Value restriction of F#

In F#, we can declare a polymorphic value

> let a = [];; 

val a : 'a list

However, if we make it mutable, fsharpi complains with value restriction error

> let mutable a = [];;

  let mutable a = [];;

/Users/kseo/stdin(1,13): error FS0030: Value restriction. The value 'a' has been inferred to have generic type
    val mutable a : '_a list    
Either define 'a' as a simple data term, make it a function with explicit arguments or, if you do not intend for it to be generic, add a type annotation.
> let a = [];; 

val a : 'a list

This looks unreasonable at first! But let’s see what happens if we get rid of this restriction.

let mutable a = []
let f x = a <- (x :: a)

f(“Hello World”);;

The type of function f is ‘a -> unit. Hence f(1), f(true) and f(“Hello World”) type check. However, a ends up having three different types [“Hello World”; true; 1]. Oops! So, the type system of F# has a rule called value restriction to prevent this kind of bad behaviour.

In fact, all ML family languages have value restriction. See Notes on SML97’s Value Restriction for further information.

Emulating Haskell type classes in F#

One language feature I like most in Haskell is type class. It was originally conceived as a way of implementing overloaded arithmetic and equality operators. It is a clever trick to support ad-hoc polymorphism, which does not require extensive modifications of the compiler or the type system.

F# does not provide type class, but we can emulate it with other F# language features such as operator overloading and inline function. Type Classes for F# shows this trick. Here’s the Functor example taken from the blog:

type Fmap = Fmap with
    static member ($) (Fmap, x:option<_>) = fun f -> f x
    static member ($) (Fmap, x:list<_>  ) = fun f ->   f x
let inline fmap f x = Fmap $ x <| f

Here, fmap function must be inline because inline functions can have statically resolved type parameters. Without the inline modifier, type inference forces the function to take a specific type. In this case, the compiler can’t decide between option and list and emits an error.

You can use it as in the following:

> fmap ((+) 2) [1;2;3] ;;
val it : int list = [3; 4; 5]
> fmap ((+) 2) (Some 3) ;;
val it : int option = Some 5

I transliterated the TreeRec example of Simon Thompson’s paper, Higher-order + Polymorphic = Reusable into F# by emulating type class in this way.

type Tree<'a> =
    | Leaf
    | Node of 'a * Tree<'a> * Tree<'a>

type LeafClass = LeafClass with
    static member ($) (LeafClass, t:'a list)  = []
    static member ($) (LeafClass, t:Tree<'a>) = Leaf
let inline leaf () : ^R = (LeafClass $ Unchecked.defaultof< ^R> )

type NodeClass = NodeClass with
    static member ($) (NodeClass, l1:'a list)  = fun a l2 -> List.concat [l1; [a]; l2]
    static member ($) (NodeClass, t1:Tree<'a>) = fun a t2 -> Node(a, t1, t2)
let inline node a x1 x2 = (NodeClass $ x1) a x2

type TreeRecClass = TreeRecClass with
    static member ($) (TreeRecClass, l:'a list) = fun f st ->
        let listToTree = function
            | [] -> failwith "listToTree"
            | a::x ->
                let n = List.length x / 2
                let l1 = Seq.take n x |> Seq.toList
                let l2 = Seq.skip n x |> Seq.toList
                (a, l1, l2)
        let rec treeRec' = function
            | [] -> st
            | l ->
                let a, t1, t2 = listToTree l
                let v1 = treeRec' t1
                let v2 = treeRec' t2
                f v1 v2 a t1 t2
        treeRec' l
    static member ($) (TreeRecClass, t:Tree<'a>) = fun f st ->
        let rec treeRec' f st = function
            | Leaf -> st
            | Node(a, t1, t2) -> f (treeRec' f st t1) (treeRec' f st t2) a t1 t2
        treeRec' f st t
let inline treeRec f st x = (TreeRecClass $ x) f st

let inline tSort x =
     // FIXME: Implement sorting!
    let mVal sort1 sort2 v = List.concat [sort1; sort2; [v]]
    let mergeVal sort1 sort2 v t1 t2 = mVal sort1 sort2 v
    treeRec mergeVal [] x

One problem with this approach is that we no longer can group related operations together into a single class. It can’t express that Tree-like type t* has three operations: leaf, node and treeRec. We end up having three distinct types LeafClass, NodeClass and TreeRecClass.