FP101x - week 2 Types and Classes

Type Error

> 1+ False
Error

Type in Haskell

• (expression)e :: (type)t

:type in GHCi

> not False
True

• calculates the type of an expression

> :type not False
not False :: Bool

Basic Types

• Bool
• Char
• String
• Int
• Integer
• Float

List Types

• sequence of value of the same type
• [False, Trye, False] :: [Bool]
• [‘a’, ‘b’, ‘c’ ] :: [Char]
• [[‘a’], [‘b’, ‘c’]] :: [‘Char’]

Tuple Types

• A tuple is a sequence of values of different types
• (False, Ture) :: (Bool, Bool)
• (False, ‘a’, True) :: (Bool, Char, Bool)

Function Types

• not :: Bool -> Bool
• isDigit :: Char -> Bool — 0, 1
• argument and resist types are unrestricted

Curried Functions

• functions as results

• add’ :: Int -> (Int -> Int) add’ x y = x+y

• more flexible then functions on tuples

• associate to the left mult x y z means (((mult x) y) z)

Polymorphic Fuctions

• a function is called polymorphic (“of many forms”) if its type contains one or more type variables.
• length :: [a] -> Int

ex )

> length [False, True]
2
> length [1,2,3,4]
4

• fst :: (a,b) -> a
• head :: [a] -> a
• take :: Int -> [a] -> [a]
• zip :: [a] -> [b] -> [(a,b)]
• id :: a -> a

Overloaded Functions

• a polymorphic function is called overloaded of its type contains one or more class contains
• sum :: Num a => [a] -> a

ex)

> sum [1,2,3]
6
> sum [‘a’,’b’,’c’]
ERROR

Haskell has a number of type classes

• Num : Numeric types
• Eq : Equality types
• Ord : Ordered types

ex )

• (+) :: Num a => a -> a -> a
• (==) :: Eq a => a -> a -> Bool
• (<) :: Ord a => a -> a -> Bool