What does this function signature mean in sml?

Question

I\'m looking through some notes that my professor gave regarding the language SML and one of the functions looks like this:

fun max gt = 
    let fun lp curr         


        

Answer 1

Just to clarify a bit on currying, from Faiz's excellent answer.

As previously stated SML only allows functions to take 1 argument. The reason for this is because a function fun foo x = x is actually a derived form of (syntactic sugar) val rec foo = fn x => x. Well actually this is not entirely true, but lets keep it simple for a second

Now take for example this power function. Here we declare the function to "take two arguments"

fun pow n 0 = 1 
  | pow n k = n * pow n (k-1)

As stated above, fun ... was a derived form and thus the equivalent form of the power function is

val rec pow = fn n => fn k => ...

As you might see here, we have a problem expressing the two different pattern matches of the original function declaration, and thus we can't keep it "simple" anymore and the real equivalent form of a fun declaration is

val rec pow = fn n => fn k =>
    case (n, k) of 
      (n, 0) => 1
    | (n, k) => n * pow n (k-1)

For the sake of completeness, cases is actually also a derived form, with anonymous functions as the equivalent form

val rec pow = fn n => fn k => 
    (fn (n,0) => 1
      | (n,k) => n * pow n (k-1)) (n,k)

Note that (n,k) is applied directly to the inner most anonymous function.