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{{DISPLAYTITLE:FP Laboratory 3}}== Usage of lists ==
Find out the results of the following operations:

== Simple functions working with list ==
Implement following functions:
* Create a function that computes length of a list.

<syntaxhighlight lang="Haskell">length' :: [a] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> length' "ABCD"
4
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
length' :: [a] -> Int
length' []  = 0
length' (_:xs) = 1 + length' xs
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that sums the list of integers.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/Yuz8lpKZiJs]]</div>
<syntaxhighlight lang="Haskell">sumIt :: [Int] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> sumIt [1,2,3]
6
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
sumIt :: [Int] -> Int
sumIt []  = 0
sumIt (x:xs) = x + sumIt xs
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that returns the first element in the list.

<syntaxhighlight lang="Haskell">getHead :: [a] -> a</syntaxhighlight> 
<syntaxhighlight lang="Haskell" class="myDark">
*Main> getHead [1,2,3]
1
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
getHead :: [a] -> a
getHead (x:_) = x
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that returns the last element in the list.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/I5AZu8_G8pQ]]</div>
<syntaxhighlight lang="Haskell">getLast :: [a] -> a</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> getLast [1,2,3]
3
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
getLast :: [a] -> a
getLast [x] = x
getLast (x:xs) = getLast xs

* Create a function that checks if an element is a member of the list.

<syntaxhighlight lang="Haskell">isElement :: Eq a => a -> [a] -> Bool</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> isElement 2 [1,2,3]
True
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
isElement :: Eq a => a -> [a] -> Bool
isElement _ [] = False
isElement a (x:xs) | a == x = True 
                   | otherwise = isElement a xs 
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that returns the list without the first element.

<syntaxhighlight lang="Haskell">getTail :: [a] -> [a]</syntaxhighlight> 
<syntaxhighlight lang="Haskell" class="myDark">
*Main> getTail [1,2,3]
[2,3]
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
getTail :: [a] -> [a]                   
getTail (_:xs) = xs
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that returns the list without the last element.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/ZLmvYTZ6fkw]]</div>
<syntaxhighlight lang="Haskell">getInit :: [a] -> [a]</syntaxhighlight> 
<syntaxhighlight lang="Haskell" class="myDark">
*Main> getInit [1,2,3]
[1,2]
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
getInit :: [a] -> [a]
getInit [_] = []
getInit (x:xs) = x : getInit xs
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that merge two lists into one list.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/FFoHC-g3f_g]]</div>
<syntaxhighlight lang="Haskell">combine :: [a] -> [a] -> [a]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> combine [1,2,3] [4,5]
[1,2,3,4,5]
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
combine :: [a] -> [a] -> [a]
combine [] y = y
combine (x:xs) y = x : combine xs y
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that finds the maximum in the list of integers.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/ybgM-YeQTco]]</div>
<syntaxhighlight lang="Haskell">max' :: [Int] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> max' [3,1,7,5]
7
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
max' :: [Int] -> Int
max' [x] = x
max' (x:y:z) | x > y = max' (x:z)
             | otherwise = max' (y:z)

* Create a function that reverse a list.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/jlUuZ5fCFgQ]]</div>
<syntaxhighlight lang="Haskell">reverse' :: [a] -> [a]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> reverse' [3,1,7,5]
[5,7,1,3]
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
reverse' :: [a] -> [a]             
reverse' [] = []
reverse' (x:xs) = (reverse' xs) ++ [x]

reverse'' :: [a] -> [a] 
reverse'' n = tmp n  []
  where tmp [] ys = ys 
        tmp (x:xs) ys = tmp xs (x:ys)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

* Create a function that product scalar multiplication of two vectors.

<syntaxhighlight lang="Haskell">scalar :: [Int] -> [Int] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> scalar [1,2,3] [4,5,6]
32
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
scalar :: [Int] -> [Int] -> Int
scalar [] [] = 0
scalar (x:xs) (y:ys) = x*y + scalar xs ys
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BEBLH60352]]
</div>
<div style="clear:both"></div>

= Additional exercises =
* Create a function that eliminates all occurrences of zeros in a list.

<syntaxhighlight lang="Haskell">nonZeros :: [Int] -> [Int]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> nonZeros [0,1,0,2,3,0,0]
[1,2,3]
</syntaxhighlight>

* Create a function that realizes the left rotation of a list by one element.

<syntaxhighlight lang="Haskell">rotateLeft1 :: [a] -> [a]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> rotateLeft1 [1,2,3,4,5]
[2,3,4,5,1]
</syntaxhighlight>

* Create a function that realizes the right rotation of a list by one element.

<syntaxhighlight lang="Haskell">rotateRight1 :: [a] -> [a]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> rotateRight1 [1,2,3,4,5]
[5,1,2,3,4]
</syntaxhighlight>

* Create a function that eliminates all even numbers from a list.

<syntaxhighlight lang="Haskell">oddMembers :: [Int] -> [Int]</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> oddMembers [0,1,0,2,3,0,0] 
[1,3]
</syntaxhighlight>

* Create a function that counts all odd numbers in a given list (define non-recursively using previously defined functions).

<syntaxhighlight lang="Haskell">countOddMembers :: [Int] -> Int</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> countOddMembers [1,0,3,1,4,5]
4
</syntaxhighlight>

* Create a function that compares lists of numbers if they are equal.

<syntaxhighlight lang="Haskell">compareLists :: Eq a => [a] -> [a] -> Bool </syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> compareLists [5,8,11] [5,8,11]
True
*Main> compareLists [5,8,11] [3,5,8]
False
*Main> compareLists [] []
True
*Main> compareLists [5,8,11] [5,8,11,13]
False
</syntaxhighlight>

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