Haskell CW II.4

Please write type signatures for all of your functions.

Introduction

demo n xs = [ n*x | x <- xs]

1. Write an example of how you would call demo.

2. What is the type signature of demo assuming we make all numbers Int.

3. Add an exception so that demo 0 anything always returns the empty list.

4. We are going to learn about the (x:xs) pattern that we use to write recursive functions, like first and rest from Racket. Use that method to write a recursive version of the demo function.

5. Check for understanding: write mylength, a recursive function that finds the length of a list of numbers.

Exercises

1. Write a function f that takes in an Int and always returns 5.

2. Change f so that when the input is 0 it returns 8, and when the input is 1 it returns 13.

3. Change f more so that it makes a Fibonacci sequence beginning with the 8 and 13 that you already have. $$f(n) = f(n-1) + f(n-2).$$

4. Write a function sub5 that takes in a list of integers and puts out a list of integers five less than the inputs.

5. Write a function skip13 that takes in a list of integers and puts out a list of integers that is the same except excluding any 13s.

6. (sumByHand): Write a recursive function that adds all of the numbers in a list.

7. Write a function before14 that takes in a list of integers and inserts a 13 before every 14 in the list.