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{{DISPLAYTITLE:FP Laboratory 6}}== Operators ==
*Define following functions that performs corresponding logic operations: <code>not', and', or', nand', xor', impl', equ'</code>
*Define the 'standard' priority for all these functions, if they are used as operators. 
*Create a function that prints the truth table of a given logical expression for two variables.

<syntaxhighlight lang="Haskell">table :: (Bool -> Bool -> Bool) -> IO ()</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
table (\a b -> (and' a (or' a b)))                                                                              
True  True  True
True  False True
False True  False
False False False
</syntaxhighlight>

not' :: Bool -> Bool
not' True = False
not' False = True
infixl 5 `not'`

and' :: Bool -> Bool -> Bool
and' True True = True
and' _ _ = False
infixl 4 `and'`

or' :: Bool -> Bool -> Bool
or' False False = False
or' _ _ = True
infixl 3 `or'`

nand' :: Bool -> Bool -> Bool
nand' x y = not' (and' x y)
infixl 4 `nand'`

xor' :: Bool -> Bool -> Bool
xor' x y = x/=y
infixl 3 `xor'`

impl' :: Bool -> Bool -> Bool
impl' True False = False
impl' _ _ = True
infixl 2 `impl'`

equ' :: Bool -> Bool -> Bool
equ' x y = x == y
infixl 7 `equ'`

table :: (Bool -> Bool -> Bool) -> IO ()
table expr = putStr (concat [nicePrint [x,y,(expr x y)] |x<-[True,False], y<-[True,False]])

*Extend the previously defined function to accept any number of variables (the number of variables will be given as a first parameter).

<syntaxhighlight lang="Haskell">tablen :: Int -> ([Bool] -> Bool) -> IO ()</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
 tablen 3 (\[a,b,c] -> a `and'` (b `or'` c) `equ'` a `and'` b `or'` a `and'` c)
True   True   True   => True
True   True   False  => True
True   False  True   => True
True   False  False  => False
False  True   True   => False
False  True   False  => False
False  False  True   => False
False  False  False  => False
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
tablen :: Int -> ([Bool] -> Bool) -> IO ()
tablen n f = putStr(concat [nicePrint x ++ " => " ++ show(f x) ++ "\n" |x<-allValues n]) where 
  allValues 1 = [[True], [False]]
  allValues n = [x:y| x<-[True,False], y<-allValues (n-1)]

== Complex function - Huffman Codes ==
*Create a function that will compute [https://en.wikipedia.org/wiki/Huffman_coding Huffman codes] for a given list of characters and their frequencies.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/HWYQZtbxMhc]]</div> 
<syntaxhighlight lang="Haskell">huffman :: [(Char, Int)] -> [(Char, String)]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main>  huffman [('a',45),('b',13),('c',12),('d',16),('e',9),('f',5)]
[('a',"0"),('b',"101"),('c',"100"),('d',"111"),('e',"1101"),('f',"1100")]
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
import Data.List (sortBy)

huffman :: [(Char, Int)] -> [(Char, String)] 
huffman input = 
  let 
    prep = [ (y, [(x,"")] ) | (x,y)<-input]            
  in sortBy (\ (x,_) (y,_) -> compare x y) (step prep) where
     step :: [(Int, [(Char, String)])] -> [(Char, String)]
     step [(_, result) ] = result
     step list = let ((a1, as2):(b1,bs2):rest) = sortBy (\ (x,_) (y,_) -> compare x y) list
                 in step ((a1+b1, [(x,'0':a2)|(x,a2)<-as2]++[(x,'1':b2)|(x,b2)<-bs2])  : rest)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/PSSTZ19890]]
</div>
<div style="clear:both"></div>

== Additional exercises ==
* Create a function that divides a list of elements into the list lists using a separator.

<syntaxhighlight lang="Haskell">splitByElement :: Eq a => [a] -> a -> [[a]]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> splitByElement "I love functional programming!" ' '
["I","love","functional","programming!"]
*Main> splitByElement [1,2,1,2,3,4,5,5,6,4,1,2,0,1,4] 1
[[2],[2,3,4,5,5,6,4],[2,0],[4]]
*Main> splitByElement [1,2,1,2,3,4,5,5,6,4,1,2,0,1,4] 5
[[1,2,1,2,3,4],[6,4,1,2,0,1,4]]
</syntaxhighlight>

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