In Standard ML, a type constructor is a function from types to types. Type constructors can be nullary, meaning that they take no arguments, as in char, int, and real. Type constructors can be unary, meaning that they take one argument, as in array, list, and vector. A program can define a new type constructor in two ways: a type definition or a datatype declaration. User-defined type constructors can can take any number of arguments.

datatype t = T of int * real            (* 0 arguments *)
type 'a t = 'a * int                    (* 1 argument *)
datatype ('a, 'b) t = A | B of 'a * 'b  (* 2 arguments *)
type ('a, 'b, 'c) t = 'a * ('b  -> 'c)  (* 3 arguments *)

Here are the syntax rules for type constructor application.

• Type constructor application is written in postfix. So, one writes int list, not list int.

• Unary type constructors drop the parens, so one writes int list, not (int) list.

• Nullary type constructors drop the argument entirely, so one writes int, not () int.

• N-ary type constructors use tuple notation; for example, (int, real) t.

• Type constructor application associates to the left. So, int ref list is the same as (int ref) list.