Power of mathematics: Reasoning about functional types

One of the most amazing aspects of mathematics is that it applies to such a wide range of areas. The same mathematical rules can be applied to completely different objects (say, forces in physics or markets in economics) and they work exactly the same way.

In this article, we'll look at one such fascinating use of mathematics - we'll use elementary school algebra to reason about functional data types.

In functional programming, the best way to start solving a problem is to think about the data types that are needed to represent the data that you will be working with. This gives you a simple starting point and a great tool to communicate and develop your ideas. I call this approach Type-First Development and I wrote about it earlier, so I won't repeat that here.

The two most elementary types in functional languages are tuples (also called pairs or product types) and discriminated unions (also called algebraic data types, case classes or sum types). It turns out that these two types are closely related to multiplication and addition in algebra...

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Tuesday, May 14, 2013

Async in C# and F#: Asynchronous gotchas in C#

Back in February, I attended the annual MVP summit - an event organized by Microsoft for MVPs. I used that opportunity to also visit Boston and New York and do two F# talks and to record a Channel9 lecutre about type providers [5]. Despite all the other activities (often involving pubs, other F# people and long sleeping in the mornings), I also managed to come to some talks!

One (non-NDA) talk was the Async Clinic [1] talk about the new async and await keywords in C# 5.0. Lucian and Stephen talked about common problems that C# developers face when writing asynchronous programs. In this blog post, I'll look at some of the problems from the F# perspective. The talk was quite lively, and someone recorded the reaction of the F# part of the audience as follows...

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Monday, April 15, 2013

F# Data: New type provider library

When F# 3.0 type providers were still in beta version, I wrote a couple of type providers as examples for talks. These included the WorldBank type provider (now available on Try F#) and also type provider for XML that infered the structure from sample.
For some time, these were hosted as part of FSharpX and the authors of FSharpX also added a number of great features.

When I found some more time earlier this year, I decided to start a new library that would be fully focused on data access in F# and on type providers and I started working on F# Data. The library has now reached a stable state and Steffen also announced that the document type providers (JSON, XML and CSV) are not going to be available in FSharpX since the next version.

This means that if you're interested in accessing data using F# type providers, you should now go to F# Data. Here are the most important links:

Before looking at the details, I would like to thank to Gustavo Guerra who made some amazing contributions to the library! (More contributors are always welcome, so continue reading if you're interested...)

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Thursday, March 28, 2013

Upcoming F# talks and trainings (London, NYC & Boston)

After a few years, I finally managed to find the time to attend the MVP Summit this year. The Summit is an annual event where people who are active in Microsoft technical communities come to the Microsoft headquarters to learn about new things (and, of course, tell them how they should be doing their job :-)). The Summit is a great place to meet interesting people (so if you're reading this and will be there, definitely get in touch!)

The good news - for those interested in F# - is that I'll be doing two F# talks on the way and we also have a new F# course scheduled for later in the year. Continue reading to learn more!

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Thursday, February 07, 2013

Announcing: Literate programming tools for F#

For some time now, I've been writing my F# blog posts (and other F# articles published elsewhere) by combining F# code snippets and Markdown formatting. In fact, I even wrote a Markdown parser in F# so that I can post-process documents (to generate references etc). You can read about the Markdown parser in an upcoming F# Deep Dives book - currently, it is available as a free chapter!

During the Christmas break, I finally found enough time to clean-up the code I was using and package it properly into a documented library that is easy to install and use. Here are the most important links:

To learn more about the tool and how to use it, continue reading!

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Tuesday, January 22, 2013

Processing trees with F# zipper computation

One of the less frequently advertised new features in F# 3.0 is the query syntax. It is an extension that makes it possible to add custom operations in an F# computation expression. The standard query { .. } computation uses this to define operations such as sorting (sortBy and sortByDescending) or operations for taking and skipping elements (take, takeWhile, ...). For example, you can write:

1: query { for x in 1 .. 10 do
2:         take 3
3:         sortByDescending x }

In this article I'll use the same notation for processing trees using the zipper pattern. I'll show how to define a computation that allows you to traverse a tree and perform transformations on (parts) of the tree. For example, we'll be able to say "Go to the left sub-tree, multiply all values by 2. Then go back and to the right sub-tree and divide all values by 2" as follows:

1: tree { for x in sample do
2:        left 
3:        map (x * 2) 
4:        up
5:        right
6:        map (x / 2) 
7:        top }

This example behaves quite differently to the usual query computation. It mostly relies on custom operations like left, right and up that allow us to navigate through a tree (descend along the left or right sub-tree, go back to the parent node). The only operation that does something is the map operation which transforms the current sub-tree.

This was just a brief introduction to what is possible, so let's take a detailed look at how this works...

val query : Linq.QueryBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.query
val x : int
custom operation: take (int)

Calls Linq.QueryBuilder.Take
custom operation: sortByDescending ('Key)

Calls Linq.QueryBuilder.SortByDescending
type Tree<'T> =
  | Node of Tree<'T> * Tree<'T>
  | Leaf of 'T
  override ToString : unit -> string

Full name: Tree-zipper-query.Tree<_>
union case Tree.Node: Tree<'T> * Tree<'T> -> Tree<'T>
union case Tree.Leaf: 'T -> Tree<'T>
val x : Tree<'T>
override Tree.ToString : unit -> string

Full name: Tree-zipper-query.Tree`1.ToString
match x with
    | Node(l, r) -> sprintf "(%O, %O)" l r
    | Leaf v -> sprintf "%O" v
type Path<'T> =
  | Top
  | Left of Path<'T> * Tree<'T>
  | Right of Path<'T> * Tree<'T>
  override ToString : unit -> string

Full name: Tree-zipper-query.Path<_>
union case Path.Top: Path<'T>
union case Path.Left: Path<'T> * Tree<'T> -> Path<'T>
union case Path.Right: Path<'T> * Tree<'T> -> Path<'T>
val x : Path<'T>
override Path.ToString : unit -> string

Full name: Tree-zipper-query.Path`1.ToString
match x with
    | Top -> "T"
    | Left(p, t) -> sprintf "L(%O, %O)" p t
    | Right(p, t) -> sprintf "R(%O, %O)" p t
type TreeZipper<'T> =
  | TZ of Tree<'T> * Path<'T>
  override ToString : unit -> string

Full name: Tree-zipper-query.TreeZipper<_>
union case TreeZipper.TZ: Tree<'T> * Path<'T> -> TreeZipper<'T>
val x : TreeZipper<'T>
override TreeZipper.ToString : unit -> string

Full name: Tree-zipper-query.TreeZipper`1.ToString
let (TZ(t, p)) = x in sprintf "%O [%O]" t p
val left : _arg1:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.left


 Navigates to the left sub-tree
val failwith : message:string -> 'T

Full name: Microsoft.FSharp.Core.Operators.failwith
val l : Tree<'a>
val r : Tree<'a>
val p : Path<'a>
val right : _arg1:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.right


 Navigates to the right sub-tree
val current : _arg1:TreeZipper<'a> -> 'a

Full name: Tree-zipper-query.current


 Gets the value at the current position
val x : 'a
val branches : Tree<int>

Full name: Tree-zipper-query.branches
val sample : TreeZipper<int>

Full name: Tree-zipper-query.sample
val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn
val up : _arg1:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.up
val top : _arg1:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.top
val t : TreeZipper<'a>
val tz : TreeZipper<'a>
Multiple items
val unit : v:'a -> TreeZipper<'a>

Full name: Tree-zipper-query.unit


 Build tree zipper with singleton tree

--------------------
type unit = Unit

Full name: Microsoft.FSharp.Core.unit
val v : 'a
val bindSub : f:('a -> TreeZipper<'a>) -> treeZip:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.bindSub


 Transform leaves in the current sub-tree of 'treeZip'
 into other trees using the provided function 'f'
val f : ('a -> TreeZipper<'a>)
val treeZip : TreeZipper<'a>
val bindT : (Tree<'a> -> Tree<'a>)
val t : Tree<'a>
val current : Tree<'a>
val path : Path<'a>
Multiple items
type TreeZipperBuilder =
  new : unit -> TreeZipperBuilder
  member Current : tz:TreeZipper<'a> -> 'a
  member For : tz:TreeZipper<'T> * f:('T -> TreeZipper<'T>) -> TreeZipper<'T>
  member Left : tz:TreeZipper<'a> -> TreeZipper<'a>
  member Right : tz:TreeZipper<'a> -> TreeZipper<'a>
  member Select : tz:TreeZipper<'a> * f:('a -> 'a) -> TreeZipper<'a>
  member Top : tz:TreeZipper<'a> -> TreeZipper<'a>
  member Up : tz:TreeZipper<'a> -> TreeZipper<'a>
  member Yield : v:'a -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder

--------------------
new : unit -> TreeZipperBuilder
val x : TreeZipperBuilder
member TreeZipperBuilder.For : tz:TreeZipper<'T> * f:('T -> TreeZipper<'T>) -> TreeZipper<'T>

Full name: Tree-zipper-query.TreeZipperBuilder.For


 Enables the 'for x in xs do ..' syntax
val tz : TreeZipper<'T>
val f : ('T -> TreeZipper<'T>)
member TreeZipperBuilder.Yield : v:'a -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Yield


 Enables the 'yield x' syntax
val tree : TreeZipperBuilder

Full name: Tree-zipper-query.tree


 Global instance of the computation builder
Multiple items
type CustomOperationAttribute =
  inherit Attribute
  new : name:string -> CustomOperationAttribute
  member AllowIntoPattern : bool
  member IsLikeGroupJoin : bool
  member IsLikeJoin : bool
  member IsLikeZip : bool
  member JoinConditionWord : string
  member MaintainsVariableSpace : bool
  member MaintainsVariableSpaceUsingBind : bool
  member Name : string
  ...

Full name: Microsoft.FSharp.Core.CustomOperationAttribute

--------------------
new : name:string -> CustomOperationAttribute
member TreeZipperBuilder.Left : tz:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Left
member TreeZipperBuilder.Right : tz:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Right
member TreeZipperBuilder.Up : tz:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Up
member TreeZipperBuilder.Top : tz:TreeZipper<'a> -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Top
member TreeZipperBuilder.Current : tz:TreeZipper<'a> -> 'a

Full name: Tree-zipper-query.TreeZipperBuilder.Current


 Extracts the current value and returns it
member TreeZipperBuilder.Select : tz:TreeZipper<'a> * f:('a -> 'a) -> TreeZipper<'a>

Full name: Tree-zipper-query.TreeZipperBuilder.Select


 Transform the current sub-tree using 'f'
Multiple items
type ProjectionParameterAttribute =
  inherit Attribute
  new : unit -> ProjectionParameterAttribute

Full name: Microsoft.FSharp.Core.ProjectionParameterAttribute

--------------------
new : unit -> ProjectionParameterAttribute
val f : ('a -> 'a)
custom operation: right

Calls TreeZipperBuilder.Right
custom operation: left

Calls TreeZipperBuilder.Left
custom operation: current

Calls TreeZipperBuilder.Current


 Extracts the current value and returns it
custom operation: map ('a)

Calls TreeZipperBuilder.Select


 Transform the current sub-tree using 'f'
custom operation: up

Calls TreeZipperBuilder.Up
custom operation: top

Calls TreeZipperBuilder.Top
val tree : TreeZipperBuilder

Full name: Tree-zipper-query.tree


 Global instance of the computation builder
val x : int
val sample : TreeZipper<int>

Full name: Tree-zipper-query.sample
custom operation: left

Calls TreeZipperBuilder.Left
custom operation: map ('a)

Calls TreeZipperBuilder.Select


 Transform the current sub-tree using 'f'
custom operation: up

Calls TreeZipperBuilder.Up
custom operation: right

Calls TreeZipperBuilder.Right
custom operation: top

Calls TreeZipperBuilder.Top

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Wednesday, December 19, 2012

Manning: F# Deep Dives deal of the day

The F# language has been around for longer than many people suspect. My first, completely outdated, blog post was from May 2006. The Microsoft Research releases, sometime around 2006 were the first stable versions that gained some interest and slowly attracted commercial users.

A lot has changed since the early days. F# now includes powerful features like computation expressions and asynchronous workflows and F# 3.0 comes with unique type provider mechanism.

There is an increasing number of users from diverse domains: F# is used to model complex domains in finance and science; asynchronous and concurrent features are used to write server-side components of social games and trading systems, but also in web programming; the expressivity of F# is used by machine learning experts to handle dirty data or classify XBox players. Moreover, the F# Software Foundation has been recently founded to support the collaboration between different commercial users, open-source community and academia.

There is an increasing interest in F#, but many of those who approach it ask (excellent) questions such as: "In what problem domains can I benefit from F#?" or "How do I use F# in finance/science/gaming or web programming?" and most importantly "How do I approach different problems in F#?"

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Tuesday, December 18, 2012

Learn F# at TechMesh and SkillsMetter

Autumn is a busy period and I already invited you to a couple of interesting events, but there are two more events that you definitely should not miss. In only two weeks, you can come to two-day Progressive F# Tutorials packed with tutorials for both F# beginners and experts. At the beginning of December, the TechMesh Conference comes with three days of talks about alternative (and future) technologies.

I'll be speaking at both Progressive F# Tutorials and TechMesh and I'm also doing a tutorial at TechMesh, so if you want to learn about F#, type providers in F# 3.0 and financial computing with F#, here are some talks that you should not miss...

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Sunday, October 21, 2012

Applicative functors: definition and syntax

In a recent blog post, Edward Z. Yang talks about applicative functors. He mentions two equivalent definitions of applicative functors - the standard definition used in Haskell libraries (Applicative) and an alternative that has been also presented in the original paper, but is generally less familiar (Monoidal).

The standard definition makes a perfect sense with the standard uses in Haskell, however I always preferred the alternative definition. Edward uses the alternative (Monoidal) definition to explain the laws that should hold about applicative functors and to explain commutative applicative functors, but I think it is even more useful.

The Monoidal definition fits nicely with a trick that you can use to encode applicative functors in C# using LINQ and I also used it as a basis for an F# syntax extension that allows writing code using applicative functors in a similar style as using monads (which is discussed in my draft paper about writing abstract computations in F#). And I also think that commutative applicative functors deserve more attention.

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Tuesday, August 21, 2012

Why type-first development matters

Using functional programming language changes the way you write code in a number of ways. Many of the changes are at a small-scale. For example, you learn how to express computations in a shorter, more declarative way using higher-order functions. However, there are also many changes at a large-scale. The most notable one is that, when designing a program, you start thinking about the (data) types that represent the data your code works with.

In this article, I describe this approach. Since the acronym TDD is already taken, I call the approach Type-First Development (TFD), which is probably a better name anyway. The development is not driven by types. It starts with types, but the rest of the implementation can still use test-driven development for the implementation.

This article demonstrates the approach using a case study from a real life: My example is a project that I started working on with a friend who needed a system to log journeys with a company car (for expense reports). Using the type-first approach made it easier to understand and discuss the problem.

In many ways, TFD is a very simple approach, so this article just gives a name to a practice that is quite common among functional and F# programmers (and we have been teaching it at our F# trainings for the last year)...

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Thursday, August 16, 2012