The F# compiler includes a Units of Measure feature which infers a measure type at compile time, which means you get measure type safety with uncompromised runtime performance.

Example of F#’s built-in Units of Measure feature (hover over shows inferred type):

Sometimes you might also want to actually infer units of measure at runtime, say to display the inferred unit type at the UI. The following F# code prototype provides such inference.

Lets start by defining some metres and seconds unit types:

let m = UnitType.Create("m")
let s = UnitType.Create("s")

Now with the source below we can explore types in F# Interactive:

> 10.0 * m;;
val it : UnitValue = 10 m {Unit = Unit ("m",1);
Value = 10.0;}
> 10.0 * m / 5.0 * s;;
val it : UnitValue = 2 m s {Unit = CompositeUnit [Unit("m",1); Unit("s",1)];
Value = 2.0;}

Source code to F# runtime units of measure:

type UnitType =
| Unit of string * int
| CompositeUnit of UnitType list
static member Create(s) = Unit(s,1)
override this.ToString() =
let exponent = function
| Unit(_,n) -> n
| CompositeUnit(_) ->
raise (new System.InvalidOperationException())
let rec toString = function
| Unit(s,n) when n=0 -> ""
| Unit(s,n) when n=1 -> s
| Unit(s,n) -> s + " ^ " + n.ToString()
| CompositeUnit(us) ->
let ps, ns =
us |> List.partition (fun u -> exponent u >= 0)
let join xs =
let s = xs |> List.map toString |> List.toArray
System.String.Join(" ",s)
match ps,ns with
| ps, [] -> join ps
| ps, ns ->
let ns = ns |> List.map UnitType.Reciprocal
join ps + " / " + join ns
match this with
| Unit(_,n) when n < 0 -> " / " + toString this
| _ -> toString this
static member ( * ) (v:ValueType,u:UnitType) = UnitValue(v,u)
static member ( * ) (lhs:UnitType,rhs:UnitType) =
let text = function
| Unit(s,n) -> s
| CompositeUnit(us) -> us.ToString()
let normalize us u =
let t = text u
match us |> List.tryFind (fun x -> text x = t), u with
| Some(Unit(s,n) as v), Unit(_,n') ->
us |> List.map (fun x -> if x = v then Unit(s,n+n') else x)
| Some(_), _ -> raise (new System.NotImplementedException())
| None, _ -> us@[u]
let normalize' us us' =
us' |> List.fold (fun (acc) x -> normalize acc x) us
match lhs,rhs with
| Unit(u1,p1), Unit(u2,p2) when u1 = u2 ->
Unit(u1,p1+p2)
| Unit(u1,p1), Unit(u2,p2) ->
CompositeUnit([lhs;rhs])
| CompositeUnit(us), Unit(_,_) ->
CompositeUnit(normalize us rhs)
| Unit(_,_), CompositeUnit(us) ->
CompositeUnit(normalize' [lhs] us)
| CompositeUnit(us), CompositeUnit(us') ->
CompositeUnit(normalize' us us')
| _,_ -> raise (new System.NotImplementedException())
static member Reciprocal x =
let rec reciprocal = function
| Unit(s,n) -> Unit(s,-n)
| CompositeUnit(us) -> CompositeUnit(us |> List.map reciprocal)
reciprocal x
static member ( / ) (lhs:UnitType,rhs:UnitType) =
lhs * (UnitType.Reciprocal rhs)
static member ( + ) (lhs:UnitType,rhs:UnitType) =
if lhs = rhs then lhs
else raise (new System.InvalidOperationException())
and ValueType = float
and UnitValue(v:ValueType,u:UnitType) =
member this.Value = v
member this.Unit = u
override this.ToString() = sprintf "%O %O" v u
static member (+) (lhs:UnitValue,rhs:UnitValue) =
UnitValue(lhs.Value+rhs.Value, lhs.Unit+rhs.Unit)
static member (*) (lhs:UnitValue,rhs:UnitValue) =
UnitValue(lhs.Value*rhs.Value,lhs.Unit*rhs.Unit)
static member (*) (lhs:UnitValue,rhs:ValueType) =
UnitValue(lhs.Value*rhs,lhs.Unit)
static member (*) (v:UnitValue,u:UnitType) =
UnitValue(v.Value,v.Unit*u)
static member (/) (lhs:UnitValue,rhs:UnitValue) =
UnitValue(lhs.Value/rhs.Value,lhs.Unit/rhs.Unit)
static member (/) (lhs:UnitValue,rhs:ValueType) =
UnitValue(lhs.Value/rhs,lhs.Unit)
static member (/) (v:UnitValue,u:UnitType) =
UnitValue(v.Value,v.Unit/u)

**Implementation details:**

Unit (*UnitType*) computations are separate from value (*UnitValue*) computations. A single unit types (say metres) just has a name and a power (default of 1):

*let metres = Unit(name = “metres”, power = 1)*

To multiply by the same unit type, simply add the powers:

*(2.0 * metres) * (3.0 metres) = 6.0 metres ^ 2*

To handle composite unit types, when multiplying 2 unit values, first try to find a matching unit type in the existing list, if successful add the powers, otherwise add the new type:

*2.0 * metres * seconds = 2 .0 metres (per) second*

To divide simply multiply by the reciprocal:

*(2.0 * metres * seconds) / (1.0 * seconds) = 2.0 metres per second * 1.0 seconds ^ -1*

**Resources:**