import Shape
len :: [a] -> Int
len [] = 0
len (x:xs) = 1 + len xs
tag1 x = (1,x)
-- Parameterized datatypes
data Option a = NONE | SOME a
pos :: Eq a => a -> [a] -> Option Int
pos a l =
 let find a [] n = NONE
 find a (x:xs) n =
 if a==x
 then SOME n
 else find a xs (n+1)
 in find a l 0
-- multiple parameterized datatypes
data Pair a b = Pair (a,b)
data Pair2 a b = Pair2 a b
-- Recursive datatypes
data Mylist a = Nil
 | Cons (a,Mylist a)
-- Recursive datatypes with multiple parameters
data Twolist a b = Twonil
 | Acons (a,Twolist a b)
 | Bcons (b,Twolist a b)
append2 Twonil ys = ys
append2 (Acons(a,xs)) ys = Acons(a,append2 xs ys)
append2 (Bcons(b,xs)) ys = Bcons(b,append2 xs ys)
rev2 Twonil = Twonil
rev2 (Acons(a,t)) = append2 (rev2 t) (Acons(a,Twonil))
rev2 (Bcons(b,t)) = append2 (rev2 t) (Bcons(b,Twonil))
-- Recursive datatypes with no parameters
data Nat = Zero | Succ Nat
 deriving Show
toNat 0 = Zero
toNat n = Succ(toNat (n-1))
-- Functions with functions as parameters
mymap f [] = []
mymap f (x:xs) = (f x):(mymap f xs)
myfoldr op e [] = e
myfoldr op e (x:xs) =
 op x (myfoldr op e xs)
-- Polymorphism from functions as arguments
applyTwice f x = f(f x)
z f x y = (f x, f y)
concat1 :: [[a]] -> [a]
concat1 = foldr (++) []
concat2 :: [[a]] -> [a]
concat2 = foldl (++) []
-----------------------------------------------------------
-- Perimiters of Shapes
-----------------------------------------------------------
perimeter :: Shape -> Float
perimeter (Rectangle s1 s2) = 2*(s1+s2)
perimeter (RtTriangle s1 s2) = s1 + s2 + sqrt(s1^2+s2^2)
perimeter (Polygon pts) = foldl (+) 0 (sides pts)
perimeter (Ellipse r1 r2)
 | r1> r2 = ellipsePerim r1 r2
 | otherwise = ellipsePerim r2 r1
 where ellipsePerim r1 r2
 = let e = sqrt (r1^2 - r2^2) / r1
 s = scanl aux (0.25*e^2)
 (map intToFloat [2..])
 aux s i = nextEl e s i
 test x = x> epsilon
 sSum = foldl (+) 0 (takeWhile test s)
 in 2*r1*pi*(1 - sSum)
sides :: [Vertex] -> [Side]
sides [] = []
sides (p:pts) = aux (p:pts)
 where aux (p1:p2:pts) = (distBetween p1 p2) : (aux (p2:pts))
 aux (pn:[]) = distBetween pn p : []
sides2 :: [Vertex] -> [Side]
sides2 pts = zipWith distBetween pts
 (tail pts ++ [head pts])
nextEl:: Float -> Float -> Float -> Float
nextEl e s i = s*(2*i-1)*(2*i-3)*(e^2) / (4*i^2)
epsilon :: Float
epsilon = 0.00001
intToFloat :: Int -> Float
intToFloat n = fromInteger (toInteger n)
--