-- Lecture 2A Part II.  Back to Lists

data Suit = Hearts | Diamonds | Clubs | Spades            
    deriving (Eq,Show)
    
data Rank =   Numeric Int  | Jack | Queen | King | Ace
  deriving (Eq,Show)

data Card = Card Rank Suit
  deriving (Eq,Show)

rank :: Card -> Rank 
rank (Card r _) = r

suit :: Card -> Suit
suit (Card _ s) = s

type Hand = [Card]

----------------------------
-- example card
oneEye :: Card
oneEye = Card King Diamonds

-- Building lists with list comprehensions

suits = [Hearts, Diamonds, Clubs, Spades]

allKings :: Hand
allKings = [ Card King s | s <- suits ]


allClubs :: Hand -> Hand
-- allClubs h = [ c | c <- h, suit c == Clubs]
allClubs h = select Clubs h

allSpades :: Hand -> Hand
-- allSpades h = [ c | c <- h, suit c == Spades]
allSpades h = select Spades h

-- select all the cards from the hand of the given suit.
select :: Suit -> Hand -> Hand
select s h = [ c | c <- h, suit c == s]

------------------------------------------
-- Programming with lists using (:) and [],
-- the basic building blocks for lists

-- Prelude functions null, head and tail

null' [] = True
null' _  = False

head' (x:_)  = x

tail' (_:xs) = xs

third (_:_:x:_) = x

last' xs = head (reverse xs)


-- polymorphic types

------------------------------------------
-- Recall recursion:
fac 0         = 1
fac n | n > 0 = n * fac (n-1)

-- example: how to compute fac 3 using these rules
-- by hand (and put in a list so you can check it)
example = [ fac 3              
          , 3 * fac 2         
          , 3 * 2 * fac 1
          , 3 * 2 * 1 * fac 0
          , 3 * 2 * 1 * 1
          , 6
          ]
-- 


-- length (called size in lab2)
size []     = 0
size (x:xs) = 1 + size xs

{- size [8,9] 
 = size (8:9:[]) 
 = 1 + size (9:[]) 
 = 1 + 1 + size [] 
 = 1 + 1 + 0 
 = 2
 -}

hasOne [_] = True
hasOne _   = False


-- sum (add all the elements in a list)

-- Two argument functions

-- append

-- reverse

-- index (!!)