Notes on exercise 6.2.(14-17)

These exercises make use of a recursively defined type that models mathematical expressions:

datatype operation = Plus | Minus | Mul | Div;
datatype expression =  Internal of operation * expression * expression
      | Leaf of int;

For example, the expression ((3 + 7) * 8) would be Internal(Mul, Internal(Plus, Leaf(3), Leaf(7)), Leaf(8)).

Exercise 6.2.14 asks you to turn a value in the expression datatype into a string showing how the expression would normally appear in mathematical notation. For example,

printExpression(Internal(Mul, Internal(Plus, Leaf(3), Leaf(7)), Leaf(8)));

should result in

((3 + 7) * 8)

We haven't done much with strings this semester, but it doesn't require very much. All you need to know is

• You can turn an int into a string by using Int.toString(). Compare the printTree() function we did in class.
• I have provided the following function that turns values of the operation datatype into strings:

  fun printOper(Plus) = "+"
    | printOper(Minus) = "-"
    | printOper(Mul) = "*"
    | printOper(Div) = "/";
  

• You can concatenate strings with ^, which works just like @ does on lists.

Also, Exercise 6.2.14 has a misprint. It isn't Section 2.5 that has information about strings but rather Section 1.7.

For Exercise 6.2.15, write a function that evaluates the expression. For example,

execute(Internal(Mul, Internal(Plus, Leaf(3), Leaf(7)), Leaf(8)));

should result in

80

I'll go one step further and give you a stub for this:

fun execute(Leaf(x)) = ??
  | execute(Internal(Plus, left, right)) = ??
  | execute(Internal(Minus, left, right)) = ??
  | execute(Internal(Mul, left, right)) = ??
  | execute(Internal(Div, left, right)) = ??