Phillip Trelford's Array

POKE 36879,255

Runtime Units of Measure for F#

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):

metres per second

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 |> toString |> List.toArray             
                    System.String.Join(" ",s)
                match ps,ns with 
                | ps, [] -> join ps
                | ps, ns ->
                    let ns = ns |> 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 |> (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), Unit(u2,p2) ->            
        | 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 |> 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) =                    
    static member (*) (lhs:UnitValue,rhs:ValueType) =        
    static member (*) (v:UnitValue,u:UnitType) = 
    static member (/) (lhs:UnitValue,rhs:UnitValue) =                    
    static member (/) (lhs:UnitValue,rhs:ValueType) =
    static member (/) (v:UnitValue,u:UnitType) = 

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


Exposing F# Dynamic Lookup to C#, WPF & Silverlight

Like C#, F# is primarily a statically typed programming language. That said both languages provide support for dynamic typing.

Sometimes dynamic typing can be a pragmatic way of solving a specific problem. For example say you’re a solutions provider with a core product and have a number of clients with bespoke requirements. One client asks for a product rating feature. This can be relatively easily achieved using dynamic properties:

  • a bunch of client specific properties are read from the database, including the rating value, which is then set as a dynamic property on the product object
  • zero changes are required to the core code
  • at the UI, on WPF, the dynamic property can simply be bound through XAML like any other object property
  • on Silverlight 4,0 direct binding is not currently possible, however there is a simple workaround - specifying the dynamic property as a parameter for a value converter (example later)

C# and F# use slightly different approaches for dynamic properties:

  • C# 4.0 provides a dynamic type, which tells the compiler that member lookup on the object should be deferred to run time
  • F# employs a dynamic lookup operator, which when overloaded defines the behaviour at runtime. This means that in F# dynamic lookup is explicit (the ? operator), and can be mixed with static lookup on the same object (the . operator)

Is it is still possible to implement dynamic properties in F# that can be consumed by other .Net languages like C#, VB.Net, IronRuby or IronPython; plus WPF and Silverlight. The trick is to inherit from .Net 4.0’s System.Dynamic.DynamicObject type and implement the System.ComponentModel.INotifyPropertyChanged interface:

open System.Dynamic

/// Dynamic Lookup type
type DynamicLookup () =
    inherit DynamicObject ()
    /// Synchronization object
    let sync = obj()
    /// Property Changed event
    let propertyChanged = Event<_,_>()    
    /// Properties
    let mutable properties = Map.empty
    /// Gets property value
    member private this.GetValue name = 
        Map.tryFind name properties
    /// Sets property value, creating a new property if none exists
    member private this.SetValue (name,value) =
        /// Atomically writes new properties reference
        let Write () = 
            properties <-
                |> Map.remove name 
                |> Map.add name value
        // Synchronize property writes
        lock sync Write
        // Trigger property changed event
        |> propertyChanged.Trigger    
    override this.TryGetMember(binder:GetMemberBinder,result:obj byref ) =     
        match this.GetValue binder.Name with
        | Some value -> result <- value; true
        | None -> false
    override this.TrySetMember(binder:SetMemberBinder, value:obj) =        
    override this.GetDynamicMemberNames() =
        properties |> (fun pair -> pair.Key)
    member this.PropertyChanged = propertyChanged.Publish
    interface System.ComponentModel.INotifyPropertyChanged with
        member this.PropertyChanged = propertyChanged.Publish     
    static member (?) (lookup:#DynamicLookup,name:string) =
        match lookup.GetValue name with
        | Some(value) -> value
        | None -> raise (new System.MemberAccessException())        
    static member (?<-) (lookup:#DynamicLookup,name:string,value:'v) =
        lookup.SetValue (name,value)
    static member GetValue (lookup:DynamicLookup,name) =

F# usage:

/// Product type inherits dynamic lookup
type Product (name,price) =
    inherit DynamicLookup ()
    member this.Name = name
    member this.Price = price
// Initiate product object with dynamic rating value
let p = Product("F# for Scientists",49.95M)
do p?Stars <- 5
// Access product's properties
let stars = System.Convert.ToInt32(p?Stars)
do printf "%s...%M %s" p.Name p.Price (System.String('*',stars))

C# usage:

// Create Product type with dynamic stars value
Product product = new Product("Expert F#",54.99M);
((dynamic)product).Stars = 5;       
// Read product properties
dynamic p = product;
string s = 
    string.Format("{0}...{1} {2}",
        p.Name, p.Price, new String('*', (int) p.Stars));

Use from Silverlight 4.0

<t:PropertyLookup x:Key="DynamicConverter"/>


<TextBox Text="{Binding Converter={StaticResource DynamicConverter},


dynamic product = new Product("Real World FP", 35.99);
product.Stars = 5;
DataContext = product;


public class PropertyLookup : IValueConverter
    public object Convert(
        object value, 
        Type targetType, 
        object parameter, 
        CultureInfo culture)
        return DynamicLookup.GetValue(
            (DynamicLookup) value,
            (string) parameter);            

    public object ConvertBack(object value, 
        Type targetType, 
        object parameter, 
        CultureInfo culture)
        throw new NotImplementedException();

Note: Silverlight 4.0 requires Microsoft.CSharp.dll to use dynamic types.

F# operator overloads for WPF dependency properties

When creating a desktop application with WPF using F# there are a number of options:

For small desktop applications, the last option, creating WPF elements directly from F# can produce good self-contained code, but at time is a little less readable than the XAML equivalent. Lets consider placing a button bound to a command on a grid at a certain position.

The XAML fragment might look like this:

<Button Content="_1" Command="{Binding Key1Command}"
        Grid.Column="0" Grid.Row="2"/>


Code equivalent:

let button = Button(Content="_1")
button.SetBinding(Button.CommandProperty,Binding("Key1Command")) |> ignore


Code equivalent using (+) operator overloads to add the dependency properties:

Button(Content="_1") + Button.Command(Binding "Key1Command") 
    + Grid.Column 0 + Grid.Row 2 


The glue is just a couple of classes that define a dependency property and value/binding pair with a (+) operator overload that sets the value on the target WPF element.

For Dependency Property values:

type DependencyPropertyValuePair(dp:DependencyProperty,value:obj) =
    member this.Property = dp
    member this.Value = value
    static member (+) 
        (target:#UIElement,pair:DependencyPropertyValuePair) =


For Dependency Property bindings:

type DependencyPropertyBindingPair(dp:DependencyProperty,binding:BindingBase) =
    member this.Property = dp
    member this.Binding = binding
    static member (+) 
        (target:#FrameworkElement,pair:DependencyPropertyBindingPair) =
        target.SetBinding(pair.Property,pair.Binding) |> ignore


Finally relevant WPF types must be extended with helper methods (note: this could be code generated):

type Grid with
    static member Column (value:int) =
    static member Row (value:int) =


Attached is a sample calculator VS2010 project showing the mechanism in action.

Calculator (3.57 kb)