Completed chapter5, minus final exercise

Author: kvsm

chapter5/src/exercises.purs

@@ -1,6 +1,9 @@
 module Exercises where
 
 import Prelude
+import Data.Maybe (Maybe(Just, Nothing))
+import Data.Picture (Point(..), Shape(..))
+import Math (pow, pi)
 
 -- Not stack safe (crashes with large inputs).
 factorial' :: Int -> Int
@@ -14,12 +17,55 @@ factorial n = fact' n 0 where
   fact' 0 acc = acc
   fact' n acc = fact' (n - 1) (acc + n)
 
--- This is not stack safe - due to double recursion tail call optimisation
--- is not possible. Although the exercise asks us to implement this algorithm
--- specifically, an entirely different approach would be required to make this
--- function safe.
+{-
+  This is not stack safe - due to double recursion tail call optimisation
+  is not possible. Although the exercise asks us to implement this algorithm
+  specifically, an entirely different approach would be required to make this
+  function safe.
+-}
 binomial :: Int -> Int -> Int
 binomial 0 n = 1
 binomial k 0 = 0
 binomial k n  | k == n    = 1
               | otherwise = (binomial (k - 1) (n - 1)) + (binomial k (n - 1))
+
+-- Pattern matching on records.
+type Address = { street :: String, city :: String }
+type Person = { name :: String, address :: Address }
+
+sameCity :: Person -> Person -> Boolean
+sameCity { address: { city: x }} { address: { city: y }}
+  | x == y    = true
+  | otherwise = false
+
+-- Pattern matching on arrays.
+fromSingleton :: forall a. a -> Array a -> a
+fromSingleton d [x] = x
+fromSingleton d _ = d
+
+-- Algebraic Data Types.
+origin :: Point
+origin = Point { x: 0.0, y: 0.0 }
+
+myCircle :: Shape
+myCircle = Circle origin 10.0
+
+scaleAndCentre :: Shape -> Shape
+scaleAndCentre (Circle _ r) = Circle origin (r * 2.0)
+scaleAndCentre (Rectangle _ w h) = Rectangle origin (w * 2.0) (h * 2.0)
+scaleAndCentre (Line (Point start) (Point end)) = Line transformStart transformEnd where
+  xdiff           = start.x - end.x
+  ydiff           = start.y - end.y
+  transformStart  = Point { x: -xdiff, y: -ydiff }
+  transformEnd    = Point { x: xdiff, y: ydiff }
+scaleAndCentre (Text _ str) = Text origin str
+
+extractString :: Shape -> Maybe String
+extractString (Text _ str) = Just str
+extractString _ = Nothing
+
+-- Vector graphics library.
+area :: Shape -> Number
+area (Circle _ r) = pi * (pow r 2.0)
+area (Rectangle _ w h) = w * h
+area _ = 0.0