Chapter12.hs

-----------------------------------------------------------------------
--
--  Haskell: The Craft of Functional Programming, 3e
--  Simon Thompson
--  (c) Addison-Wesley, 1996-2011.
--
--  Chapter 12
--
-----------------------------------------------------------------------

-- For Rock-Paper-Scissors examples see RPS.hs

module Chapter12 where

import Pictures hiding (flipH,rotate,flipV,beside,invertColour,
                        superimpose,printPicture)


-- Revisiting the Pictures example, yet again.

flipV :: Picture -> Picture
flipV      = map reverse

beside :: Picture -> Picture -> Picture
beside = zipWith (++)


-- Revisiting the Picture example
-- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

-- Some of the functions are already (re)defined in this script.
-- Among the other functions mentioned were 

invertColour :: Picture -> Picture
invertColour = map (map invert)

superimpose  :: Picture -> Picture -> Picture
superimpose = zipWith (zipWith combineChar)

-- The definition of combineChar is left as an exercise: it's a dummy definition
-- here.

combineChar :: Char -> Char -> Char
combineChar = combineChar

-- Printing a picture: uses putStr after a newline has been added at the end of
-- every line and the lines are joined into a single string.

printPicture :: Picture -> IO ()
printPicture = putStr . concat . map (++"\n")

-- Regular expressions

type RegExp = String -> Bool

char :: Char -> RegExp

epsilon = (=="")

char ch = (==[ch])

(|||) :: RegExp -> RegExp ->  RegExp

e1 ||| e2 = 
    \x -> e1 x || e2 x

(<*>) :: RegExp -> RegExp ->  RegExp

e1 <*> e2 =
    \x -> or [ e1 y && e2 z | (y,z) <- splits x ]

(<**>) :: RegExp -> RegExp ->  RegExp

e1 <**> e2 =
    \x -> or [ e1 y && e2 z | (y,z) <- fsplits x ]

splits xs = [splitAt n xs | n<-[0..len]]
    where
      len = length xs

star :: RegExp -> RegExp

star p = epsilon ||| (p <**> star p)
--           epsilon ||| (p <*> star p)
-- is OK as long as p can't have epsilon match

fsplits xs = tail (splits xs)

--
-- Case studies: functions as data
--

-- Natural numbers as functions.

type Natural a = (a -> a) -> (a -> a)

zero, one, two :: Natural a

zero f = id 
one f  = f 
two f  = f.f

int :: Natural Int -> Int 

int n = n (+1) 0

-- sends representation of n to rep. of n+1

succ :: Natural a -> Natural a
succ = error "succ"

-- sends reps. of n and m to rep. of n+m

plus :: Natural a -> Natural a -> Natural a
plus = error "plus"

-- sends reps. of n and m to rep. of n*m
times :: Natural a -> Natural a -> Natural a
times = error "times"

-- Creating an index
-- ^^^^^^^^^^^^^^^^^

-- See Index.hs

-- Development in practice
-- ^^^^^^^^^^^^^^^^^^^^^^^
-- Defining the .. notation (not executable code).
-- 
-- [m .. n]
--   | m>n         = []
--   | otherwise   = m : [m+1 .. n]

-- [1 .. n] 
--   | 1>n         = []
--   | otherwise   = [1 .. n-1] ++ [n]

-- A simple palindrome check.

simplePalCheck :: String -> Bool
simplePalCheck st = (reverse st == st)

-- The full check

palCheck = simplePalCheck . clean

-- where the clean function combines mapping (capitals to smalls) and
-- filtering (removing punctuation)

clean :: String -> String 

clean = map toSmall . filter notPunct

toSmall  = toSmall  -- dummy definition
notPunct = notPunct -- dummy definition

-- Auxiliary functions

-- When is one string a subsequence of another? 

subseq :: String -> String -> Bool

subseq []    _  = True
subseq (_:_) [] = False
subseq (x:xs) (y:ys)
  = subseq (x:xs) ys || frontseq (x:xs) (y:ys)

-- When is one strong a subsequece of another, starting at the front?

frontseq :: String -> String -> Bool
frontseq []     _  = True
frontseq (_:_)  [] = False
frontseq (x:xs) (y:ys)
  = (x==y) && frontseq xs ys


-- Understanding programs
-- ^^^^^^^^^^^^^^^^^^^^^^

mapWhile :: (a -> b) -> (a -> Bool) -> [a] -> [b]

mapWhile f p []    = [] 
mapWhile f p (x:xs)
  | p x            = f x : mapWhile f p xs
  | otherwise      = [] 

example1 = mapWhile (2+) (>7) [8,12,7,13,16]