What is the difference between 'a and '_l?

Question

What is the difference between 'a and '_l?

I was looking at this error, and couldn't comprehend it:

Error: This expression has type ('a -> float polynomial) list but an expression was expected of type float polynomial list derivlist: ('_l → float polynomial) list

Answer 1

_ denotes a weakly polymorphic variable : it is in a position where it cannot be generalized.

There are two explanations related to weak polymorphism in the OCaml FAQ: see A function obtained through partial application is not polymorphic enough and the next one.

This generally happens when you're using a non-local reference (whose type cannot be generalized), or when defining polymorphic functions that are not syntactically functions (they do not begin with fun x -> .. but rather a function application). In some cases there is an easy fix (eta-expansion, see the FAQ), sometimes there isn't, and sometimes your program was just unsound.

An easy example : let a = ref [] does not get the polymorphic a list ref type. Otherwise you could use both as a int list and a bool list, and mix elements of different types by mutating the reference. It instead get a '_a list ref type. This mean that the type is not polymorphic, but merely unknown. Once you do something with a with a particular type, it fixes '_a once and for all.

# let a = ref [];;
val a : '_a list ref = {contents = []}
# let sum_of_a = List.fold_left (+) 0 !a;;
val sum_of_a : int = 0
# a;;
- : int list ref = {contents = []}

For an in-depth explanation of value restriction and the "relaxed" value restriction actually implemented in the OCaml type checker, see the Relaxing the Value Restriction paper by Jacques Garrigue (2004).

Answer 2

There is a weak type variable in the error message from the compiler, but I am not sure that the weak variable is related to the error (I do not see how the status of the type variable could be the cause of this message).

Are you sure that you are not defining two types polynomial? That's the question just above the two pointed out by gashe in his answer in the FAQ ("Error message: a type is not compatible with itself").