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?
There are various things wrong:
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.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
Regarding the anonymous functions,
fun implies x y = (not x) orelse y
can be written as
val implies = fn x => fn y => (not x) orelse y
however as you see, it doesn't really make any sense to do it this way (in this particular case).
Anonymous functions in SML only take one argument. Currying of arguments works because the fun keyword is syntactic sugar (also called a derived form) of
val rec implies = fn x => fn y =>
case (x, y) of
(x,y) => (not x) orelse y
The case is used because we could have had some pattern matching in the original function, which is then translated directly down into the case, and the rec is because the original function might have been recursive.
Thus the second example @pad gave is equivalent to:
val rec implies = fn x => fn y =>
case (x, y) of
(false, false) => true
| (false, true) => true
| (true, false) => false
| (true, true) => true
