https://twitter.com/eiriktsarpalis/status/469943697678012416

gistfile1.fs

open System

type StringToExnClass = StringToExnClass with
    static member StringToExn (_: ArgumentNullException) = fun (s: string) -> ArgumentNullException s
    static member StringToExn (_: AccessViolationException) = fun (s: string) -> AccessViolationException s
    static member StringToExn (_: ArrayTypeMismatchException) = fun (s: string) -> ArrayTypeMismatchException s
    // etc (need to wrap all relevant types)

let inline iStringToExn (a: ^a, b: ^b) =
    ((^a or ^b) : (static member StringToExn: ^b -> (string -> ^b)) b)

let inline strToExn (x: string) : 'a when 'a :> exn = iStringToExn (StringToExnClass, Unchecked.defaultof<'a>) x

let inline failwithe (msg: string) : 'a when 'a :> exn = 
    let e = iStringToExn (StringToExnClass, Unchecked.defaultof<'a>) msg // to use strToExn here apparently you need to redeclare the static member constraints.
    raise e // shouldn't really return 'a

let _ : ArgumentNullException = failwithe "blah"

exception SomeOtherException
let _ : SomeOtherException = failwithe "whee" // does not compile because there is no string -> 'a constructor and SomeOtherException is not part of the StringToExn "typeclass"

In the end, I came up with this https://gist.github.com/eiriktsarpalis/8feb78f1f2ee7b6bfd02

The implementation is much more trivial than the typeclass approach and is cumbersome for anything other than F# exceptions, but I figured that it is probably easier to actually use and read. Plus, the F# compiler should optimise away any redundant lambdas.