Question

val implies =
    fn x y = case x of false andalso case y of false => true
     | fn x y = case x of false andalso case y of true => true
     | fn x y = case x of true andalso case y of false => false
     | fn x y = case x of true andalso case y of true => true;  

I can’t get this to compile. I’m relatively new to SML so not quite getting the general language and syntax. What have I done wrong?

Answer 1

There are various things wrong:

• There is no arguments in implies to do pattern matching directly.
• case x of is for pattern matching with specific values, not like if/else expression which accepts boolean expressions.
• The syntax for lambda should start with fn x => ....

A quick fix:

fun implies x y =
    case (x, y) of
      (false, false) => true
    | (false, true) => true
    | (true, false) => false
    | (true, true) => true

which can be rewritten for readability as:

fun implies false false = true
  | implies false true = true
  | implies true false = false
  | implies true true = true

or more concise by using propositional logic rule:

fun implies x y = (not x) orelse y