"operator is not a function" on `$` Usage - sml

Question

Given the following:
// credit to http://stackoverflow.com/questions/28802305/trying-to-define-type
datatype 'alpha susp = $ of 'alpha
fun sum n = if n = 0 then 1
else n + sum(n-1)
What does this error mean?
- use "Lazy.sml";
[opening Lazy.sml]
datatype 'a susp = $ of 'a
val sum = fn : int -> int
val it = () : unit
- val foo = $sum 100000000000;
stdIn:17.5-17.28 Error: operator is not a function [tycon mismatch]
operator: (int -> int) susp
in expression:
($ sum) 100000000000

Answer 1

after you declare a new datatype, you should use it as a function(actually it is indeed turned into a function):
- datatype 'alpha susp = $ of 'alpha;
datatype 'a susp = $ of 'a
- fun sum n = if n = 0 then 1
= else n + sum(n-1);
val sum = fn : int -> int
- $(sum 10);
val it = $ 56 : int susp
- $;
val it = fn : 'a -> 'a susp
update
in your question, you have error:
- val foo = $sum 100000000000;
stdIn:17.5-17.28 Error: operator is not a function [tycon mismatch]
operator: (int -> int) susp
in expression:
($ sum) 100000000000
notice that:
[tycon mismatch]
and
operator: (int -> int) susp
in expression:
($ sum) 100000000000
it means it's a type error, the type mismatched. you should know function in sml takes only one parameter, so it's very easy to find out the association:
the expression $ sum 100000000000 is equivalent to (($ sum) 100000000000), which means you create a variable ($ sum) first, which has a type of (int -> int) susp, and then use it as a function and pass parameters to it, which cause this error.
actually the way you call this functions as a chain has a name in sml(or even in general functional programming), called curry. you can have a look at corresponding documentation.