Type

A collection of related values.

Type Error

Applying a function to arguments with the wrong types.

• Found at compile time
  • Safe
  • Fast

Type Inference

• Every well-formed expression has a type
• Type can be automatically calculated at compile time

Basic Types

Bool
Char
String     -- A list of Char
Int        -- Fixed-precision
Integer    -- Arbitrary-precision
Float

Other Types

List

• A sequence of values of the same type
• No information about the length

Tuple

• A sequence of values of the different types
• Encodes information about the size

Function

• A mapping from a value to another

Curried Function

• Functions that take arguments one at a time
• Useful functions can be made by partially applying a curried function
• Currying conventions
  • Arrow -> associates to the right
  • Function applications associate to the left

add' :: Int -> Int -> Int     -- Right associative
add' x y = x + y              -- add' x = \y -> x + y

-- Compared to
add :: (Int, Int) -> Int
add x y = x + y

Polymorphic Function

• Type contains one or more type variables
  • Must begin with a lower-case letter, usually named a, b, c, etc.

length [a] -> Int

Overloaded Function

• Type contains one or more class constraints

Num
Eq
Ord

Example:

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