1. 12 Haskell

2.  ftp://web.ntnu.edu.tw/WWW/func_prog/ghc-6-8-2.zip ftp://web.ntnu.edu.tw/WWW/func_prog/ghc-6-8-2.zip  Haskell is  Lazy evaluated  Case-sensitive  Purely functional

3.  Lazy evaluated  No computation takes place unless it is forced to take place when the result of that computation is used  Pseudo-code List makeList() { List current = new List(); current.value = 1; current.next = makeList(); return current; } It attempt to get a value out of it. This leads to an infinite loop  Hashall makeList = 1 : makeList 把 makelist 定義為 element1 加上 makelist

4.  Purely functional  Functions that do not have side effects are called pure  If you have a value x  you must not think of x as a register, a memory location or anything else of that nature  x is simply a name, just as “Mary” is your name  You cannot arbitrarily decide to store a different person in my name any more than you can arbitrarily decide to store a different value in x  A call like x = x + 1 is called destructive  Destructive update does not exist in Haskell

5.  Prelude> sum [1..10] 55  Prelude> 5+2*3 11  Prelude> sin 0.3 0.29552020666134  Prelude> length [1,5,9,3] 4  Prelude> reverse [1..10] [10,9,8,7,6,5,4,3,2,1]

6.  Prelude> let pi = 3.14159265358979323846264338327950  Prelude> pi 3.141592653589793 The missing digits are just skipped when displaying the value  Prelude> pi * 5^2 78.53981633974483  Prelude> pi * 25^2 1963.4954084936207  Prelude> let r = 25.0 Prelude> let area = pi * r ^ 2 Prelude> area 1963.4954084936207

7.  Prelude> (5,3) (5,3)  The first element of a pair need not have the same type as the second element  Prelude> fst (5, "hello") 5  Prelude> snd (5, "hello") "hello“  Exercise Use a combination of fst and snd to extract the character out of the tuple ((1,’a’),"foo")

8.  The primary limitation of tuples  hold only a fixed number of elements: pairs hold two, triples hold three, and so on  List  Hold an arbitrary number of elements  Prelude> [1,2] [1,2]  Prelude> [1,2,3] [1,2,3]

9.  : cons  Prelude> 0:[1,2] [0,1,2]  Prelude> 5:[1,2,3,4]  [5,1,2,3,4]  Prelude> 5:1:2:3:4:[] [5,1,2,3,4]  If we write something using the [5,1,2,3,4] notation, the compiler simply translates it to the expression using (:) and []

10.  Tuples are heterogeneous  Lists must be homogenous  Prelude> [(1,1),(2,4),(3,9),(4,16)] [(1,1),(2,4),(3,9),(4,16)]  Prelude> ([1,2,3,4],[5,6,7]) ([1,2,3,4],[5,6,7])  Prelude> length [1,2,3,4,10] 5  Prelude> head [1,2,3,4,10] 1  Prelude> length (tail [1,2,3,4,10]) 4

11.  String is simply a list of Chars  Prelude> ’H’:’e’:’l’:’l’:’o’:[] "Hello“  ++  Prelude> "Hello " ++ "World“ "Hello World“  Prelude> "Five squared is " ++ show (5*5) "Five squared is 25"

12.  Map  Takes as arguments a list of values and a function that should be applied to each of the values  Prelude> map Char.toUpper "Hello World“ "HELLO WORLD“  Filter  Remove certain elements from a list depending on their value  Prelude> filter Char.isLower "Hello World“ "elloorld“  Foldr  Replaces occurences of the list cons operator (:) with the function parameter and replaces the empty list constructor ([]) with the initial value  Prelude> foldr (+) 0 [3,8,12,5] 28

13.  Prelude> foldr (*) 1 [4,8,5] 160  Prelude> foldr (-) 1 [4,8,5] 0  foldr (-) 1 [4,8,5] ==> 4 - (foldr (-) 1 [8,5]) ==> 4 - (8 - foldr (-) 1 [5]) ==> 4 - (8 - (5 - foldr (-) 1 [])) ==> 4 - (8 - (5 - 1)) ==> 4 - (8 - 4) ==> 4 - 4 ==> 0

14.  Foldl  Goes the other way and effectively produces the opposite bracketing  Prelude> foldl (+) 0 [3,8,12,5] 28  Prelude> foldl (-) 1 [4,8,5] -16  foldl (-) 1 [4,8,5] ==> foldl (-) (1 - 4) [8,5] ==> foldl (-) ((1 - 4) - 8) [5] ==> foldl (-) (((1 - 4) - 8) - 5) [] ==> ((1 - 4) - 8) - 5 ==> ((-3) - 8) - 5 ==> (-11) - 5 ==> -16

15.  Exercise Use map to convert a string into a list of booleans, each element in the new list representing whether or not the original element was a lower-case character.That is, it should take the string “aBCde” and return [True,False,False,True,True].

16.  test.hs module Test where x = 5 y = (6, "Hello") z = x * fst y  Prelude> :l Test.hs  Test>  Test> x 5  Test> y (6,"Hello")  Test> z 30

17.  main = putStrLn "Hello World“  C:\ghc> ghc –make c:\\xxx\\test.hs -o test.exe or Prelude> :! ghc --make c:\\xxx\\test.hs -o test.exe  C:\ghc> test.exe Hello World

18.  Test.hs module Test -- 注意大寫 where sig x = if x < 0 -- 注意縮排 then -1 else if x > 0 then 1 else 0  Test> sig 5 1  Test> sig 0 0  Test> sig (5-10) -1  Test> sig (-1) -1

19.  f x = case x of 0 -> 1 1 -> 5 2 -> 2 _ -> -1  f x = case x of { 0 -> 1 ; 1 -> 5 ; 2 -> 2 ; _ -> 1 }  f x = case x of { 0 -> 1 ; 1 -> 5 ; 2 -> 2 ; _ -> 1 }  f 0 = 1 f 1 = 5 f 2 = 2 f _ = -1

20.  Test.hs module Test where -- 注意縮排 signum2 x = if x < 0 then -1 else if x > 0 then 1 else 0 f x = case x of 0 -> 1 1 -> 5 2 -> 2 _-> -1  Prelude > (sig. f) 2 1

21.  roots a b c = let det = sqrt (b*b - 4*a*c) in ((-b + det) / (2*a), (-b - det) / (2*a))  roots a b c = let det = sqrt (b*b - 4*a*c) twice_a = 2*a in ((-b + det) / twice_a, (-b - det) / twice_a)

22.  Imperative version int factorial(int n) { int fact = 1; for (int i=2; i <= n; i++) fact = fact * i; return fact; } int factorial(int n) { if (n == 1) return 1; else return n * factorial(n-1); }  Haskell factorial 1 = 1 factorial n = n * factorial (n-1)

23.  Exercise  exponent a 1 = a exponent a b = a * exponent a (b-1)

24.  Test.hs module Name where import IO name = do --do specifies the order of operations hSetBuffering stdin LineBuffering putStrLn "Please enter your name: " name <- getLine putStrLn ("Hello, " ++ name ++ ", how are you?")  Name > name Please enter your name: Mary Hello, Mary, how are you? Name>

25.  Prelude > (\x->2*x) 2  Prelude> map (\x -> x*x) [1..10] [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]  square = \x -> x*x f = \x y -> 2*x + y

26.  Guess.hs module Main where import IO import Random main = do hSetBuffering stdin LineBuffering num <- randomRIO (1::Int, 100) putStrLn "I’m thinking of a number between 1 and 100" doGuessing num doGuessing num = do putStrLn "Enter your guess:" guess <- getLine let guessNum = read guess if guessNum < num then do putStrLn "Too low!" doGuessing num else if guessNum> num then do putStrLn "Too high!" doGuessing num else do putStrLn "You Win!"