Give an example of a WHILE-statement list S (written in core WHILE without extensions) such that: S{Xn,Y: m³} → {X: ˜n+2m³, Y:"0"} for all natural numbers n and m.
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- Define a function shuffle that takes a sequence with an even number of elements (cards) and creates a new list that interleaves the elements of the first half with the elements of the second half. Let's better understand what it means to shuffle a list in this way. Let's say there is some list [1, 2, 3, 4, 5, 6, 7, 8]. To interleave the first half [1, 2, 3, 4] with the second half [5, 6, 7, 8] means that your final list should contain the first element from the first half, then the first element from the second half, then the second element of the first half, then the second element of the second half and so on. So the interleaved version of [1, 2, 3, 4, 5, 6, 7, 8] would be [1, 5, 2, 6, 3, 7, 4, 8]. def card (n): """Return the playing card numeral as a string for a positive n 0 and n >> shuffle (range(6)) [0, 3, 1, 4, 2, 5] >>> suits = ['H', 'D', 'S', 'C'] >>> cards = [card (n) + suit for n in range (1,14) for suit in suits] >>> cards [:12] ['AH', 'AD', 'AS', 'AC', '2H', '2D', '25',…Python Using recursion only No loops Using such type()function, len()function, indexing, slicing The function must return true(boolean) if a list has sets otherwise returns false def hasSet(lst):Given the definition in Haskell: fmap :: (a -> b) -> [a] -> [b] fmap g xs = reverse (map g xs) With Functor law: (fmap g . fmap h) xs = fmap (g . h) xs Using list xs :: [Int], prove the definition does not satisfy the law:
- Define a function shuffle that takes a sequence with an even number of elements (cards) and creates a new list that interleaves the elements of the first half with the elements of the second half. Let's better understand what it means to shuffle a list in this way. Let's say there is some list [1, 2, 3, 4, 5, 6, 7, 8]. To interleave the first half [1, 2, 3, 4] with the second half [5, 6, 7, 8] means that your final list should contain the first element from the first half, then the first element from the second half, then the second element of the first half, then the second element of the second half and so on. So the interleaved version of [1, 2, 3, 4, 5, 6, 7, 8] would be [1, 5, 2, 6, 3, 7, 4, 8]. def card (n): """Return the playing card numeral as a string for a positive n 0 and n >> shuffle (range(6)) [0, 3, 1, 4, 2, 5] >>> suits = ['H', 'D', 'S', 'C'] >>> cards = [card (n) + suit for n in range (1,14) for suit in suits] >>> cards [:12] ['AH', 'AD', 'AS', 'AC', '2H', '2D', '25',…Write a legal WHILE-program that translates into the following programs-as-data notation: [ 0, ] 3 ] [ [while, [hd, [var, 0]], [[:=, 1, [hd, [t1 [var, 0]]]], [ if, [var, 1] [[:, 2, [cons, [quote, nil], [var, 1]]] , [:=, 3, [tl, [ tl, [var, 2]]]] ] [] ] ] ]Algorithm for Closing under multiplication with generatorsInput : a set S of generators of a group G;Output : a list of elements of the group G;
- Implement a function countMultiples in Python that: accepts a single argument, a 2-dimensional list (e.g, list of lists) containing non-negative integers, and returns the count of those integers that are multiples of 5 but that are not not multiples of 10. (e.g., 65 should be counted, but 80 should not be counted) sample usage: >>> countMultiples( [[1,2,3],[4,5],[6,7,8,9]] ) # 5 counts1Write a JavaScript function to sort a list with the insertion sort algorithm, but without mutation. And write a recursive lambda expression sum(l) in JavaScript to add all elements in the list. Assume l has ints.Write a python program to implement the different set operation Union, Intersection, Difference and Symmetric for the set. E= {Q, R, T, S, U} N= {B, Q, R, F, A}
- Define a Haskell function filterTriples that, given a list of integer triples, removes those that are not in ascending order of size. Use list comprehension to implement the function. Example: filterTriples [(1,2,3), (6,5,4), (7,7,7)] ↝ [(1,2,3), (7,7,Write a java function to find minimum moves required for making 2 List<Integer> equal. public int minimumOps(List<Integer> S, List<Integer> T){} The two possible moves are: shift(list) returns a new list after moving the front number to the back—i.e., [1, 2, 3 ,4 ] -----> [2, 3, 4, 1] reverse(list) returns the reverse of the list—i.e., [1, 2, 3, 4] -------> [4, 3, 2, 1] for example: consider S = {1, 2, 3, 4} and T = {2, 1, 4, 3}, we can see that T = shift ( shift( reverse( S ))) S = [1, 2 , 3 ,4] -----> [4, 3, 2, 1] ------>[3, 2, 1, 4] -------->[2, 1, 4, 3] = T = 3 moves total. But this is not the only way to transform S to T. To illustrate, here are some other sequence of operations : T = reverse(shift(shift(S))) T = shift(reverse(shift(S))) T = reverse(shift(shift(reverse(reverse(S)))))) Goal is to find the minimum moves on S list to form T list. Some more input/ output examples of length 5 minimumOps(List.of(1,2,3,4,5),…What are the conditions for testing whether a linked list T is empty, if T is a(i) simple singly linked list, (ii) headed singly linked list, (iii) simple circularlylinked list or (iv) headed circularly linked list?