import Test.QuickCheck

-- Lecture Week 1, part A
--   David Sands, 2017

-- Plan: FPFTW

--  Price calculation
--   concepts: simple data, types, testing, def by cases

--  The price of prawns: 275kr/Kg

unitPrice     = 275.0 -- kr/Kg
discountPrice = unitPrice - discount
discount      = 75.0 -- kr/Kg
-- functions
price kg = unitPrice * kg
discountedPrice kg = discountPrice * kg
threshold = 50

{-
 Suppose price gets cheaper if we buy more:
 275/Kg up to 50 kg, and a discount of 75 kr/Kg
 for everything above 50kg
 -}
price2 kg
  | kg <= threshold = price kg
  | kg > threshold = price threshold
                   + discountedPrice (kg - threshold)

prop_price2 kg delta = price2 (abs kg) <= price2 (abs kg + abs delta)


-- Example of def by cases

abs' n | n >= 0 = n
       | n < 0  = -n



-- Definition by cases (guards)

-----------------------------------------------------------
-- Definition by recursion

-- 5! = 5 * 4 * 3 * 2 * 1

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

{- fac 3
   3 * fac 2
   3 * 2 * fac 1
   3 * 2 * 1 * fac 0
   3 * 2 * 1 * 1
   6
 -}
 

-- power2 k computes 2 to the power k,
-- for natural numbers k.

-- power2 3 = 2 * 2 * 2
power2 n
   | n == 0 = 1
   | n > 0  = 2 * power2 (n-1)

-- Other types: Lists and comprehensions

-- Literal lists
-- Strings
-- Simple generators
-- List comprehensions


-- Further info: online materials


-----------
upto n = [1..n]

fac' n = product [1..n]

-- List comprehensions (on Friday)