Evaluating this function:

val constantly = fn k => (fn a => k);

Yields this SML signature:

val constantly = fn : 'a -> 'b -> 'a

yet Harper's book says the function has this signature:

'a -> ('b -> 'a)

My questions are

1. how does Harper's signature differ from the one given by SML?

2. how would the SML signature differ in meaning from this:

val constantly = fn : ('a -> 'b) -> 'a

3. Is it possible that the 'b in the SML signature could actually be the same type as 'a ? Is there something which restricts the type of the input to the function returned from constantly from being the same as it outputs?

---

sweeks speaks:

[12:15] <sweeks> 1. 'a -> 'b -> 'a is the same as 'a -> ('b -> 'a)

[12:17] <sweeks> 2. 'a -> ('b -> 'a) takes an argument of type 'a, while ('a -> 'b) -> 'a takes a function as an argument.

[12:18] <sweeks> 3. When instantiating a polymorphic function, different type variables can be instantiated with the same types.

two-step use of closure

I wanted to bind the closure to a variable and then get the result of calling the closure, but it was not so easy:

- val g = constantly 5.0; 
stdIn:35.1-35.23 Warning: type vars not generalized because of 
   value restriction are instantiated to dummy types (X1,X2,...) 
val g = fn : ?.X1 -> real 
- g 50; 
stdIn:36.1-36.5 Error: operator and operand don't agree [literal] 
  operator domain: ?.X1 
  operand:         int 
  in expression: 
    g 50 
- (g) 50; 
stdIn:1.1-1.7 Error: operator and operand don't agree [literal] 
  operator domain: ?.X1 
  operand:         int 
  in expression: 
    g 50 
-

but sweeks saved the day:

[12:38] <sweeks> True, but the type system requires a type to be chosen at the declaration of g.
[12:39] <sweeks> You can work around this peculiarity with val g: 'a -> real = fn z => constantly 5.0 z
[12:40] <metaperl> ok and when you provide arguments to constantly with a space in between, what does that  mean?
[12:40] <metaperl> e.g., val m = constantly 5.0 9;
[12:41] <sweeks> As you said, the type of "constantly 5.0" is "ANY -> real", i.e. it is a function.
[12:41] *** palomer (~palomer@MTL-ppp-147087.qc.sympatico.ca) joined
[12:41] <sweeks> So, "constantly 5.0 9" applies that function.
[12:43] <metaperl> you mean constantly 5.0 9 is the same as (constantly 5.0) 9
[12:43] <sweeks> yes
[12:43] <metaperl> or perhaps ( (constantly 5.0) 9)
[12:43] <metaperl> both work?
[12:43] <sweeks> yes