Tail Call Optimization in F# - f#

Question

I could really do with some help with tail call optimization in F#.
I am trying to parse a tree like structure and perform a calculation on each leaf.
The function I'm having problems with is calcLength
type Location = float * float
type Radius = float
type Width = float
type Angle = float
type Primitive =
| Circle of Location * Radius
| Ellipse of Location * Radius * Radius
| Square of Location * Width * Angle
| MultiPrimitive of Primitive List
type Primitive with
member x.Length =
let rec calcLength x =
match x with
| Circle (_,r) -> System.Math.PI * r * 2.
| Ellipse (_,r1,r2) -> System.Math.PI * 2. * sqrt( (r1 * r1 ) + (r2 * r2 ) / 2.)
| Square (_, w,_) -> w * 4.
| MultiPrimitive [] -> 0.
| MultiPrimitive (head::tail) -> calcLength (MultiPrimitive tail) + (calcLength head)
[<Fact>]
let ``test discriminated unions``() =
let pattern = MultiPrimitive(
[
MultiPrimitive(
[
MultiPrimitive(
[
Square( (10.,10.), 10., 45. );
Circle( (3.,7.), 3. );
Circle( (7.,7.), 3. );
Square( (5.,2.), 3., 45. );
] );
Square( (10.,10.), 10., 45. );
Circle( (3.,7.), 3. );
Circle( (7.,7.), 3. );
Square( (5.,2.), 3., 45. );
] );
Square( (10.,10.), 10., 45. );
Circle( (3.,7.), 3. );
Circle( (7.,7.), 3. );
Square( (5.,2.), 3., 45. );
] )
let r = pattern.Length
I attempted to use the continuation approach with the following:
let rec calcLength x f =
match x with
| Circle (_,r) -> f() + System.Math.PI * r * 2.
| Ellipse (_,r1,r2) -> f() + System.Math.PI * 2. * sqrt( (r1 * r1 ) + (r2 * r2 ) / 2.)
| Square (_, w,_) -> f() + w * 4.
| MultiPrimitive [] -> f()
| MultiPrimitive (head::tail) -> calcLength head (fun () -> calcLength(MultiPrimitive tail) f )
calcLength x (fun () -> 0.)
But stepping through with the debugger showed the stack growing, any help would be Really appreciated.

Answer 1

The usual way to use CPS is to pass the result to the given continuation:
let rec calcLength x k =
match x with
| Circle (_,r) -> k (System.Math.PI * r * 2.)
| Ellipse (_,r1,r2) -> k (System.Math.PI * 2. * sqrt( (r1 * r1 ) + (r2 * r2 ) / 2.))
| Square (_, w,_) -> k (w * 4.)
| MultiPrimitive [] -> k 0.
| MultiPrimitive (head::tail) -> (calcLength head (fun h -> calcLength(MultiPrimitive tail) (fun t -> k (h + t))))
so in the MultiPrimitive case you need to pass another continuation to deal with the result from calculating the head.