Solve exercise 2

Exercises/exercise-2/Solution.hs

@@ -0,0 +1,205 @@
+import Data.List (sort)
+
+--------------------
+-- Exercise 1
+--------------------
+data Car = Car
+ { model :: Model
+ , make :: Make
+ , year :: Integer
+ , color :: Color
+ , power :: Horsepower
+ } deriving (Show, Eq, Ord)
+
+----------
+-- a)
+----------
+
+newtype Model = Model String
+    deriving (Show, Eq, Ord)
+
+newtype Make = Make String
+    deriving (Show, Eq, Ord)
+
+data Color = RGB
+    { r :: Integer
+    , g :: Integer
+    , b :: Integer
+    } deriving (Show, Eq, Ord)
+
+type Horsepower = Integer
+
+----------
+-- b)
+----------
+ford = Car {
+    make = Make "Ford",
+    model = Model "Fiesta",
+    color = RGB {
+        r = 0xFF,
+        g = 0x00,
+        b = 0x00
+    },
+    power = 70,
+    year = 2017
+}
+
+ferrari = Car {
+    make = Make "Ferrari",
+    model = Model "Testarossa",
+    color = RGB 0x00 0xFF 0x00,
+    power = 27,
+    year = 1991
+}
+
+zoe = Car {
+    make = Make "Renault",
+    model = Model "Zoe",
+    color = RGB 0xFF 0xFF 0xFF,
+    power = 70,
+    year = 2023
+}
+
+sorted = sort [zoe, ferrari, ford]
+-- >>> sorted
+-- [Car {model = Model "Fiesta", make = Make "Ford", year = 2017, color = RGB {r = 255, g = 0, b = 0}, power = 70},Car {model = Model "Testarossa", make = Make "Ferrari", year = 1991, color = RGB {r = 0, g = 255, b = 0}, power = 27},Car {model = Model "Zoe", make = Make "Renault", year = 2023, color = RGB {r = 255, g = 255, b = 255}, power = 70}]
+
+--------------------
+-- Exercise 2
+--------------------
+data Tree a
+    = Node (Tree a) a (Tree a)
+    | Leaf a
+
+----------
+-- a)
+----------
+collect :: Tree a -> [a]
+collect x =
+    case x of
+        Node a b c -> [b] ++ concat (map collect [a, c])
+        Leaf a -> [a]
+
+----------
+-- b)
+----------
+data PolyTree a =
+    PolyTree a [PolyTree a]
+    deriving (Show)
+
+----------
+-- c)
+----------
+tree =
+    PolyTree 1 [
+        PolyTree 2 [
+            PolyTree 5 [],
+            PolyTree 6 [],
+            PolyTree 7 []
+        ],
+        PolyTree 3 [
+            PolyTree 8 []
+        ]
+    ]
+
+-- >>> show tree
+-- "PolyTree 1 [PolyTree 2 [PolyTree 5 [],PolyTree 6 [],PolyTree 7 []],PolyTree 3 [PolyTree 8 []]]"
+
+--------------------
+-- Exercise 3
+--------------------
+data NatNumber =
+    Z
+    | S NatNumber
+    deriving (Show)
+
+eval :: NatNumber -> Integer
+eval x =
+    case x of
+        Z -> 0
+        S a -> 1 + eval a
+
+-- >>> Z
+-- Z
+-- >>> eval (S (S (S Z)))
+-- 3
+
+uneval :: Integer -> NatNumber
+uneval x
+    | x < 0 = error "negative numbers are not natural numbers"
+    | x == 0 = Z
+    | otherwise = S (uneval (x - 1))
+
+-- >>> uneval (-1)
+-- negative numbers are not natural numbers
+-- >>> uneval 0
+-- Z
+-- >>> uneval 1
+-- S Z
+-- >>> uneval 3
+-- S (S (S Z))
+
+addNat :: NatNumber -> NatNumber -> NatNumber
+addNat a b =
+    case (a, b) of
+        (Z, b) -> b
+        (S a, b) -> S (addNat a b)
+
+-- >>> eval (addNat (uneval 7) (uneval 2))
+-- 9
+
+mulNat :: NatNumber -> NatNumber -> NatNumber
+mulNat a b =
+    case (a, b) of
+        (Z, b) -> Z
+        (S a, b) -> addNat (mulNat a b) b
+
+-- >>> eval (mulNat (uneval 3) (uneval 2))
+-- 6
+
+fact :: NatNumber -> NatNumber
+fact x =
+    case x of
+        Z -> S Z
+        S a -> mulNat (S a) (fact a)
+
+-- >>> eval (fact Z)
+-- 1
+-- >>> eval (fact (S (S Z)))
+-- 2
+
+--------------------
+-- Exercise 3
+--------------------
+type Program = [(Integer, Integer)]
+type Input = Integer
+type Output = [Integer]
+
+execute :: Program -> Input -> Output
+execute program input =
+    reverse (internal program input [])
+    where
+        internal :: Program -> Input -> Output -> Output
+        internal [] input output = input:output
+
+        internal ((a,b):coefficients) input output
+            | mod (input * a) b == 0 =
+                internal program (div (input * a) b) (input:output)
+            | otherwise = internal coefficients input output
+
+fibProgram :: Program
+fibProgram =
+    [ (91,33)
+    , (11,13)
+    , (1,11)
+    , (399,34)
+    , (17,19)
+    , (1,17)
+    , (2,7)
+    , (187,5)
+    , (1,3)
+    ]
+
+-- Should evaluate to True
+-- >>> sum (execute fibProgram 31250) == 26183978971946924
+-- True