The purpose of this worksheet is to practice using laziness, by creating some cyclic structures.
module Lazy where import Test.QuickCheck import Data.Ratio -- ones is an infinite list of ones. i.e. [1,1,1,1,...] ones:: [Int] ones = undefined prop_ones n = all (==1) (take n ones) -- from n is an infinite list of ascending numbers starting at n from:: Int -> [Int] from n = undefined prop_from n m = ok (take n (from m)) where ok  = True ok [x] = True ok (x:y:zs) = (x+1)==y && ok (y:zs) -- Another way to compute an infinite list of ascending unmbers from2 = 2 : (map (+1) from2) -- Define a property for quickcheck to test for from2 prop_from2 = undefined -- Use the technique of from2 to create the list [1, 1/2, 1/4, 1/8, 1/16, ...] -- You will need to use the operator (%) that builds ratios. (1 % 4) --> 1/4 -- Two important ratios are: one :: Ratio Integer one = 1 half :: Ratio Integer half = 1 % 2 converge :: [Ratio Integer] converge = undefined -- write test that shows the sum of the first n terms of -- converge is always less than 2 prop_converge n = undefined
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