Local procedures and recursion

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: The last element
  • Exercise 2: Alternating lists
  • Exercise 3: Iota, revisited
  • Exercise 4: Taking some elements
  • Exercise 5: Intersection
• Notes

Exercises

Exercise 0: Preparation

Read the corresponding notes on letrec and name let.

Exercise 1: The last element

Write a letrec-expression in which (a) the identifier last-of-list is locally bound to a procedure that finds and returns the last element of a given list, and (b) the body of the expression computes the sum of the last elements of the lists (3 8 2), (7), and (8 5 9 8), invoking last-of-list three times.

Exercise 2: Alternating lists

A non-empty list is an s-n-alternator if its elements are alternately symbols and numbers, beginning with a symbol. It is an n-s-alternator if its elements are alternately numbers and symbols, beginning with a number.

Write a letrec-expression in which (a) the identifiers s-n-alternator? and n-s-alternator? are bound to mutually recursive predicates, each of which determines whether a given non-empty list has the indicated characteristic, and (b) the body invokes each of these predicates to determine whether the list (2 a 3 b 4 c 5) fits either description.

Exercise 3: Iota, revisited

As you may recall, Iota takes a natural number as argument and returns a list of all the lesser natural numbers in ascending order.

a. Define and test a version of the iota procedure that uses letrec to pack a tail-recursive kernel inside a husk that performs precondition testing.

b. Define and test a version of the iota procedure that uses a named let.

Exercise 4: Taking some elements

Define and test a procedure named take that takes a list ls and a non-negative integer len as arguments and returns a list consisting of the first len elements of ls, in their original order. The procedure should signal an error if ls is not a list, if len is not an exact integer, if len is negative, or if len is greater than the length of ls.

Exercise 5: Intersection

a. Define and test a procedure named intersection that takes two lists of symbols, left and right, as arguments and returns a list of which the elements are precisely those symbols that are elements of both left and right.

b. What does your proceduer do if a symbol appears in both lists and appears more than once in one or both of the lists?

Notes