PsAccelerator: Monad

Showing posts with label Monad. Show all posts

Thursday, September 1, 2011

Monads for .NET developers

I have written an article for the Dutch developer magazine of SDN (Magazine 111). It is titled: “Monads voor de .NET-ontwikkelaar”.

In this post I will list some of the available resources on monads for .NET developers:

C# resources

Books:

Tomas Petricek & Jon Skeet: Real World Functional Programming: With Examples in F# and C#, website
Oliver Sturm: Functional Programming in C#: Classic Programming Techniques for Modern Projects, website

Web:

Wes Dyer: The marvels of monads
Mike Hadlow: Monads in C#–1. Introduction.
Derick Bailey: Monads in C#: Which Part Is The Monad?
Matthew Podwysocki: Functional .NET - LINQ or Language Integrated Monads?
Tomas Petricek: Beyond the Monad fashion (I.): Writing idioms in LINQ
Mauricio Scheffer: Refactoring to monadic C#
Erik Meijer: The World According to LINQ

F# resources

Computation Expressions are addressed in most of the available F# books (Professional F# 2.0 does not): F# and functional programming

Sunday, August 7, 2011

Adding xml strings in C# using LINQ

This is follow up on my previous blog post:Adding xml strings in F# using computation expressions. The text is nearly identical, the language is C# instead of F#.

In some cases classes are enhanced wrappers of simple classes. For instance in .NET:

DateTime is a point in time and provides, among others things, extra functionality related to representing date and time formats.
XElement is an xml string and provides, among others things, checks to determine the validity of the xml string.
Option can contain a value and can tell you if there is value available.

Sometimes you have to deal with underling class and reuse some of the functionality of the wrapper. In this case you could consider using LINQ. We first define the Return, Bind and SelectMany functions to create the required functions.

For details more details see:

All excellent resources.

public static classXmlMonad
{
//monad
public staticXElement Return(this stringtext)
{
    try
   {
      returnXElement.Parse(text);
    }
    catch(XmlException exc)
    {
      returnXElement.Parse(String.Format("<XmlException>{0}</XmlException>", exc.Message));
    }
}

public staticXElement Bind(thisXElement el, Func<string, XElement> f)
{
    try
   {
      returnf(el.ToString());
    }
    catch(XmlException exc)
    {
      returnXElement.Parse(String.Format("<XmlException>{0}</XmlException>", exc.Message));
    }
}

public staticXElement SelectMany(thisXElement el, Func<string, XElement> f, Func<string, string, string> select)
{
    returnel.Bind(text => f(text).Bind(x => select(text, x).Return()));
}
}

We can now define a add function that will xml elements by using a string manipulation:

private static XElement Add(XElement el1, XElement el2)
{
  XElement result =
  from x1 in el1
  from x2 in el2
  select x1.Substring(0, x1.LastIndexOf("<")) + x2.Substring(x2.IndexOf(">") + 1);

  return result;
}

Add in action:

var el1 = XElement.Parse("<a><b>1</b><b>2</b></a>");
var el2 = XElement.Parse("<a><b>3</b><b>4</b></a>");

Console.WriteLine(string.Format("Add: {0}", Add(el1,el2)));

Results in:

When we change the xml into:

var el2 = XElement.Parse("<c><b>3</b><b>4</b></c>");

The result is:

Thursday, August 4, 2011

Adding xml strings in F# using computation expressions

In some cases types are enhanced wrappers of simple types. For instance in .NET:

DateTime is a point in time and provides, among others things, extra functionality related to representing date and time formats.
XElement is an xml string and provides, among others things, checks to determine the validity of the xml string.
Option can contain a value and can tell you if there is value available.

Sometimes you have to deal with underling type and reuse some of the functionality of the wrapper. In this case you could consider using computation expressions.

This is a simple xml example. We create a xmlBuilder and reuse the validation logic of XElement:

open System
open System.Xml
open System.Xml.Linq

type xmlBuilder()=
    member x.Bind(el:XElement,(f:string -> XElement)) =
        try
            f(el.ToString())
        with
            | :? XmlException as exc -> XElement.Parse(String.Format("<XmlException>{0}</XmlException>", exc.Message))
    member x.Return(text) = 
        try
            XElement.Parse(text)
        with
            | :? XmlException as exc -> XElement.Parse(String.Format("<XmlException>{0}</XmlException>", exc.Message))

The string “123” creates an error:

let xml = new xmlBuilder()

let error =
    xml { 
            return "123"
        }

val error : XElement = <XmlException>Data at the root level is invalid. Line 1, position 1.</XmlException>

The expression can now be used to reuse sting functions:

let toUpper el =
    xml { 
            let! x = el
            return x.ToUpper()
        }

let el = XElement.Parse("<a><b>1</b><b>2</b></a>")
let result1 = el |> toUpper 

val result1 : XElement = <A>
  <B>1</B>
  <B>2</B>
</A>

In the same way we can define a simple add function for xml:

let (+) (el1:XElement) (el2:XElement) =
    xml { 
            let! x1 = el1
            let! x2 = el2
            return x1.Substring(0, x1.LastIndexOf("<")) + x2.Substring(x2.IndexOf(">") + 1)
        }

let el1 = XElement.Parse("<a><b>1</b><b>2</b></a>")
let el2 = XElement.Parse("<a><b>3</b><b>4</b></a>")
let result2 = el1 + el2

val result2 : XElement =
  <a>
  <b>1</b>
  <b>2</b>
  <b>3</b>
  <b>4</b>
</a>

let el3 = XElement.Parse("<c><b>3</b><b>4</b></c>")
let result3 = el1 + el3

val result3 : XElement = <XmlException>The 'a' start tag on line 1 position 2 does not match the end tag of 'c'. Line 7, position 3.</XmlException>

This may not be in line with the concept of information hiding, but it can help you in case you have to deal with the simple type to get the work done.

Tuesday, June 28, 2011

WTF is a Monad by Robert C. Martin in F#

I have read some material describing Computation Expressions and knew computation expressions are the F# implementation of monads, but I did know why one should use a monad.

A few days ago saw the video of presentation by Robert C. Martin (Uncle Bob) at the Norwegian Developers Conference called “WTF is a Monad” and now it makes sense to me.

It is a proven way of solving problems. If you:

have a problem in one domain
you can transform it to another domain
solve the problem in the other domain
and can transform it back

you have a solution.

I have translated some of the code of the presentation to F#. I tried to stay as close to the original code as possible and did not do much refactoring. I skipped the last two examples (distributions an state).

Update: ~~I did not implement the examples that required lift. I have not figured out how to do that.~~ I have created the lift myself (details: http://bugsquash.blogspot.com/2010/12/notes-on-haskell-functors-and-f.html)

I like to thank Robert for the permission to share the code. Feel free to add improvements in the comments.

//Non-Monadic dots

let dotsToN (d:string) =
    d.Length

let result1 = dotsToN "....."

let nToDots (n:int) =
    new string('.', n)

let result2 = nToDots 5

let addDots da db =
    let a = dotsToN da
    let b = dotsToN db
    nToDots (a+b)

let result3 = addDots "..." "..."

//Monadic dots

let dotResult = nToDots

let dotBind d (f:int -> string) =
    d |> dotsToN |> f

let addDots' da db =
    dotBind da (fun a ->
        dotBind db (fun b ->
            dotResult (a + b)))
    
let result4= addDots' "..." "..."

//dot-Monad
type dotBuilder()=
    member x.Bind(d,(f:int -> string)) = d |> dotsToN |> f
    member x.Return(n) = new string('.', n)

let dot = new dotBuilder()

let addDots'' da db =
    dot { let! x = da
          let! y = db
          return x + y
        }

let result5= addDots'' "..." "..."

let multiplyDots da db =
    dot { let! x = da
          let! y = db
          return x*y
        }

let result6= multiplyDots "..." "..."

let dcd dt du =
    dot { let! tens = dt
          let! units = du
          return (10 * tens + units)
        }

let result7= dcd "..." "....."

// In Clojure the monad gets the lift for free
// In F# we have to create it ourselves
// More info: http://bugsquash.blogspot.com/2010/12/notes-on-haskell-functors-and-f.html --
//

let liftDots_1 f a1 = 
    dot { 
            let! x1 = a1 
            return f x1 
        }

let liftDots_2 f a1 a2 = 
    dot { 
            let! x1 = a1
            let! x2 = a2
            return f x1 x2
        }

let liftDots_4 f a1 a2 a3 a4 = 
    dot { 
            let! x1 = a1
            let! x2 = a2
            let! x3 = a3
            let! x4 = a4
            return f x1 x2 x3 x4
        }

let substractDots = liftDots_2 (-)

let result7a= substractDots "....." ".."

let mean4 a b c d = (a+b+c+d)/4

let dmean4 = liftDots_4 mean4

let result7b= dmean4 "..." ".." "..." "...."

//
//complex number (inspection)
//

open System.Numerics

let c_0 = Complex.Zero
let c_1 = Complex.One
let c_i = Complex.ImaginaryOne

type complexBuilder()=
    member b.Return(x:float) = new Complex(x,0.0) 
    member b.Bind((c:Complex),(f:float -> Complex)) = 
        if c.Imaginary = 0.0 then
            f c.Real
        else 
            failwithf "Imaginary"
   
let complex = new complexBuilder()

let addComplex c1 c2 =
    complex { let! x = c1
              let! y = c2
              return x + y
            }

let result8= addComplex c_1 c_1;;
let result9= addComplex c_1 c_i;; //System.Exception: Imaginary
let result10= addComplex c_i c_i;; //System.Exception: Imaginary

//null

type noNullBuilder()=
    member b.Return(mv) = mv 
    member b.Bind(mv,f) = if (mv = null) then null else f mv

let nuNull = new noNullBuilder()

// int can not be null in .Net

let fragile (a:string) (b:string) (c:string) =
    if (a= null||b=null||c=null)
    then
        "CRASH"
    else
        a + b + c

let result11 = fragile "a" "b" "c"
let result12 = fragile "a" null "c" //"CRASH"

let safeFragile (a:string) (b:string) (c:string) =
    nuNull { let! x = a
             let! y = b
             let! z = c
             return x + y + z
            }

let result13 = safeFragile "a" "b" "c"
let result14 = safeFragile "a" null "c" //val result14 : string = null

//List
let l_a = [1;2;3]
let l_b = [4;5;6]

let addList = seq {for a in l_a do
                    for b in l_b do 
                    yield a+b
                  }|> Seq.toList

let multList = seq {for a in l_a do
                    for b in l_b do 
                    yield a*b
                  }|> Seq.toList

//helper for the demo
let flatten l = 
    let rec flatten' l result =
        match l with 
        |[] -> result
        |h::t -> flatten' t (h@result)
    flatten' (l|>List.rev) []

let result15 = flatten [[1;2;3];[7;8;9]]

type listBuilder()=
    member b.Return(v) = [v]
    member b.Bind(mv,f) = mv |> List.map f |> flatten

let list = new listBuilder()

let addList' a b = list {
                       let! x = a
                       let! y = b
                       return x + y 
                    }

let result16 = addList' l_a l_b

let multList' a b = list {
                       let! x = a
                       let! y = b
                       return x * y 
                    }

let result17 = multList' l_a l_b

//distribution example see Expert F# of Don Syme page 239..244
//state http://fsharpcode.blogspot.com/2008/12/f-state-monad-type-state-state-state-of.html

Thursday, September 1, 2011

Monads for .NET developers

C# resources

Books:

Web:

F# resources

Web:

Presentations

Some theory

Code:

Sunday, August 7, 2011

Adding xml strings in C# using LINQ

Thursday, August 4, 2011

Adding xml strings in F# using computation expressions

Tuesday, June 28, 2011

WTF is a Monad by Robert C. Martin in F#

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