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fp2024:hw1 [2024/03/21 17:48]
pdmatei 		fp2024:hw1 [2024/03/21 19:12] (current)
pdmatei
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 </​code>​ </​code>​
  
-**7.** Write a function which computes the sum $math[b + e_0 + e_1 + ... e_n] where each $math[e_i] is in the interval $math[ [start,​stop] ​] and also in $math[s]. Use a tail-end recursive function:+**7.** Write a function which computes the sum $math[b + e_0 + e_1 + ... e_n] where each $math[e_i] is in the interval $$ [start,​stop] ​$$ and also in $math[s]. Use a tail-end recursive function:
 <code scala> <code scala>
   def sumSet(b: Int)(start: Int, stop: Int)(s: Set): Int = {   def sumSet(b: Int)(start: Int, stop: Int)(s: Set): Int = {
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 </​code>​ </​code>​
  
-**8.** Generalise the previous function such that we can **fold** a set using any binary commutative operation over integers. Make sure this is a **left** fold: Folding the set: ''​{x,​y,​z}''​ with ''​b''​ should produce: ''​( (b op x) op y) op z''​+**8.** Generalise the previous function such that we can **fold** a set using any binary commutative operation over integers. Make sure this is a **left** fold: Folding the set: ''​{x,​y,​z}''​ with initial value ''​b''​ should produce: ''​( (b op x) op y) op z''​
 <code scala> <code scala>
   def foldLeftSet   def foldLeftSet
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 </​code>​ </​code>​
  
-**9.** Implement an alternative to the previous function, namely **foldRight**. Applying ''​foldRight''​ on the set ''​{x,​y,​z}''​ with ''​b''​ should produce: ''​a op (b op (c op b))''​. Use direct recursion instead of tail recursion.+**9.** Implement an alternative to the previous function, namely **foldRight**. Applying ''​foldRight''​ on the set ''​{x,​y,​z}''​ with initial value ''​b''​ should produce: ''​a op (b op (c op b))''​. Use direct recursion instead of tail recursion.
 <code scala> <code scala>
   def foldRightSet   def foldRightSet
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 </​code>​ </​code>​
  
-**10.** Implement operation ''​filter''​ which takes a set and returns ​another one containing only those elements ​that satisfy the predicate:+**10.** Implement operation ''​filter''​ which takes a set and returns ​the set containing only those elements ​$math[e] for which $math[p(e)] is true:
 <code scala> <code scala>
-def filter(p: Int => Boolean)(set: Set): Set = ???+def filter(p: Int => Boolean)(s: Set): Set = ???
 </​code>​ </​code>​
  
-**11.** Implement a function which **partitions** a set into two sets. The left-most contains those elements that satisfy the predicate, while the right-most contains those elements that do not satisfy the predicate. Use pairs. A pair is constructed with simple parentheses. E.g. ''​(1,​2)''​ is a pair of two integers. Suppose ''​val p: (Int,​Int)''​ is another ​pair of two integers. Then ''​p._1''​ is the left-most part of the pair while ''​p._2''​ is the right-most part of the pair.+**11.** Implement a function which **partitions** a set into two sets. The left-most contains those elements that satisfy the predicate ​$math[p], while the right-most contains those elements that do not satisfy the predicate. Use pairs. A pair is constructed with simple parentheses. E.g. ''​(1,​2)''​ is a pair of two integers. Suppose ''​val p: (Int,​Int)''​ is a pair of two integers. Then ''​p._1''​ is the left-most part of the pair while ''​p._2''​ is the right-most part of the pair.
 <code scala> <code scala>
-  def partition(p:​ Int => Boolean)(set: Set): (Set,Set) = ???+  def partition(p:​ Int => Boolean)(s: Set): (Set,Set) = ???
 </​code>​ </​code>​
  
-**12.** Implement a function ''​forall''​ which checks if all elements in a given range of a set satisfy ​a predicate ​(condition). (Such a condition may be that all elements from given bounds are even numbers).+**12.** Implement a function ''​forall''​ which checks if all elements in a given range from a set satisfy ​the predicate ​$math[p]. (For instance $math[p] might be used to describe ​even numbers).
 <code scala> <code scala>
   def forall(cond:​ Int => Boolean) // condition to be checked   def forall(cond:​ Int => Boolean) // condition to be checked
             (start: Int, stop: Int) // start,stop values (inclusive)             (start: Int, stop: Int) // start,stop values (inclusive)
-            (set: Set): Boolean ​ // set to be checked+            (s: Set): Boolean ​ // set to be checked
             = ???             = ???
 </​code>​ </​code>​
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 **13.** Implement a function ''​exists''​ which checks if a predicate holds for **some** element from the range of a set. Hint: it is easier to implement ''​exists''​ using the logical relation: $math[ \exists x. P(X) \iff \lnot \forall x.\lnot P(X)]. **13.** Implement a function ''​exists''​ which checks if a predicate holds for **some** element from the range of a set. Hint: it is easier to implement ''​exists''​ using the logical relation: $math[ \exists x. P(X) \iff \lnot \forall x.\lnot P(X)].
  
-**14.** Implement the function ''​setOfDivByK''​ which returns the set of integers divisible by a value ''​k''​. Use the appropriate functions you have defined.+**14.** Implement the function ''​setOfDivByK''​ which returns the set of integers divisible by a value ''​k''​. Use the appropriate functions you have defined ​previously in the homework.
 <code scala> <code scala>
 def setOfDivByK(k:​ Int): Set = ?? def setOfDivByK(k:​ Int): Set = ??
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 ===== Submission rules ===== ===== Submission rules =====
  
-  * Please follow the [[fp2023:​submission-guidelines| Submission guidelines]] which are the same for all homework. +  * Please follow the [[fp2024:​submission-guidelines| Submission guidelines]] which are the same for all homework. 
-  * To solve your homework, download the {{:fp2023:​hw1-functions-as-sets.zip|Project template}}, import it in IntellIJ, and you are all set. Do not rename the project manually, as this may cause problems with IntellIJ.+  * To solve your homework, download the {{:fp2024:​hw1-functions-as-sets.zip| Project template}}, import it in IntellIJ, and you are all set. Do not rename the project manually, as this may cause problems with IntellIJ.