Trying numl on OSX with F# and Xamarin

Today, at devLink 2014, my last session of the day is “Practical Machine Learning – Predicting Things” by Seth Juarez. In his presentation, Seth talks about machine learning and his machine learning library, numl. The session is very entertaining and I learn a lot from it.

Fun fact: Seth originally called his library, Machine Learning Library for .NET. But when he met Phil Haack at Mix 2011, Phil recommended him to find a shorter name. So Seth just changed his library name to numl to make it sounded like nuGet. 🙂

I have played with numl earlier this year by writing short F# script. After the session today, I just want to look at it again and see if my short F# script could still be run on OSX with Xamarin/Mono.

Here are some quick instructions:

1. Open Xamarin Studio and create a F# Library project.

Screen Shot 2014-08-28 at 10.37.51 PM

2. Create C# Library project and add numl NuGet package to C# library.

Screen Shot 2014-08-28 at 10.39.35 PM

Screen Shot 2014-08-28 at 10.43.00 PM

Screen Shot 2014-08-28 at 10.43.46 PM

3. Add Tennis class and data set from here or here.

Screen Shot 2014-08-28 at 10.44.25 PM

4. In F# Library project, I copy my existing F# code, adjust reference locations a little bit, and run it. Everything seems to work flawlessly!

Screen Shot 2014-08-29 at 2.49.52 PM

That’s it. It’s good to learn that my existing F# code can run smoothly on OSX. Hopefully, I’ll have sometime playing with numl more when I am back to Nashville.

Good night from Chattanooga!


Make IIS Express works with

I never notice that IIS Express doesn’t listen to web requests other than localhost. So, to my surprise, when I try, I got HTTP 400, Bad Request instead.


Change to localhost and everything is fine.



Anyway, you can set your IIS Express to let it listen to a request for easily.

1. Look for a file applicationhost.config. It’d be under /documents/IISExpress/config.

2. Go to <sites> section and look for your site. In this example, I have my web project named MyWeb.


3. Change localhost to


4. Stop IIS Express and run your web site again.



Now you should be able to access your web site thru address now!


Hope this helps! 🙂

Could not run the “GenerateResource” task because MSBuild could not create or connect to a task host with runtime “CLR2” and architecture “x86”.

Since I have experienced the same error more than three times while creating Windows Service (.NET 3.5) on Visual Studio 2012 and/or 2013, I think I should post a solution here for my quick reference. If you create a Windows Service and target .NET 3.5 on Visual Studio 2012 or 2013, you might experience the error message while compiling the project.

Here is the full error message:

Could not run the “GenerateResource” task because MSBuild could not create or connect to a task host with runtime “CLR2” and architecture “x86”. Please ensure that (1) the requested runtime and/or architecture are available on the machine, and (2) that the required executable “C:\Program Files (x86)\MSBuild\12.0\bin\MSBuildTaskHost.exe” exists and can be run.

To resolve it, go to your csproj file and add the following line under the default property group:



And that should resolve the issue, everything should be compiled.


IE8 Object doesn’t support property or method ‘map’

One function that I used very frequently in Functional Programming language like F# is map. For C# I can use Select function in LINQ to do the same thing. With ECMAScript5, JavaScript also comes with built-in map function.

Here are how map functions looks like in JavaScript:

var sqrt = function(x){ return x*x;};
var numbers = [1,2,3];
var squares =;
// squares is [1,4,9]

However, if you still have to support IE8, unfortunately, it doesn’t support map function.

To make IE8 supports the map function, you can add a Polyfill that you can find on this page. Or if you use either jQuery or Lo-Dash, you can use or as well.

// jQuery
var squares =, sqrt);

// Lo-Dash
var squares =, sqrt);

Using F# and R Provider with Kaggle’s Facial Keypoints Detection

Lately, I have been trying to learn more about Data Science and Machine Learning. Following a coursera’s machine learning class and reading some books like, Data Science for Business and Mining the Social Web is very useful. However, you may want to get your hands dirty and learn the topics by solving the real-world problems. Fortunately, there is a site called Kaggle which provides data and problems for you to solve.

Basically, Kaggle is a platform allowing companies and researchers to post their data, so that people like data scientist, statisticians, data miners, and so on can compete to produce the best predictive models. Most competitions are real-world problems that big companies are trying to solve, and if you come up with the best model, you could win some prizes or even get a job!  For a newbie like me, Kaggle also has 101-type competitions that could help you learn the basic while having fun solving the real-world problem. One of the problem that I am looking at is Facial Keypoints Detection which should also help me learn computer vision in addition to data science and machine learning.

Many languages and environments like R, MATLAB, Octave, and Python are generally used in Data Science and Machine Learning fields. However, F# is also a great language for data-oriented problem-solving, data science, and machine learning tasks as well. REPL and succinctness of F# allows you to explore and manipulate the data in both functional and imperative styles. With type providers, acquiring data from various sources like CSV, XML, JSON, and databases as well as interoperability with R can be done within F#. In addition, there are libraries like Deedle and FSharp.Charting that will be very useful. And as F# is a .NET languages, you can use .NET libraries like Math.NET and numl to help as well.

To get start quickly, we can just install the FsLab NuGet package that put together useful F# libraries for Data Science task.


NOTE: As of 4/26/2014, FsLab is still beta, so you have to select “Include Prerelease” option.

This post, I will show how we can use F# and R Provider with the Facial Keypoints Detection. I won’t try to solve the problem yet :-), but I will follow the R tutorial that let me learn R as well as getting familiar with the data.

The first step is to download the training data from here. The training file is in csv format with 7049 rows and has 31 columns, 30 of those columns keep 15 (x,y) keypoints such as nose tip, left eye, etc. The last column is a list of pixels representing a 96×96 image.

I want to use my own type, so I just create a Face type and write a simple parser in F#.

type Face =

let lines = File.ReadAllLines("D:/kaggle/facial-keypoints-detection/training.csv")

let faces =      
    let d = Decimal.TryParse
    let toXy v1 v2 =         
        match d v1 with
        | false, _ -> None
        | true, x ->
            match d v2 with
            | false, _ -> None
            | true,y -> Some(x,y)        

    |> Seq.skip 1
    |> (fun (row:string) -> 
            let r = row.Split(',')
               LeftEyeCenter = toXy r.[0] r.[1]
               RightEyeCenter = toXy r.[2] r.[3]
               LeftEyeInnerCorner = toXy r.[4] r.[5]
               LeftEyeOuterCorner = toXy r.[6] r.[7]
               RightEyeInnerCorner = toXy r.[8] r.[9]
               RightEyeOuterCorner = toXy r.[10] r.[11]
               LeftEyeBrowInnerEnd = toXy r.[12] r.[13]
               LeftEyeBrowOuterEnd = toXy r.[14] r.[15]
               RightEyeBrowInnerEnd = toXy r.[16] r.[17]
               RighttEyeBrowOuterEnd = toXy r.[18] r.[19]
               NoseTip = toXy r.[20] r.[21]
               MouthLeftCorner = toXy r.[22] r.[23]
               MouthRightCorner = toXy r.[24] r.[25]
               MouthCenterTopLip = toXy r.[26] r.[27]
               MouthCenterBottomLip = toXy r.[28] r.[29]
               Image = (r.[30].Split(' ') |> (Int32.Parse))

If you want you can use CSV Type Provider, but you should specify the InferRows to be zero to check the whole file and set PreferOptionals to be true to use Options type.

type FaceCsv = CsvProvider<"D:/kaggle/facial-keypoints-detection/training.csv", InferRows=0, PreferOptionals = true>
let faces = new FaceCsv()

After we get all training data, the first thing is to visualize the face data. R already has nice graphics library that we can use to display the image, so we can use R Provider to call those functions from F#.

Let’s get values from the first face data.

// R Stuff
open RProvider
open RProvider.``base``
open RProvider.grDevices

// helper functions
let o x = x :> obj
let imXy p = match p with Some(x,y) -> (96m-x),(96m-y) | _ -> (0m,0m)     
let face i = faces |> Seq.nth i
let imPointParams (x,y) color = ["x",o x;"y",o y;"col",o color] |> namedParams

// get values from face
let im = R.matrix(nrow=96,ncol=96,data=Array.rev((face 0).Image))
let noseTipXy = imXy (face 0).NoseTip
let leftEyeCenterXy = imXy (face 0).LeftEyeCenter
let rightEyeCenterXy = imXy (face 0).RightEyeCenter

NOTE: To use R.NET and R Provider, you still have to download and install R,

Now we have all values, we can put them in a format that R expects and call the R functions.

// Visualize image using R
// image(1:96, 1:96, im, col=gray((0:255)/255))
let imageParams = 
        "col",R.gray(["level",R.c(seq { for i in 0. .. 255. -> i/255.})]|>namedParams)
    ] |> namedParams

// add points for nose tip, left eye, right eye
// points(96-d.train$nose_tip_x[1], 96-d.train$nose_tip_y[1], col="red")
R.points(imPointParams noseTipXy "red")
R.points(imPointParams leftEyeCenterXy "blue")
R.points(imPointParams rightEyeCenterXy "green")

And you should see the sample image.


Although, you should be able to call R functions directly from F#, sometimes trying to figure out R format can be cumbersome. What we can do is to use REngine.Evaluate like this as well.

im.Engine.SetSymbol("im", im)
im.Engine.Evaluate("image(1:96, 1:96, im, col=gray((0:255)/255))")

Now since I know how to use R to display gray-scale image, I can use the same trick to display the image for Digit-Recognizer data :-).


You should see the power of F# which allows us to process and manipulate data with F# and utilize R for statistical computing and graphics!

In the future post, I plan to share more about my journey with Data Science and Machine Learning in F#. Happy data mining!

Using F# fold function to implement recursion

In the last post, we talked about techniques to implement tail-recursion in F#. We also learned that to write pure functional code we can only use immutable data structures which means we have to implement loop using recursion.

Writing recursive function can be cumbersome (e.g., the function has to have one or more base cases) and hard to understand. It’s also harder to make sure that your recursive function is a tail-recursive one.

Fortunately, using higher-order function and data structure like list (which is a recursive data structure) can help easing the pain.

Let’s look at our non-tail-recursive factorial function from last post again.

let rec factorial x =
    if x <= 1 then
        x * factorial (x - 1)

Since the function basically multiplies numbers (e.g., x, x-1, x-2, …) together, we can actually think of the input as a list of numbers like [5,4,3,2,1] instead.

With that in mind, we can now implement factorial function using List functions like List.fold.

Here is the List.fold signature:

(‘State -> ‘T -> ‘State) -> ‘State -> ‘T list –> ‘State

List.fold is a higher-order function that takes the following parameters:

(‘State –> ‘T –> ‘State)

A function that takes ‘State which we can think of it as an accumulator, ‘T which in this case is each value in the list, and returns new accumulator.


An initial state of an accumulator.

‘T list

The input list

The last ‘State is the final out put that we want.

Now, let’s see how we can implement our factorial function with only one line of code :-).

let foldFactorial x = [1..x] |> List.fold (fun acc i -> acc * i) 1

The most important part is the lambda expression, (fun acc i -> acc * i), that we pass to the fold function. The acc parameter in the lambda expression is the accumulated result like the acc parameter in accTailRecursiveFactorial recursive function from the last post.

let accFactorial x =
    let rec accTailRecursiveFactorial x acc =
        if x <= 1 then 
            accTailRecursiveFactorial (x - 1) (acc * x)

    accTailRecursiveFactorial x 1

Using fold also gives us tail recursive function. Here is the IL generated by foldFactorial function.


(NOTE: some lines have been cut to make the screenshot fit the page)

If you are curious, below is what List.fold looks like (NOTE: The code below is from list.fs in F# compiler and code library on GitHub). You probably notice that it has the nested recursive function that is tail-recursive!

let fold<'T,'State> f (s:'State) (list: 'T list) = 
	match list with 
    | [] -> s
    | _ -> 
		let f = OptimizedClosures.FSharpFunc<_,_,_>.Adapt(f)
        let rec loop s xs = 
			match xs with 
            | [] -> s
            | h::t -> loop (f.Invoke(s,h)) t
		loop s list

And as a bonus, you can even make the factorial code shorter by using operator (*) which is actually a normal function in F#.

let foldFactorial2 x =  [1..x] |> List.fold (*) 1

Better yet, the code can be made shorter by using List.reduce which is a specialized version of fold that treat the first input on the list as accumulator.

let reduceFactorial x = [1..x] |> List.reduce (*)

This post shows how tail-recursive code could be implemented using List.fold and List.reduce. Since implementing recursive algorithm is important in functional programming, using built-in F# function like fold and reduce really reduces (no pun-intended 🙂 ) our work.

Recursion and Tail-recursion in F#

While imperative programming language paradigm depends on updating mutable variables (or introducing side effect) to change state of the program, pure functional programming only uses immutable data structures to represent their state. Side effect is required if you need your program to do any work (i.e., I/O), but undesirable side-effects are the root of many bugs. Immutability makes you write safer code as the code is more predictable.

When people (most of us!) with imperative programming languages background start looking at functional programming, we probably think that if we aren’t allowed to change anything, how we can even do anything useful at all. The answer is that instead of writing program as a sequence of statements that change the state like we do in imperative style programming, we write functional programs differently.

Today, we are going to look at recursion which is a technique that allows functional programs to implement loop-like algorithm without using mutable variables. Basically, a recursive function is a function that calls itself.

Let’s see implementations of factorial function using loop and recursion in C#:

// using recursion
int Factorial(int n)
    return n<=1?1:n*Factorial(n - 1);

// using loop
int FactorialLoop(int n)
    var ret = 1;
    while (n >= 1)
        ret *= n--;

    return ret;

Now let’s see our F# implemetations:

let rec factorial x =
    if x <= 1 then
        x * factorial (x - 1)

let factorialLoop x = 
    let mutable n = x
    let mutable ret = 1
    while n >= 1 do
        ret <- ret * n
        n <- (n - 1)

In C#, the recursive and non-recursive function signature are the same. However, in F#, the rec keyword is needed by the F# type inference system. (I show F# implementation in loop just to show that we can also write F# code in imperative style by using mutable keyword as well although it’s not preferable.)

NOTE: Writing the recursive functions like this every time we need loop-like algorithm can be cumbersome, so most functional languages provide an easier way for doing recursion with higher-order function technique (i.e., Map or Reduce functions). I will write about it in the later post.

Stack Overflow

Ok. Now we can use recursion to implement loop-like algorithm even we aren’t allowed to use mutable variable. However, there is one problem. As you might already know, internally, when a function is called, the caller state will be put into the stack. So if we have a recursive function that call itself deeper and deeper, the program might experience Stack overflow.

Let’s set a break point at the base case and look at our call stack when we call F# factorial 10:


Although we should not have any stack overflow issue here, stack is not infinite resource, the naive recursive function can cause stack overflow with large number of iterations eventually.

Intermediate Language

Before we talk about tail recursion, let’s talk about IL or Intermediate Language.

What is IL or Intermediate Language? When you compile CLI languages like C#, VB, or F#, the .NET compiler generates IL. You can think about it as the native or assembly language of .NET which runs on CLR. When the .NET application is run, each IL method is translated into native machine code Just-In-Time before it’s first executed.

Although it looks just like normal assembly language, IL is a stack-based language and has no concept of registers. As we walk through each samples, we will talk about some of those instructions and learn what it does.

Tail Recursion

Now we understand recursion, stack overflow, and IL, let me introduce tail call and tail recursion. Tail recursion is a special form of recursion, where the compiler can optimize the recursive call in tail position to not allocate stack space to keep caller state. The idea is that if a compiler can guarantee that the call to the recursive function is the tail call or last action that happens before the function returns, there is no need to keep the caller state in the stack at all!

F# is a functional-first language and its compiler is designed to provide tail-call optimization if possible. The most efficient way is to turn the recursive function into a function with a loop. If the compiler can’t do that because the recursive function is more complex, then the compiler generate call IL with a tail. prefix to let the JIT compiler uses the tail call.

Let’s look at the recursive version of the factorial function in F# again:

let rec factorial x =
    if x <= 1 then
        x * factorial (x - 1)

At the first glance, we might think that factorial (x-1) is the last action of the function. However, the last action is actually a multiply operation. If you don’t believe me, you can just look at the IL generated from this function.


Don’t worry if you don’t understand most of the IL, what I want you to see is mul, which is a multiply operation, is executed before ret, which return from the function, and after call that is the IL that call the function. In this case, it calls its own function recursively.

If F# code above is not tail-recursive function, then how we can create tail-recursive function. In functional programming we have patterns that we can use to make sure that our recursive function is tail-recursive.

Accumulator Pattern

The first pattern is called Accumulator Pattern. In this pattern, we introduce another parameter, accumulator, that keeps the current state of the recursion, so that information doesn’t need to be kept in the call stack and used later. Let’s see how we can apply the pattern to our factorial function above.

let accFactorial x =
    let rec accTailRecursiveFactorial x acc =
        if x <= 1 then 
            accTailRecursiveFactorial (x - 1) (acc * x)

    accTailRecursiveFactorial x 1

So we basically create a non-recursive function that will get called by the consumer. The non-recursive function has the nested recursive function that accepts two parameters, one is the same recursive parameter, and another one, acc, is a parameter that accumulates multiplied result together. Let’s see the call stack when we execute accFactorial 10.


As you can see, our call stack is pretty clean now!

When F# compiler sees that the last action is a call to a recursive function, it knows that it can generates IL with tail. prefix. When JIT sees the tail. prefix, it knows that it must use a tail call.


(NOTE: some lines have been cut to make the screenshot fit the page)


In this pattern (aka continuation passing style), we will see the power of F# and functional programming language! When we treat a function as a value, we can pass it around, make a copy, or create a new one on the fly. So instead of pass another parameter with the accumulated value like in Accumulator Pattern case, why don’t we just build expressions on the fly and pass them via function instead!

Let’s implement the same factorial function with this pattern:

let contFactorial x =
    let rec contTailRecursiveFactorial x f =
        if x <= 1 then 
            contTailRecursiveFactorial (x - 1) (fun () -> x * f())

    contTailRecursiveFactorial x (fun () -> 1)

The implementation looks just like the Accumulator Pattern. In this pattern, we also have an outer function which is non-recursive and the nested recursive function. However, instead of passing an accumulator, we pass a function!

Let’s see the call stack and we should see the clean call stack:


Now let’s see the generated IL and we should see tail. prefix again:


The advantage of using Continuations is that you are not limited to passing a single computed value which might not be possible to do in more complicated recursive function which I can post about it later.

Happy Coding!