function become the input of the next. Read shout . show . length from right to left.
Predict the result of map ((+ 1) . (* 2)) [1, 2, 3] before evaluating it.
Reveal solution
Each number is doubled and then incremented, producing [3, 5, 7].