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== Types ==

*Using the GHCi command <code>:info</code>, learn the type of the following functions (and operators): <code>+, sqrt, succ, max</code>
*Get the information about the data type of following expressions and evaluate them. it is possible using the command <code>:type</code>. You can switch this option on for all commands by <code>:set +t</code> (removing by <code>:unset +t</code>).
<syntaxhighlight lang="Haskell" >
5 + 8
3 * 5 + 8
2 + 4
sqrt 16
succ 6
succ 7
pred 9
pred 8
sin (pi / 2)
truncate pi
round 3.5
round 3.4
floor 3.7
ceiling 3.3
mod 10 3
odd 3
</syntaxhighlight>
* At presentations, we have spoken about some basic types: <code> Int, Double, Bool, Char</code>. For each of previous expressions assign them the most appropriate of these basic data types. You can verify your guess by using <code>::</code>. For example, for the first expression, let's assume it is <code>Int</code>. We can cast the result to integer and get the following result.
<syntaxhighlight lang="Haskell" class="myDark" >
Prelude> :type (5 + 8) :: Int
(5 + 8) :: Int :: Int
</syntaxhighlight>
If we try incorrect conversion to <code>Char</code>, we get the following result.
<syntaxhighlight lang="Haskell" class="myDark" >
Prelude> :type (5 + 8) :: Char

<interactive>:1:2: error:
* No instance for (Num Char) arising from a use of `+'
* In the expression: (5 + 8) :: Char
</syntaxhighlight>
For this expression, also the type <code>Double</code> works.
<syntaxhighlight lang="Haskell" class="myDark" >
Prelude> :type (5 + 8) :: Double
(5 + 8) :: Double :: Double
</syntaxhighlight>
== Simple functions ==

Implement following functions:
* Function that computes a factorial of a given number.
<syntaxhighlight lang="Haskell">factorial :: Int -> Int</syntaxhighlight>
* Function that computes n-th number in Fibonacci sequence.
<syntaxhighlight lang="Haskell">fib :: Int -> Int</syntaxhighlight>
* Function that checks if a year is a leap-year (divisible without remainder by 4 and it is not divisible by 100. If it is divisible by 400, it is a leap-year).
<syntaxhighlight lang="Haskell">leapYear :: Int -> Bool</syntaxhighlight>
* Implement two functions that returns a maximum from 2 respectively 3 given parameters.
<syntaxhighlight lang="Haskell">
max2 :: Int -> Int -> Int
max3 :: Int -> Int -> Int -> Int
</syntaxhighlight>
* Term combination is a selection of items from a collection, such that (unlike permutations) the order of elements in this selection does not matter. Compute the number of possible combinations if we are taking k things from the collection of n things.
<syntaxhighlight lang="Haskell">combinations :: Int -> Int -> Int</syntaxhighlight>
* Implement a function that computes the number of solutions for a quadratic equation. This quadratic equation will be given using standard coefficients: a, b, c.
<syntaxhighlight lang="Haskell">numberOfRoots :: Int -> Int -> Int -> Int
-- To simplify the solution, let construct can be used
f x y = let a = x + y
in a * a
</syntaxhighlight>
* Implement a function that computes greatest common divider for two given numbers.
<syntaxhighlight lang="Haskell">gcd' :: Int -> Int -> Int</syntaxhighlight>
* Implement a function that compute, if a given number is a prime number.
<syntaxhighlight lang="Haskell">isPrime :: Int -> Bool</syntaxhighlight>

← Older revision		Revision as of 08:38, 19 September 2023
Line 243:		Line 243:
	</div>		</div>
	<div style="clear:both"></div>		<div style="clear:both"></div>
		+
		+	== Additional exercises ==
		+	* Define a function that returns true iff all three arguments are different.
		+
		+	<syntaxhighlight lang="Haskell">threeDifferent :: Int -> Int -> Int -> Bool</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> threeDifferent 4 5 6
		+	True
		+	*Main> threeDifferent 6 5 6
		+	False
		+	</syntaxhighlight>
		+
		+	* Define a function that returns true iff all four arguments are equal.
		+
		+	<syntaxhighlight lang="Haskell">fourEqual :: Int -> Int -> Int -> Int-> Bool</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> fourEqual 4 5 6 7
		+	False
		+	*Main> fourEqual 4 4 4 4
		+	True
		+	</syntaxhighlight>
		+
		+	* Define a function that computes the average of three integers.
		+
		+	<syntaxhighlight lang="Haskell">averageThree :: Int -> Int -> Int -> Float</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> averageThree 4 10 20
		+	11.333333
		+	</syntaxhighlight>
		+
		+	* Define a function that returns how many of its inputs are larger than their average value.
		+
		+	<syntaxhighlight lang="Haskell">howManyAboveAverage :: Int -> Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> howManyAboveAverage 5 5 5
		+	0
		+	*Main> howManyAboveAverage 10 50 50
		+	2
		+	</syntaxhighlight>
		+
		+	* Using the multiplication over the integer numbers, implement a recursive function that realizes the n-th power of an integer number.
		+	<syntaxhighlight lang="Haskell">power :: Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> power 2 3
		+	8
		+	*Main> power 4 2
		+	16
		+	*Main> power 4 3
		+	64
		+	</syntaxhighlight>
		+
		+	* Using the addition over the integer numbers, implement a recursive function that realizes the multiplication of integer numbers.
		+	<syntaxhighlight lang="Haskell">mult :: Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> mult 4 5
		+	20
		+	*Main> mult 4 9
		+	36
		+	*Main> mult 4 0
		+	0
		+	</syntaxhighlight>
		+
		+	* Define a recursive function that computes the remainder of integer division.
		+	<syntaxhighlight lang="Haskell">mod' :: Int -> Int -> Int</syntaxhighlight>
		+	<syntaxhighlight lang="Haskell" class="myDark">
		+	*Main> mod' 40 7
		+	5
		+	*Main> mod' 30 5
		+	0
		+	*Main> mod' 20 7
		+	6
		+	</syntaxhighlight>

@@ Line 81: / Line 81: @@
 factorial'' n = if n==0 then 1 else n * factorial'' (n-1)
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 104: / Line 105: @@
    tmp x a b = tmp (x-1) b (a+b)
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 130: / Line 132: @@
              | otherwise = x `mod` 4 == 0
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 153: / Line 156: @@
 max3 x y z = (x `max2` y) `max2` z
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 174: / Line 178: @@
 combinations' n k = fromIntegral(factorial n) `div` fromIntegral(factorial k * factorial (n-k))
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 193: / Line 198: @@
                        in if d<0 then 0 else if d == 0 then 1 else 2
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 214: / Line 220: @@
 gcd2 a b = gcd2 b (a `mod` b)
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>
@@ Line 233: / Line 240: @@
                    | otherwise = isPrimeTest n (x-1)
 </syntaxhighlight>
 </div>
 <div style="clear:both"></div>

@@ Line 84: / Line 84: @@
 <div style="clear:both"></div>
-* Function that computes n-th number in Fibonacci sequence.
+* Function that computes n-th number in Fibonacci sequence. <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/GBxb_cFQG14]]</div>
 <syntaxhighlight lang="Haskell">fib :: Int -> Int</syntaxhighlight>
@@ Line 196: / Line 196: @@
 <div style="clear:both"></div>
-* Implement a function that computes greatest common divider for two given numbers.
+* Implement a function that computes greatest common divider for two given numbers. <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/uNs9Zqetu7k]]</div>
 <syntaxhighlight lang="Haskell">gcd' :: Int -> Int -> Int</syntaxhighlight>
 <syntaxhighlight lang="Haskell" class="myDark">
@@ Line 217: / Line 217: @@
 <div style="clear:both"></div>
-* Implement a function that compute, if a given number is a prime number.
+* Implement a function that compute, if a given number is a prime number. <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/XSc8qjd4StQ]]</div>
 <syntaxhighlight lang="Haskell">isPrime :: Int -> Bool</syntaxhighlight>
 <syntaxhighlight lang="Haskell" class="myDark">

@@ Line 104: / Line 104: @@
 leapYear' :: Int -> Bool
 leapYear' x | x `mod` 400 == 0 = True
-             | x `mod` 100 /= 0 = False
+             | x `mod` 100 == 0 = False
              | otherwise = x `mod` 4 == 0
 </syntaxhighlight>

@@ Line 60: / Line 60: @@
 Implement following functions:
-* Function that computes a factorial of a given number.
+* Function that computes a factorial of a given number. <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/WHkBFQIHmsw]]</div>
 <syntaxhighlight lang="Haskell">factorial :: Int -> Int</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
@@ Line 81: / Line 86: @@
 * Function that computes n-th number in Fibonacci sequence.
 <syntaxhighlight lang="Haskell">fib :: Int -> Int</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
 <syntaxhighlight lang="Haskell">
@@ Line 97: / Line 108: @@
 * Function that checks if a year is a leap-year (divisible without remainder by 4 and it is not divisible by 100. If it is divisible by 400, it is a leap-year).
 <syntaxhighlight lang="Haskell">leapYear :: Int -> Bool</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
 <syntaxhighlight lang="Haskell">
@@ Line 114: / Line 137: @@
 max3 :: Int -> Int -> Int -> Int
 </syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
 <syntaxhighlight lang="Haskell">
@@ Line 127: / Line 157: @@
 * Term combination is a selection of items from a collection, such that (unlike permutations) the order of elements in this selection does not matter. Compute the number of possible combinations if we are taking k things from the collection of n things.
 <syntaxhighlight lang="Haskell">combinations :: Int -> Int -> Int</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
 <syntaxhighlight lang="Haskell">
@@ Line 146: / Line 181: @@
 f x y = let a = x + y
          in a * a
 </syntaxhighlight>
@@ Line 159: / Line 198: @@
 * Implement a function that computes greatest common divider for two given numbers.
 <syntaxhighlight lang="Haskell">gcd' :: Int -> Int -> Int</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
@@ Line 176: / Line 219: @@
 * Implement a function that compute, if a given number is a prime number.
 <syntaxhighlight lang="Haskell">isPrime :: Int -> Bool</syntaxhighlight>
 <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">

@@ Line 39: / Line 39: @@
 (5 + 8) :: Double :: Double
 </syntaxhighlight>
 == Simple functions ==