GIML: Tutorial Four

Recursion with lists

1. Define sum and doublist as shown. Execute both functions on the list [5,3,1]. fun sum nil = 0 | sum(h::t) = h + sum t; fun doublist nil = nil | doublist(h::t) = 2*h :: doublist t;
2. Define and test the following functions. An example execution has been given for each case. len [4, 2, 5, 1] = 4 triplist [4, 2, 5, 1] = [12, 6, 15, 3] duplist [4, 2, 5, 1] = [4, 4, 2, 2, 5, 5, 1, 1] prodlist [4, 2, 5, 1] = 40 Check the function prodlist. If you always get the result zero it is probably because you have the base case wrong. Consider how ML executes a simple case such as prodlist [1]. Consider also that just as the result of adding all the elements in an empty list is zero - the identity element for addition, so the result of multiplying all the elements of an empty list is one, the identity element for multiplication. If you still need convincing of this then remember that 5³ is five to the power three - what you get from multiplying three fives. However 5⁰ is one, the result of multiplying no fives.
3. Define the function vallist which turns character digits into integers. You will need to use the in-built function ord. vallist ["4","2","5","1"] = [4,2,5,1]
4. Define the function rev which reverses the order of a list. Note the comments made about adding elements to lists earlier. fun rev nil = nil | rev(h::t) = (rev t)@ ??;
5. Define the following functions. space ["a","b","c"] = ["a"," ","b"," ","c"," "] flatten [[1,2],[3],[4,5]] = [1,2,3,4,5] count_1's [4,3,1,6,1,1,2,1] = 4 timeslist 4 [4, 2, 5, 1] = [16, 8, 20, 4] last [4, 2, 5, 1] = 1 member (3, [4, 2, 5, 1]) = false member (5, [4, 2, 5, 1]) = true