From: Ramakrishnan Muthukrishnan Date: Mon, 22 Dec 2014 15:36:30 +0000 (+0530) Subject: hw6: Fibonacci - mostly done till half of exercise 6 X-Git-Url: https://git.rkrishnan.org/%5B/%5D%20/uri/%22doc.html/(%5B%5E?a=commitdiff_plain;h=1adac606aa0f431ab41a698b763dbee3928cede7;p=yorgey.git hw6: Fibonacci - mostly done till half of exercise 6 --- diff --git a/hw6/Fibonacci.hs b/hw6/Fibonacci.hs new file mode 100644 index 0000000..9a15712 --- /dev/null +++ b/hw6/Fibonacci.hs @@ -0,0 +1,88 @@ +{-# OPTIONS_GHC -Wall #-} +{-# OPTIONS_GHC -fno-warn-missing-methods #-} +{-# LANGUAGE InstanceSigs #-} +{-# LANGUAGE FlexibleInstances #-} +module Fibonacci where + +-- exercise 1 +fib :: Integer -> Integer +fib 0 = 0 +fib 1 = 1 +fib n = fib (n - 1) + fib (n - 2) + +fibs1 :: [Integer] +fibs1 = map fib [0..] + +-- exercise 2: define a more efficient fibs +fibs2 :: [Integer] +fibs2 = 0 : 1 : fs + where fs = zipWith (+) fibs2 (tail fibs2) + +-- exercise 3 -- streams +data Stream a = Cons a (Stream a) + +-- stream to infinite list +streamToList :: Stream a -> [a] +streamToList (Cons x sx) = x : streamToList sx + +-- instance of Show for Stream +instance Show a => Show (Stream a) where + show :: Stream a -> String + show sx = init (tail (show (take 20 (streamToList sx)))) ++ "..." + +-- exercise 4 - stream repeat +streamRepeat :: a -> Stream a +streamRepeat x = Cons x (streamRepeat x) + +-- streamMap +streamMap :: (a -> b) -> Stream a -> Stream b +streamMap f (Cons x xs) = Cons (f x) (streamMap f xs) + +-- streamFromSeed +streamFromSeed :: (a -> a) -> a -> Stream a +streamFromSeed f x = Cons x (streamFromSeed f (f x)) + +-- exercise 5: define a few streams + +-- nats +nats :: Stream Integer +nats = streamFromSeed (+1) 0 + +-- ruler +{- | ruler stream +Define the stream + +ruler :: Stream Integer + +which corresponds to the ruler function +0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, . . . + +where the nth element in the stream (assuming the first element +corresponds to n = 1) is the largest power of 2 which evenly +divides n + +-} +interleaveStreams :: Stream a -> Stream a -> Stream a +interleaveStreams (Cons x xs) ys = (Cons x (interleaveStreams ys xs)) + +ruler :: Stream Integer +ruler = interleaveStreams (streamRepeat 0) (foldr interleaveStreams (streamRepeat 0) (map streamRepeat [1..])) + +-- fibonacci numbers via generating functions +-- exercise 6 + +-- define x :: Stream Integer +-- x = 0 + 1.x + 0.x^2 + 0.x^3 + 0.x^4 + ... +x' :: Stream Integer +x' = Cons 0 (Cons 1 (streamRepeat 0)) + +-- implement an instance of Num type class for Stream Integer +instance Num (Stream Integer) where + fromInteger :: Integer -> Stream Integer + fromInteger n = Cons n (streamRepeat 0) + negate :: Stream Integer -> Stream Integer + negate sx = streamMap (* (-1)) sx + (+) :: Stream Integer -> Stream Integer -> Stream Integer + (+) (Cons x sx) (Cons y sy) = (Cons (x+y) ((+) sx sy)) + (*) :: Stream Integer -> Stream Integer -> Stream Integer + (*) (Cons x sx) (Cons y sy) = Cons (x*y) ((streamMap (* x) sy) + sx*(Cons x sx))