203 lines
5 KiB
Haskell
203 lines
5 KiB
Haskell
{- Contents
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A short integerroduction to Haskell;
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On how to create simple functions.
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-}
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-----------------------------------------------------------
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-- Elementary Functions
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-----------------------------------------------------------
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{- General Syntax for functions
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* Input on the left, output on the right.
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* Functions also have a type: input type on the left
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side, output type on the right side, arrow inbetween.
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-}
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inc1 :: Integer -> Integer
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inc1 n = n + 1
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{- Lambda notation
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Everything can also be written on the right side (lambda
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notation). In fact, `inc1` is just syntactic sugar for
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`inc2`.
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-}
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inc2 :: Integer -> Integer
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inc2 = \n -> n + 1
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{- Function application
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To apply a function, write the function to the left of
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the input/argument (no brackets needed).
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-}
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two :: Integer
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two = inc1 1
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someGreeting :: String -> String
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someGreeting person = "Hello " ++ person
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{- Exercise
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Define a function `square`, that squares the given input
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and write down its type. Define the same function using
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the lambda notation.
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-}
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square :: Integer -> Integer
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square x = x * x
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-----------------------------------------------------------
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-- Functions of Several Variables
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-----------------------------------------------------------
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{- Tupled Inputs
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'addTupled' is binary function, its output depends on
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two separate integers.
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-}
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addTupled :: (Integer, Integer) -> Integer
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addTupled (x, y) = x + y
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{-
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'avg3Tupled' is a function that depends on three input
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variables.
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-}
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avg3Tupled :: (Float, Float, Float) -> Float
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avg3Tupled ( x, y, z ) = (x + y + z) / 3
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{- Evaluating with Tuples
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We evaluate a function of several variables by providing
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values *for each* input variabele.
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-}
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four :: Float
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four = avg3Tupled ( 3, 4, 5 )
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{-
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If we want to evaluate a multivariable function before
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we have all inputs ready, we have to properly
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parametrize it. We can do this with curried functions.
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More on that later!
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-}
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{- A Curried Function
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'add' is the parametrized (a.k.a curried) version of
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`add`. It is a function that returns a (unary) function.
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Note that the following three lines are equivalent
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declarations:
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'add = \x -> \y -> x + y'
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'add x = \y -> x + y'
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'add x y = x + y'
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Also note that the parenthesis are not needed in the
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declaration of the type of 'add'.
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-}
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add :: Int -> (Int -> Int)
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add n m = n + m
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{- Partial Application
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'add3' is the function that adds '3' to any given input.
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Thanks to currying, we can realize 'add3' as a special
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case of 'add'. Thanks to partial application, this
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corresponds to a single function call.
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-}
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add3 :: Int -> Int
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add3 = add 3
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{- Exercise
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Declare a curried version of the function 'avg3Tupled'
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as a lambda term.
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-}
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avg3 :: Float -> Float -> Float -> Float
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-- avg3 x y z = (x + y + z) / 3
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-- avg3 x y = \ z -> (x + y + z) / 3
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-- avg3 x = \y z -> (x + y + z) /3
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avg3 = \x -> \y -> \z -> (x + y + z) / 3
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{- Exercise
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use the binary function '(++)' that concatenates strings
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to specify a function that prepends "=> " to any given
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input string. Use partial application
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-}
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prepArrow :: String -> String
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prepArrow = (++) "=> "
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-----------------------------------------------------------
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-- Higher Order Functions
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-----------------------------------------------------------
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{- Function as Input
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'apply' is a function that accepts a function as input
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(and applies it to the remaining input)
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-}
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apply :: (a -> b) -> a -> b
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apply f x = f x
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{- Function as Input and Output
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'twice' is a function that accepts and returns a
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function.
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-}
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twice :: (a -> a) -> (a -> a)
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twice f x = f (f x)
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-- twice = f . f
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{- Exercise
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Write a function `thrice` that applies a function three
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times.
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-}
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thrice :: (a -> a) -> a -> a
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thrice f x = f (twice f x)
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-- thrice f = f . f . f
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{- Exercise
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Write a function 'compose' that accepts two functions
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and applies them to a given argument in order.
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-}
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compose :: (a -> b) -> (b -> c) -> a -> c
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compose f g x = g (f x)
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{- Exercise
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reimplement 'twice' and 'thrice' with as an application
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of the function 'compose'.
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-}
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twiceByComp :: (a -> a) -> a -> a
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twiceByComp f = compose f f
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thriceByComp :: (a -> a) -> a -> a
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thriceByComp f = compose f (twiceByComp f)
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{- List map
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A often used higher function is ``mapping'' of lists.
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This function will apply a function (given as an
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argument) to every element in a list (also given as an
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argument) and return a new list containig the changed
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values. There are a lot of other functions to work
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with lists (and similar types). We will learn about
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these functions later.
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-}
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mapping :: [Integer]
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mapping = map (\n -> n + 1) [1, 2, 3]
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{-| Exercise
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greet all friends using 'friends', 'map' and
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'greeting'.
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-}
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friends :: [String]
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friends =
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[ "Peter"
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, "Nina"
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, "Janosh"
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, "Reto"
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, "Adal"
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, "Sara"
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]
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greeting :: String -> String
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greeting person = "Hello " ++ person
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greetFriends :: [String]
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greetFriends = map greeting friends
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