comparing with equal operator in fsharp - f#

Question

If I have the next type:
type Color(r: float, g: float, b:float) =
member this.r = r
member this.g = g
member this.b = b
static member ( * ) (c1:Color, c2:Color) =
Color (c1.r*c2.r, c1.g*c2.g, c1.b*c2.b)
static member Zero = Color(0.0,0.0,0.0)
and I do:
let ca = Color(1.,1.,1.)
let cb = Color(1.,1.,1.)
ca = cb
I should obtain true, but the F# interactive via a script is giving me false
Instead, If I define as:
let ca = Color(1.,1.,1.)
let cb = ca
ca = cb
It returns true
Am I doing something wrong trying to compare two values of a defined type in this way?
How can I do it to obtain true as a result?
Thanks

Answer 1

The OP definition of Color is a class. Classes have referential equality by default, just like in C#. That means they're only equal if they literally are the same object (points to the same memory address).
Only the functional data types in F# have structural equality. These include records, discriminated unions, lists, and a few other types.
It'd be more idiomatic to define Color as a record:
type Color = { Red : float; Green : float; Blue : float }
This type has structural equality built in:
> let ca = { Red = 1.; Green = 1.; Blue = 1. };;
val ca : Color = {Red = 1.0;
Green = 1.0;
Blue = 1.0;}
> let cb = { Red = 1.; Green = 1.; Blue = 1. };;
val cb : Color = {Red = 1.0;
Green = 1.0;
Blue = 1.0;}
> ca = cb;;
val it : bool = true
If you want to define multiplication and zero for the type, you can do that as well:
let (*) x y = {
Red = x.Red * y.Red
Green = x.Green * y.Green
Blue = x.Blue * y.Blue }
let zero = { Red = 0.0; Green = 0.0; Blue = 0.0 }
This enables you to write, e.g.:
> let product = ca * cb;;
val product : Color = {Red = 1.0;
Green = 1.0;
Blue = 1.0;}

Answer 2

F# implements automatic memberwise comparison for records and unions, but not for classes. If you want to have it and construct values with the Color(r, g, b) syntax, you can use a single-case union. You will get pattern matching as a bonus (see my implementation of (*)).
type Color =
| Color of r: float * g: float * b: float
member this.r = let (Color(r, _, _)) = this in r
member this.g = let (Color(_, g, _)) = this in g
member this.b = let (Color(_, _, b)) = this in b
static member (*) (Color(r1, g1, b1), Color(r2, g2, b2)) =
Color(r1 * r2, g1 * g2, b1 * b2)
static member Zero = Color(0., 0., 0.)

Answer 3

To start you should read this page:
http://blogs.msdn.com/b/dsyme/archive/2009/11/08/equality-and-comparison-constraints-in-f-1-9-7.aspx
It does a great job of illustrating how equality works in F#.
As to your specific issue, you are looking at the difference between Reference Equality and Structural Equality. You can add the following annotation
[<CustomEquality; CustomComparison>]
And you can add overloads to the Equals method override x.Equals(other) to do your memberwise comparision