Info on typeclasses and types

haskell.html.markdown

@@ -293,7 +293,13 @@ foldr (\x y -> 2*x + y) 4 [1,2,3] -- 16
 -- 7. Data Types
 ----------------------------------------------------
 
--- Here's how you make your own data type in Haskell
+-- A data type is declared with a 'type constructor' on the left
+-- and one or more 'data constructors' on the right, separated by
+-- the pipe | symbol. This is a sum/union type. Each data constructor
+-- is a (possibly nullary) function that creates an object of the type
+-- named by the type constructor.
+
+-- This is essentially an enum
 
 data Color = Red | Blue | Green
 
@@ -304,7 +310,57 @@ say Red   = "You are Red!"
 say Blue  = "You are Blue!"
 say Green = "You are Green!"
 
--- Your data types can have parameters too:
+-- Note that the type constructor is used in the type signature
+-- and the data constructors are used in the body of the function
+-- Data constructors are primarily pattern-matched against
+
+-- This next one is a traditional container type holding two fields
+-- In a type declaration, data constructors take types as parameters
+-- Data constructors can have the same name as type constructors
+-- This is common where the type only has a single data constructor
+
+data Point = Point Float Float
+
+-- This can be used in a function like:
+
+distance :: Point -> Point -> Float
+distance (Point x y) (Point x' y') = sqrt $ dx + dy
+    where dx = (x - x') ** 2
+          dy = (y - y') ** 2
+          
+-- Types can have multiple data constructors with arguments, too
+
+data Name = Mononym String | FirstLastName String String | FullName String String String
+
+-- To make things clearer we can use record syntax
+
+data Point2D = CartesianPoint2D { x :: Float, y :: Float } | PolarPoint2D { r :: Float, theta :: Float }
+
+myPoint = CartesianPoint2D { x = 7.0, y = 10.0 }
+
+-- Using record syntax automatically creates accessor functions (the name of the field)
+
+xOfMyPoint = x myPoint
+
+-- xOfMyPoint is equal to 7.0
+
+-- Record syntax also allows a simple form of update
+
+myPoint' = myPoint { x = 9.0 }
+
+-- myPoint' is CartesianPoint2D { x = 9.0, y = 10.0 }
+
+-- Even if a type is defined with record syntax, it can be declared like
+-- a simple data constructor. This is fine:
+
+myPoint'2 = CartesianPoint2D 3.3 4.0
+
+-- It's also useful to pattern match data constructors in `case` expressions
+
+distanceFromOrigin x = case x of (CartesianPoint2D x y) -> sqrt $ x ** 2 + y ** 2
+                                 (PolarPoint2D r _) -> r
+
+-- Your data types can have type parameters too:
 
 data Maybe a = Nothing | Just a
 
@@ -313,8 +369,93 @@ Just "hello"    -- of type `Maybe String`
 Just 1          -- of type `Maybe Int`
 Nothing         -- of type `Maybe a` for any `a`
 
+-- For convenience we can also create type synonyms with the 'type' keyword
+
+type String = [Char]
+
+-- Unlike `data` types, type synonyms need no constructor, and can be used 
+-- anywhere a synonymous data type could be used. Say we have the 
+-- following type synonyms and items with the following type signatures
+
+type Weight = Float
+type Height = Float
+type Point = (Float, Float)
+getMyHeightAndWeight :: Person -> (Height, Weight)
+findCenter :: Circle -> Point
+somePerson :: Person
+someCircle :: Circle
+distance :: Point -> Point -> Float
+
+-- The following would compile and run without issue, even though it does not make
+-- sense semantically, because the type synonyms reduce to the same base types
+
+distance (getMyHeightAndWeight somePerson) (findCenter someCircle)
+
 ----------------------------------------------------
--- 8. Haskell IO
+-- 8. Typeclasses
+----------------------------------------------------
+
+-- Typeclasses are one way Haskell does polymorphism
+-- They are similar to interfaces in other languages
+-- A typeclass defines a set of functions that must work on any type that is in
+-- that typeclass.
+
+-- The Eq typeclass is for types whose instances can be tested for equality with one another
+
+class Eq a where  
+    (==) :: a -> a -> Bool  
+    (/=) :: a -> a -> Bool  
+    x == y = not (x /= y)  
+    x /= y = not (x == y)
+    
+-- This defines a typeclass that requires two functions, (==) and (/=)
+-- It also declares that one function can be declared in terms of another
+-- So it is enough that *either* the (==) function or the (/=) is defined
+-- And the other will be 'filled in' based on the typeclass definition
+
+-- To make a type a member of a type class, the instance keyword is used
+
+instance Eq TrafficLight where  
+    Red == Red = True  
+    Green == Green = True  
+    Yellow == Yellow = True  
+    _ == _ = False 
+    
+-- Now we can use (==) and (/=) with TrafficLight objects
+
+canProceedThrough :: TrafficLight -> Bool
+canProceedThrough t = t /= Red
+
+-- You can NOT create an instance definition for a type synonym
+
+-- Functions can be written to take typeclasses with type parameters, rather than types,
+-- assuming that the function only relies on features of the typeclass
+
+isEqual (Eq a) => a -> a -> Bool
+isEqual x y = x == y
+
+-- Note that x and y MUST be the same type, as they are both defined as being of type parameter 'a'
+-- A typeclass does state that different types in the typeclass can be mixed together
+-- So `isEqual Red 2` is invalid, even though 2 is an Int which is an instance of Eq, and Red is
+-- a TrafficLight which is also an instance of Eq
+
+-- Other common typeclasses are:
+-- Ord for types that can be ordered, allowing you to use >, <=, etc.
+-- Read for types that can be created from a string representation
+-- Show for types that can be converted to a string for display
+-- Num, Real, Integral, Fractional for types that can do mathematical calculation
+-- Enum for types that can be stepped through
+-- Bounded for types with a maximum and minimum
+
+-- Haskell can automatically make types part of Eq, Ord, Read, Show, Enum, and Bounded
+-- with the `deriving` keyword at the end of the type declaration
+
+data Point = Point Float Float deriving (Eq, Read, Show)
+    
+-- In this case it is NOT necessary to create an 'instance' definition
+
+----------------------------------------------------
+-- 9. Haskell IO
 ----------------------------------------------------
 
 -- While IO can't be explained fully without explaining monads,
@@ -395,7 +536,7 @@ main'' = do
 
 
 ----------------------------------------------------
--- 9. The Haskell REPL
+-- 10. The Haskell REPL
 ----------------------------------------------------
 
 -- Start the repl by typing `ghci`.