Understanding F# Value Restriction Errors

EDIT

Better/recent info is here: Keeping partially applied function generic

(original below)

I think a pragmatic thing here is not to try to understand this too deeply, but rather to know a couple general strategies to get past the VR and move on with your work. It’s a bit of a ‘cop out’ answer, but I’m not sure it makes sense to spend time understanding the intracacies of the F# type system (which continues to change in minor ways from release to release) here.

The two main strategies I would advocate are these. First, if you’re defining a value with a function type (type with an arrow ‘->’), then ensure it is a syntactic function by doing eta-conversion:

// function that looks like a value, problem
let tupleList = List.map (fun x -> x,x)
// make it a syntactic function by adding argument to both sides
let tupleList l = List.map (fun x -> x,x) l

Second, if you still encounter VR/generalizing problems, then specify the entire type signature to say what you want (and then ‘back off’ as F# allows):

// below has a problem...
let toleq (e:float<_>) a b = (abs ( a - b ) ) < e
// so be fully explicit, get it working...
let toleq<[<Measure>]'u> (e:float<'u>) (a:float<'u>) (b:float<'u>) : bool = 
    (abs ( a - b ) ) < e
// then can experiment with removing annotations one-by-one...
let toleq<[<Measure>]'u> e (a:float<'u>) b = (abs ( a - b ) ) < e

I think those two strategies are the best pragmatic advice. That said, here’s my attempt to answer your specific questions.

1. I don’t know.

2. ‘>’ is a fully generic function (‘a -> ‘a -> bool) which works for all types, and thus is_bigger generalizes. On the other-hand, ‘+’ is an ‘inline’ function which works on a handful of primitive types and a certain class of other types; it can only be generalized inside other ‘inline’ functions, otherwise it must be pinned down to a specific type (or will default to ‘int’). (The ‘inline’ method of ad-hoc polymorphism is how the mathematical operators in F# overcome the lack of “type classes”.)

3. This is the ‘syntactic function’ issue I discussed above; ‘let’s compile down into fields/properties which, unlike functions, cannot be generic. So if you want it to be generic, make it a function. (See also this question for another exception to this rule.)