An Introduction to Functional Programming Through Lambda Calculus

- 207 -iv) find the sum of applying a function fun to the numbers between n and zero in steps of s.2) (c.f. Chapter 6 Exercise 2)i) Write a function which indicates whether or not a list starts with a sub-list. For example:(lstarts ’(1 2 3) ’(1 2 3 4 5)) ->t(lstarts ’(1 2 3) ’(4 5 6)) ->nilii) Write a function which indicates whether or not a list contains a given sub-list. For example:(lcontains ’(4 5 6) ’(1 2 3 4 5 6 7 8 9)) ->t(lcontains ’(4 5 6) ’(2 4 6 8 10)) ->niliii) Write a function which counts how often a sub-list appears in another list. For example:(lcount ’(1 2) ’(1 2 3 1 2 3 1 2 3)) ->3iv) Write a function which removes a sub-list from the start of a list, assuming that you know that the sub-liststarts the list. For example:(lremove ’(1 2 3) ’(1 2 3 4 5 6 7 8 9)) ->(4 5 6 7 8 9)v) Write a function which deletes the first occurence of a sub-list in another list. For example:(ldelete ’(4 5 6) ’(1 2 3 4 5 6 7 8 9) ->(1 2 3 7 8 9)(ldelete ’(4 5 6) ’(2 4 6 8 10)) ->(2 4 6 8 19)vi) Write a function which inserts a sub-list after the first occurence of another sub-list in a list. For example:(linsert ’(4 5 6) ’(1 2 3) ’(1 2 3 7 8 9)) ->(1 2 3 4 5 6 7 8 9)(linsert ’(4 5 6) ’(1 2 3) ’(2 4 6 8 10)) ->(2 4 6 8 10)vii) Write a function which replaces a sub-list with another sub-list in a list. For example:(lreplace ’(6 5 4) ’(4 5 6) ’(9 8 7 6 5 4 3 2 1)) ->(9 8 7 4 5 6 3 2 1)(lreplace ’(6 5 4) ’(4 5 6) ’(2 4 6 8 10)) ->(2 4 6 8 10)3) (c.f. Chapter 6 Exercise 3)