CODEWITHSUNDEEP
smlsmlnj
JAN
JAN

Reputation: 21875

SML - Error: right-hand-side of clause doesn't agree with function result type [circularity]

Consider the following code :

fun g(a) =
let     fun h(b)=g(a) 
in  h end;

When I run it in SML , I get : 

- fun g(a) =
= let   fun h(b)=g(a)
= in    h end;
stdIn:55.5-57.10 Error: right-hand-side of clause doesn't agree with function re
sult type [circularity]
  expression:  'Z -> 'Y
  result type:  'Y
  in declaration:
    g = (fn a => let val <binding> in h end)

I can't understand the problem here : g(a) return h , but I don't see any specific return value in the declaration fun g(a) (i.e. nothing like fun g(a):int) , so why the error ?

Thanks

Upvotes: 1

Views: 3634

Answers (2)

cgon
cgon

Reputation: 1981

ML type inference system first identified your function g as an expression which takes a 'Z and returns 'Y. But then it sees that the result type of g is just 'Y and also which is the result type of earlier binding h. It can be expected to see binding of type Z -> Z->Y . However your function closure has an environment which is itself. So it is like binding g like this.

fun g a= g

ML type inference can not guess the types if your closure has an environment which is also itself.

You can declare these functions as follows. 

fun g(a) =
    let     
    fun h(b)=g(a) 
    in  
    h(a)
    end;

It is like 

fun g a = g a

This time your closure has just a body of itself. But it makes no sense...just an example of why you are getting a circularity error.

Upvotes: 1

molbdnilo
molbdnilo

Reputation: 66459

Since g has one parameter it has type 'X -> 'Y.

h(b) = g(a) means that h and g must have the same result type 'Y,
and h has the type 'Z -> 'Y.

Thus, g(x), for any x of type 'X, must have type 'Y.
But the return value of g(x) is h, which has type 'Z -> 'Y.
This means that 'Y must be the same type as 'Z -> 'Y, which is impossible.

As SML says, 'Z -> 'Y (the type of h) doesn't agree with 'Y (the type of g(a)).

If you try to work it out by hand, you'll find that

g 1

would be a function h such that

h 3

is the value of 

g 1

which is a function h such that...

and so on, indefinitely.

Upvotes: 3

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