# Assignment 8

due

module A08 where -- Here is a definition of a pseudo-random number generator that works -- by passing around its state. data Seed = Seed { unSeed :: Int } deriving (Eq, Show) type Gen a = Seed -> (a, Seed) rand :: Gen Int rand (Seed s) = (s', Seed s') where s' = (s * 16807) `mod` 0x7FFFFFFF -- Now let's make an enumerated type for representing coin flips. A -- coin flip can be head or tails. This is 'isomorphic' to a Boolean -- value -- we could just represent heads as True and tails as False (or -- vice-versa), but for clarity it's sometimes helpful to declare such -- things as types. data Coin = Heads | Tails deriving (Eq, Show, Bounded, Enum) -- Make a function to convert any integer to a coin flip. You want the -- coin to be fair (or as close as possible), so use even or odd to -- determine whether you produce Heads or Tails. coinFromInt :: Int -> Coin coinFromInt = error "TODO" -- Now create a random generator for coin flips. You can call rand -- and/or coinFromInt within this code. flipCoin :: Gen Coin flipCoin = error "TODO" -- This function creates a pair of random integers, by calling rand -- twice. But note how it has to thread the PRNG state through both -- calls. Given s0, we get s1 from the first rand, then give s1 to the -- next rand and get s2. If we mess that up, and end up reusing a state -- that has already been used, then duplicate results will appear. randPair :: Gen (Int, Int) randPair s0 = ((i1, i2), s2) where (i1,s1) = rand s0 (i2,s2) = rand s1 -- Now, generalize randPair so that instead of calling rand twice, it -- can call *any two generators* given as arguments. For example, you -- should be able to do (genPair rand rand) to reproduce what randPair -- can do. Or you can do (genPair flipCoin rand) or (genPair flipCoin -- flipCoin). genPair :: Gen a -> Gen b -> Gen (a,b) genPair = error "TODO" -- Generators are functors -- see if you can implement fmap! fmapGen :: (a -> b) -> Gen a -> Gen b fmapGen = error "TODO" -- Finally, let's try to iterate a generator to produce a list of -- results. The integer specifies the length of the list, so when -- that's zero the result can be empty. iterGen :: Gen a -> Int -> Gen [a] iterGen = error "TODO"