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Introduction to monoids, semigroups, and similar concepts, for object-oriented programmers.

This article series is part of an even larger series of articles about the relationship between design patterns and category theory.

Functional programming has often been criticised for its abstruse jargon. Terminology like zygohistomorphic prepromorphism doesn't help sell the message, but before we start throwing stones, we should first exit our own glass house. In object-oriented design, we have names like Bridge, Visitor, SOLID, cohesion, and so on. The words sound familiar, but can you actually explain or implement the Visitor design pattern, or characterise cohesion?

That Bridge is a word you know doesn't make object-oriented terminology better. Perhaps it even makes it worse. After all, now the word has become ambiguous: did you mean a physical structure connecting two places, or are you talking about the design pattern? Granted, in practical use, it will often be clear from the context, but it doesn't change that if someone talks about the Bridge pattern, you'll have no idea what it is, unless you've actually learned it. Thus, that the word is familiar doesn't make it better.

More than one object-oriented programmer have extolled the virtues of 'operations whose return type is the same as the type of its argument(s)'. Such vocabulary, however, is inconvenient. Wouldn't it be nice to have a single, well-defined word for this? Perhaps monoid, or semigroup?

Object-oriented hunches #

In Domain-Driven Design, Eric Evans discusses the notion of Closure of Operations, that is, operations "whose return type is the same as the type of its argument(s)." In C#, it could be a method with the signature public Foo Bar(Foo f1, Foo f2). This method takes two Foo objects as input, and returns a new Foo object as output.

As Evans points out, object designs with that quality begins to look like arithmetic. If you have an operation that takes two Foo and returns a Foo, what could it be? Could it be like addition? Multiplication? Another mathematical operation?

Some enterprise developers just 'want to get stuff done', and don't care about mathematics. To them, the value of making code more mathematical is disputable. Still, even if you 'don't like maths', you understand addition, multiplication, and so on. Arithmetic is a powerful metaphor, because all programmers understand it.

In his book Test-Driven Development: By Example, Kent Beck seems to have the same hunch, although I don't think he ever explicitly calls it out.

What Evans describes are monoids, semigroups, and similar concepts from abstract algebra. To be fair, I recently had the opportunity to discuss the matter with him, and he's perfectly aware of those concepts today. Whether he was aware of them when he wrote DDD in 2003 I don't know, but I certainly wasn't; my errand isn't to point fingers, but to point out that clever people have found this design principle valuable in object-oriented design long before they gave it a distinct name.

Relationships #

Monoids and semigroups belong to a larger group of operations called magmas. You'll learn about those later, but we'll start with monoids, move on to semigroups, and then explore other magmas. All monoids are semigroups, while the inverse doesn't hold. In other words, monoids form a subset of semigroups.

All magmas describe binary operations of the form: an operation takes two Foo values as input and returns a Foo value as output. Both categories are governed by (intuitive) laws. The difference is that the laws governing monoids are stricter than the laws governing semigroups. Don't be put off by the terminology; 'law' may sound like you have to get involved in complicated maths, but these laws are simple and intuitive. You'll learn them as you read on.

• Monoids
  • Angular addition monoid
  • Strings, lists, and sequences as a monoid
  • Money monoid
  • Convex hull monoid
  • Tuple monoids
  • Function monoids
  • Endomorphism monoid
  • Maybe monoids
  • Lazy monoids
  • Monoids accumulate
• Semigroups
  • Bounding box semigroup
  • Semigroups accumulate
• Quasigroups
• Magmas
  • Rock Paper Scissors magma
  • Colour-mixing magma

Summary #

To the average object-oriented programmer, terms like monoid and semigroup smell of mathematics, academia, and ivory-tower astronaut architects, but they're plain and simple concepts that anyone can understand, if they wish to invest 15 minutes of their time.

Whether or not an object is a magma tells us whether Evans' Closure of Operations is possible. It might teach us other things about our code, as well.

Next: Monoids.

Comments

How do you design good abstractions? By using abstractions that already exist.

When I was a boy, I had a cassette tape player. It came with playback controls like these:

Soon after cassette players had become widely adopted, VCR manufacturers figured out that they could reuse those symbols to make their machines easier to use. Everyone could play a video tape, but 'no one' could 'program' them, because, while playback controls were already universally understood by consumers, each VCR came with its own proprietary interface for 'programming'.

Then came CD players. Same controls.

MP3 players. Same controls.

Streaming audio and video players. Same controls.

If you download an app that plays music, odds are that you'll find it easy to get started playing music. One reason is that all playback apps seem to have the same common set of controls. It's an abstraction that you already know.

Understanding source code #

As I explain in my Humane Code video, you can't program without abstractions. To summarise, in the words of Robert C. Martin

"Abstraction is the elimination of the irrelevant and the amplification of the essential"

Not only can a good abstraction shield you from having to understand all the details in a big system, but if you're familiar with the abstraction, you may be able to quickly get up to speed.

While the above definition is great for identifying a good abstraction, it doesn't tell you how to create one.

Design patterns #

Design Patterns explains that a design pattern is a general reusable solution to a commonly occurring problem. As I interpret the original intent of the Gang of Four, the book was an attempt to collect and abstract solutions that were repeatedly observed 'in the wild'. The design patterns in the book are descriptive, not prescriptive.

Design patterns are useful in two ways:

• They offer solutions
• They form a vocabulary

I have no problems with ready-made solutions, but I think that the other advantage may be even bigger. When you're looking at unfamiliar source code, you struggle to understand how it's structured, and what it does. If, hypothetically, you discover that pieces of that unfamiliar source code follows a design pattern that you know, then understanding the code becomes much easier.

There are two criteria for this to happen:

• The reader (you) must already know the pattern
• The original author (also you?) must have implemented the pattern without any surprising deviations

Ambiguous specification #

Programming to a well-known abstraction is a force multiplier, but it does require that those two conditions are satisfied: prior knowledge, and correct implementation.

I don't know how to solve the prior knowledge requirement, other than to tell you to study. I do, however, think that it's possible to formalise some of the known design patterns.

Most design patterns are described in some depth. They come with sections on motivation, when to use and not to use, diagrams, and example code. Furthermore, they also come with an overview of variations.

Picture this: as a reader, you've just identified that the code you're looking at is an implementation of a design pattern. Then you realise that it isn't structured like you'd expect, or that its behaviour surprises you. Was the author incompetent, after all?

While you're inclined to believe the worst about your fellow (wo)man, you look up the original pattern, and there it is: the author is using a variation of the pattern.

Design patterns are ambiguous.

Universal abstractions #

Design Patterns was a great effort in 1994, and I've personally benefited from it. The catalogue was an attempt to discover good abstractions.

What's a good abstraction? As already quoted, it's a model that amplifies the essentials, etcetera. I think a good abstraction should also be intuitive.

What's the most intuitive abstractions ever?

Mathematics.

Stay with me, please. If you're a normal reader of my blog, you're most likely an 'industry programmer' or enterprise developer. You're not interested in mathematics. Perhaps mathematics even turns you off, and at the very least, you never had use for mathematics in programming.

You may not find n-dimensional differential topology, or stochastic calculus, intuitive, but that's not the kind of mathematics I have in mind.

Basic arithmetic is intuitive. You know: 1 + 3 = 4, or 3 * 4 = 12. In fact, it's so intuitive that you can't formally prove it -without axioms, that is. These axioms are unprovable; you must take them at face value, but you'll readily do that because they're so intuitive.

Mathematics is a big structure, but it's all based on intuitive axioms. Mathematics is intuitive.

Writers before me have celebrated the power of mathematical abstraction in programming. For instance, in Domain-Driven Design Eric Evans discusses how Closure of Operations leads to object models reminiscent of arithmetic. If you can design Value Objects in such a way that you can somehow 'add' them together, you have an intuitive and powerful abstraction.

Notice that there's more than one way to combine numbers. You can add them together, but you can also multiply them. Could there be a common abstraction for that? What about objects that can somehow be combined, even if they aren't 'number-like'? The generalisation of such operations is a branch of mathematics called category theory, and it has turned out to be productive when applied to functional programming. Haskell is the most prominent example.

By an interesting coincidence, the 'things' in category theory are called objects, and while they aren't objects in the sense that we think of in object-oriented design, there is some equivalence. Category theory concerns itself with how objects map to other objects. A functional programmer would interpret such morphisms as functions, but in a sense, you can also think of them as well-defined behaviour that's associated with data.

The objects of category theory are universal abstractions. Some of them, it turns out, coincide with known design patterns. The difference is, however, that category theory concepts are governed by specific laws. In order to be a functor, for example, an object must obey certain simple and intuitive laws. This makes the category theory concepts more specific, and less ambiguous, than design patterns.

The coming article series is an exploration of this space:

• Monoids, semigroups, and friends
  • Monoids
    • Angular addition monoid
    • Strings, lists, and sequences as a monoid
    • Money monoid
    • Convex hull monoid
    • Tuple monoids
    • Function monoids
    • Endomorphism monoid
    • Maybe monoids
    • Lazy monoids
    • Monoids accumulate
  • Semigroups
    • Bounding box semigroup
    • Semigroups accumulate
  • Quasigroups
  • Magmas
    • Rock Paper Scissors magma
    • Colour-mixing magma
• Functors, applicatives, and friends
  • Functors
    • The Maybe functor
    • An Either functor
    • A Tree functor
    • A rose tree functor
    • A Visitor functor
    • Reactive functor
    • The Identity functor
    • The Lazy functor
    • Asynchronous functors
    • The State functor
    • The Reader functor
    • The IO functor
    • Monomorphic functors
    • Set is not a functor
  • Applicative functors
    • Full deck
    • An applicative password list
    • Applicative combinations of functions
    • The Maybe applicative functor
    • Applicative validation
    • The Test Data Generator applicative functor
    • Danish CPR numbers in F#
    • The Lazy applicative functor
    • Applicative monoids
  • Bifunctors
    • Tuple bifunctor
    • Either bifunctor
    • Rose tree bifunctor
  • Contravariant functors
    • The Command Handler contravariant functor
    • The Specification contravariant functor
    • The Equivalence contravariant functor
    • Reader as a contravariant functor
    • Functor variance compared to C#'s notion of variance
    • Contravariant Dependency Injection
  • Profunctors
    • Reader as a profunctor
  • Invariant functors
    • Endomorphism as an invariant functor
    • Natural transformations as invariant functors
    • Functors as invariant functors
    • Contravariant functors as invariant functors
  • Monads
    • Kleisli composition
    • Monad laws
    • The List monad
    • The Maybe monad
    • An Either monad
    • The Identity monad
    • The Lazy monad
    • Asynchronous monads
    • The State monad
    • The Reader monad
    • The IO monad
    • Test Data Generator monad
  • Functor relationships
    • Natural transformations
    • Traversals
    • Functor compositions
    • Functor products
    • Functor sums
• Software design isomorphisms
  • Unit isomorphisms
  • Function isomorphisms
  • Argument list isomorphisms
  • Uncurry isomorphisms
  • Object isomorphisms
  • Abstract class isomorphism
  • Inheritance-composition isomorphism
  • Tester-Doer isomorphisms
  • Builder isomorphisms
• Church encoding
  • Church-encoded Boolean values
  • Church-encoded natural numbers
  • Church-encoded Maybe
  • Church-encoded Either
  • Church-encoded payment types
  • Church-encoded rose tree
• Catamorphisms
  • Boolean catamorphism
  • Peano catamorphism
  • Maybe catamorphism
  • List catamorphism
  • Either catamorphism
  • Tree catamorphism
  • Rose tree catamorphism
  • Full binary tree catamorphism
  • Payment types catamorphism
• Some design patterns as universal abstractions
  • Composite as a monoid
    • Coalescing Composite as a monoid
    • Endomorphic Composite as a monoid
  • Null Object as identity
  • Builder as a monoid
  • Visitor as a sum type
  • Chain of Responsibility as catamorphisms
  • The State pattern and the State monad
    • Refactoring the TCP State pattern example to pure functions
    • Refactoring a saga from the State pattern to the State monad
  • Postel's law as a profunctor
  • The Liskov Substitution Principle as a profunctor
  • Backwards compatibility as a profunctor

Motivation #

The purpose of this article series is two-fold. Depending on your needs and interests, you can use it to

• learn better abstractions
• learn how functional programming is a real alternative to object-oriented programming

The other goal of these articles may be less clear. Object-oriented programming (OOP) is the dominant software design paradigm. It wasn't always so. When OOP was new, many veteran programmers couldn't see how it could be useful. They were schooled in one paradigm, and it was difficult for them to shift to the new paradigm. They were used to do things in one way (typically, procedural), and it wasn't clear how to achieve the same goals with idiomatic object-oriented design.

The same sort of resistance applies to functional programming. Tasks that are easy in OOP seem impossible in functional programming. How do you make a for loop? How do you change state? How do you break out of a routine?

This leads to both frustration, and dismissal of functional programming, which is still seen as either academic, or something only interesting in computation-heavy domains like science or finance.

It's my secondary goal with these articles to show that:

1. There are clear equivalences between known design patterns and concepts from category theory
2. Thus, functional programming is as universally useful as OOP
3. Since equivalences exist, there's a learning path

Work in progress #

I've been thinking about these topics for years. What's a good abstraction? When do abstractions compose?

My first attempt at answering these questions was in 2010, but while I had the experience that certain abstractions composed better than others, I lacked the vocabulary. I've been wanting to write a better treatment of the topic ever since, but I've been constantly learning as I've grappled with the concepts.

I believe that I now have the vocabulary to take a stab at this again. This is hardly the ultimate treatment. A year from now, I hope to have learned even more, and perhaps that'll lead to further insights or refinement. Still, I can't postpone writing this article until I've stopped learning, because at that time I'll either be dead or senile.

I'll write these articles in an authoritative voice, because a text that constantly moderates and qualifies its assertions easily becomes unreadable. Don't consider the tone an indication that I'm certain that I'm right. I've tried to be as rigorous in my arguments as I could, but I don't have a formal education in computer science. I welcome feedback on any article, both if it's to corroborate my findings, or if it's to refute them. If you have any sort of feedback, then please leave a comment.

I consider the publication of these articles as though I submit them to peer review. If you can refute them, they deserve to be refuted. If not, they just may be valuable to other people.

Summary #

Category theory generalises some intuitive relations, such as how numbers combine (e.g. via addition or multiplication). Instead of discussing numbers, however, category theory considers abstract 'objects'. This field of mathematics explore how object relate and compose.

Some category theory concepts can be translated to code. These universal abstractions can form the basis of a powerful and concise software design vocabulary.

The design patterns movement was an early attempt to create such a vocabulary. I think using category theory offers the chance of a better vocabulary, but fortunately, all the work that went into design patterns isn't wasted. It seems to me that some design patterns are essentially ad-hoc, informally specified, specialised instances of basic category theory concepts. There's quite a bit of overlap. This should further strengthen the argument that category theory is valuable in programming, because some of the concepts are equivalent to design patterns that have already proven useful.

Next: Monoids, semigroups, and friends.

Comments

How do you do AOP with Pure DI?

One of my readers, Nick Ball, asks me this question:

"Just spent the last couple of hours reading chapter 9 of your book about Interceptors. The final few pages show how to use Castle Windsor to make the code DRYer. That's cool, but I'm quite a fan of Pure DI as I tend to think it keeps things simpler. Plus I'm working in a legacy C++ application which limits the tooling available to me.

"So, I was wondering if you had any suggestions on how to DRY up an interceptor in Pure DI? I know in your book you state that this is where DI containers come into their own, but I also know through reading your blog that you prefer going the Pure DI route too. Hence I wondered whether you'd had any further insight since the book publication?"

It's been more than 15 years since I last did C++, so I'm going to give an answer based on C#, and hope it translates.

Position #

I do, indeed, prefer Pure DI, but there may be cases where a DI Container is warranted. Interception, or Aspect-Oriented Programming (AOP), is one such case, but obviously that doesn't help if you can't use a DI Container.

Another option for AOP is some sort of post-processor of your code. As I briefly cover in chapter 9 of my book, in .NET this is typically done by a custom tool using 'IL-weaving'. As I also outline in the book, I'm not a big fan of this approach, but perhaps that could be an option in C++ as well. In any case, I'll proceed under the assumption that you want a strictly code-based solution, involving no custom tools or build steps.

All that said, I doubt that this is as much of a problem than one would think. AOP is typically used for cross-cutting concerns such as logging, caching, instrumentation, authorization, metering, or auditing. As an alternative, you can also use Decorators for such cross-cutting concerns. This seems daunting if you truly need to decorate hundreds, or even thousands, of classes. In such a case, convention-based interception seems like a DRYer option.

You'd think.

In my experience, however, this is rarely the case. Typically, even when applying caching, logging, or authorisation logic, I've only had to create a handful of Decorators. Perhaps it's because I tend to keep my code bases to a manageable size.

If you only need a dozen Decorators, I don't think that the loss of compile-time safety and the added dependency warrants the use of a DI Container. That doesn't mean, however, that I can't aim for as DRY code as possible.

Instrument #

If you don't have a DI Container or an AOP tool, I believe that a Decorator is the best way to address cross-cutting concerns, and I don't think there's any way around adding those Decorator classes. The aim, then, becomes to minimise the effort involved in creating and maintaining such classes.

As an example, I'll revisit an old blog post. In that post, the task was to instrument an OrderProcessor class. The solution shown in that article was to use Castle Windsor to define an IInterceptor.

To recapitulate, the code for the Interceptor looks like this:

public class InstrumentingInterceptor : IInterceptor
{
    private readonly IRegistrar registrar;
 
    public InstrumentingInterceptor(IRegistrar registrar)
    {
        if (registrar == null)
            throw new ArgumentNullException(nameof(registrar));
 
        this.registrar = registrar;
    }
 
    public void Intercept(IInvocation invocation)
    {
        var correlationId = Guid.NewGuid();
        this.registrar.Register(correlationId,
            string.Format("{0} begins ({1})",
                invocation.Method.Name,
                invocation.TargetType.Name));
 
        invocation.Proceed();
 
        this.registrar.Register(correlationId,
            string.Format("{0} ends   ({1})",
                invocation.Method.Name,
                invocation.TargetType.Name));
    }
}

While, in the new scenario, you can't use Castle Windsor, you can still take the code and make a similar class out of it. Call it Instrument, because classes should have noun names, and instrument is a noun (right?).

public class Instrument
{
    private readonly IRegistrar registrar;
 
    public Instrument(IRegistrar registrar)
    {
        if (registrar == null)
            throw new ArgumentNullException(nameof(registrar));
 
        this.registrar = registrar;
    }
 
    public T Intercept<T>(
        string methodName,
        string typeName,
        Func<T> proceed)
    {
        var correlationId = Guid.NewGuid();
        this.registrar.Register(
            correlationId,
            string.Format("{0} begins ({1})", methodName, typeName));
 
        var result = proceed();
 
        this.registrar.Register(
            correlationId,
            string.Format("{0} ends   ({1})", methodName, typeName));
 
        return result;
    }
 
    public void Intercept(
        string methodName,
        string typeName,
        Action proceed)
    {
        var correlationId = Guid.NewGuid();
        this.registrar.Register(
            correlationId,
            string.Format("{0} begins ({1})", methodName, typeName));
 
        proceed();
 
        this.registrar.Register(
            correlationId,
            string.Format("{0} ends   ({1})", methodName, typeName));
    }
}

Instead of a single Intercept method, the Instrument class exposes two Intercept overloads; one for methods without a return value, and one for methods that return a value. Instead of an IInvocation argument, the overload for methods without a return value takes an Action delegate, whereas the other overload takes a Func<T>.

Both overload also take methodName and typeName arguments.

Most of the code in the two methods is similar. While you could refactor to a Template Method, I invoke the Rule of three and let the duplication stay for now.

Decorators #

The Instrument class isn't going to magically create Decorators for you, but it reduces the effort of creating one:

public class InstrumentedOrderProcessor2 : IOrderProcessor
{
    private readonly IOrderProcessor orderProcessor;
    private readonly Instrument instrument;
 
    public InstrumentedOrderProcessor2(
        IOrderProcessor orderProcessor,
        Instrument instrument)
    {
        if (orderProcessor == null)
            throw new ArgumentNullException(nameof(orderProcessor));
        if (instrument == null)
            throw new ArgumentNullException(nameof(instrument));
 
        this.orderProcessor = orderProcessor;
        this.instrument = instrument;
    }
 
    public SuccessResult Process(Order order)
    {
        return this.instrument.Intercept(
            nameof(Process),
            this.orderProcessor.GetType().Name,
            () => this.orderProcessor.Process(order));
    }
}

I called this class InstrumentedOrderProcessor2 with the 2 postfix because the previous article already contains a InstrumentedOrderProcessor class, and I wanted to make it clear that this is a new class.

Notice that InstrumentedOrderProcessor2 is a Decorator of IOrderProcessor. It both implements the interface, and takes one as a dependency. It also takes an Instrument object as a Concrete Dependency. This is mostly to enable reuse of a single Instrument object; no polymorphism is implied.

The decorated Process method simply delegates to the instrument's Intercept method, passing as parameters the name of the method, the name of the decorated class, and a lambda expression that closes over the outer order method argument.

For simplicity's sake, the Process method invokes this.orderProcessor.GetType().Name every time it's called, which may not be efficient. Since the orderProcessor class field is readonly, though, you could optimise this by getting the name once and for all in the constructor, and assign the string to a third class field. I didn't want to complicate the example with irrelevant code, though.

Here's another Decorator:

public class InstrumentedOrderShipper : IOrderShipper
{
    private readonly IOrderShipper orderShipper;
    private readonly Instrument instrument;
 
    public InstrumentedOrderShipper(
        IOrderShipper orderShipper,
        Instrument instrument)
    {
        if (orderShipper == null)
            throw new ArgumentNullException(nameof(orderShipper));
        if (instrument == null)
            throw new ArgumentNullException(nameof(instrument));
 
        this.orderShipper = orderShipper;
        this.instrument = instrument;
    }
 
    public void Ship(Order order)
    {
        this.instrument.Intercept(
            nameof(Ship),
            this.orderShipper.GetType().Name,
            () => this.orderShipper.Ship(order));
    }
}

As you can tell, it's similar to InstrumentedOrderProcessor2, but instead of IOrderProcessor it decorates IOrderShipper. The most significant difference is that the Ship method doesn't return any value, so you have to use the Action-based overload of Intercept.

For completeness sake, here's a third interesting example:

public class InstrumentedUserContext : IUserContext
{
    private readonly IUserContext userContext;
    private readonly Instrument instrument;
 
    public InstrumentedUserContext(
        IUserContext userContext,
        Instrument instrument)
    {
        if (userContext == null)
            throw new ArgumentNullException(nameof(userContext));
        if (instrument == null)
            throw new ArgumentNullException(nameof(instrument));
 
        this.userContext = userContext;
        this.instrument = instrument;
    }
 
    public User GetCurrentUser()
    {
        return this.instrument.Intercept(
            nameof(GetCurrentUser),
            this.userContext.GetType().Name,
            this.userContext.GetCurrentUser);
    }
 
    public Currency GetSelectedCurrency(User currentUser)
    {
        return this.instrument.Intercept(
            nameof(GetSelectedCurrency),
            this.userContext.GetType().Name,
            () => this.userContext.GetSelectedCurrency(currentUser));
    }
}

This example demonstrates that you can also decorate an interface that defines more than a single method. The IUserContext interface defines both GetCurrentUser and GetSelectedCurrency. The GetCurrentUser method takes no arguments, so instead of a lambda expression, you can pass the delegate using method group syntax.

Composition #

You can add such instrumenting Decorators for all appropriate interfaces. It's trivial (and automatable) work, but it's easy to do. While it seems repetitive, I can't come up with a more DRY way to do it without resorting to some sort of run-time Interception or AOP tool.

There's some repetitive code, but I don't think that the maintenance overhead is particularly great. The Decorators do minimal work, so it's unlikely that there are many defects in that area of your code base. If you need to change the instrumentation implementation in itself, the Instrument class has that (single) responsibility.

Assuming that you've added all desired Decorators, you can use Pure DI to compose an object graph:

var instrument = new Instrument(registrar);
var sut = new InstrumentedOrderProcessor2(
    new OrderProcessor(
        new InstrumentedOrderValidator(
            new TrueOrderValidator(),
            instrument),
        new InstrumentedOrderShipper(
            new OrderShipper(),
            instrument),
        new InstrumentedOrderCollector(
            new OrderCollector(
                new InstrumentedAccountsReceivable(
                    new AccountsReceivable(),
                    instrument),
                new InstrumentedRateExchange(
                    new RateExchange(),
                    instrument),
                new InstrumentedUserContext(
                    new UserContext(),
                    instrument)),
            instrument)),
    instrument);

This code fragment is from a unit test, which explains why the object is called sut. In case you're wondering, this is also the reason for the existence of the curiously named class TrueOrderValidator. This is a test-specific Stub of IOrderValidator that always returns true.

As you can see, each leaf implementation of an interface is contained within an InstrumentedXyz Decorator, which also takes a shared instrument object.

When I call the sut's Process method with a proper Order object, I get output like this:

4ad34380-6826-440c-8d81-64bbd1f36d39  2017-08-25T17:49:18.43  Process begins (OrderProcessor)
c85886a7-1ce8-4096-8a30-5f87bf0014e3  2017-08-25T17:49:18.52  Validate begins (TrueOrderValidator)
c85886a7-1ce8-4096-8a30-5f87bf0014e3  2017-08-25T17:49:18.52  Validate ends   (TrueOrderValidator)
8f7606b6-f3f7-4231-808d-d5e37f1f2201  2017-08-25T17:49:18.53  Collect begins (OrderCollector)
28250a92-6024-439e-b010-f66c63903673  2017-08-25T17:49:18.55  GetCurrentUser begins (UserContext)
28250a92-6024-439e-b010-f66c63903673  2017-08-25T17:49:18.56  GetCurrentUser ends   (UserContext)
294ce552-201f-41d2-b7fc-291e2d3720d6  2017-08-25T17:49:18.56  GetCurrentUser begins (UserContext)
294ce552-201f-41d2-b7fc-291e2d3720d6  2017-08-25T17:49:18.56  GetCurrentUser ends   (UserContext)
96ee96f0-4b95-4b17-9993-33fa87972013  2017-08-25T17:49:18.57  GetSelectedCurrency begins (UserContext)
96ee96f0-4b95-4b17-9993-33fa87972013  2017-08-25T17:49:18.58  GetSelectedCurrency ends   (UserContext)
3af884e5-8e97-44ea-aa0d-2c9e0418110b  2017-08-25T17:49:18.59  Convert begins (RateExchange)
3af884e5-8e97-44ea-aa0d-2c9e0418110b  2017-08-25T17:49:18.59  Convert ends   (RateExchange)
b8bd0701-515b-44fe-949f-5f5fb5a4590d  2017-08-25T17:49:18.60  Collect begins (AccountsReceivable)
b8bd0701-515b-44fe-949f-5f5fb5a4590d  2017-08-25T17:49:18.60  Collect ends   (AccountsReceivable)
8f7606b6-f3f7-4231-808d-d5e37f1f2201  2017-08-25T17:49:18.60  Collect ends   (OrderCollector)
beadabc4-df17-468f-8553-34ae4e3bdbfc  2017-08-25T17:49:18.60  Ship begins (OrderShipper)
beadabc4-df17-468f-8553-34ae4e3bdbfc  2017-08-25T17:49:18.61  Ship ends   (OrderShipper)
4ad34380-6826-440c-8d81-64bbd1f36d39  2017-08-25T17:49:18.61  Process ends   (OrderProcessor)

This is similar to the output from the previous article.

Summary #

When writing object-oriented code, I still prefer Pure DI over using a DI Container, but if I absolutely needed to decorate many services, I'd seriously consider using a DI Container with run-time Interception capabilities. The need rarely materialises, though.

As an intermediate solution, you can use a delegation-based design like the one shown here. As always, it's all a matter of balancing the constraints and goals of the specific situation.

A Test Data Generator modelled as a functor.

In a previous article series, you learned that while it's possible to model Test Data Builders as a functor, it adds little value. You shouldn't, however, dismiss the value of functors. It's an abstraction that applies broadly.

Closely related to Test Data Builders is the concept of a generator of random test data. You could call it a Test Data Generator instead. Such a generator can be modelled as a functor.

A C# Generator #

At its core, the idea behind a Test Data Generator is to create random test data. Still, you'll like to be able control various parts of the process, because you'd often need to pin parts of the generated data to deterministic values, while allowing other parts to vary randomly.

In C#, you can write a generic Generator like this:

public class Generator<T>
{
    private readonly Func<Random, T> generate;
 
    public Generator(Func<Random, T> generate)
    {
        if (generate == null)
            throw new ArgumentNullException(nameof(generate));
 
        this.generate = generate;
    }
 
    public Generator<T1> Select<T1>(Func<T, T1> f)
    {
        if (f == null)
            throw new ArgumentNullException(nameof(f));
 
        Func<Random, T1> newGenerator = r => f(this.generate(r));
        return new Generator<T1>(newGenerator);
    }
 
    public T Generate(Random random)
    {
        if (random == null)
            throw new ArgumentNullException(nameof(random));
 
        return this.generate(random);
    }
}

The Generate method takes a Random object as input, and produces a value of the generic type T as output. This enables you to deterministically reproduce a particular randomly generated value, if you know the seed of the Random object.

Notice how Generator<T> is a simple Adapter over a (lazily evaluated) function. This function also takes a Random object as input, and produces a T value as output. (For the FP enthusiasts, this is simply the Reader functor in disguise.)

The Select method makes Generator<T> a functor. It takes a map function f as input, and uses it to define a new generate function. The return value is a Generator<T1>.

General-purpose building blocks #

Functors are immanently composable. You can compose complex Test Data Generators from simpler building blocks, like the following.

For instance, you may need a generator of alphanumeric strings. You can write it like this:

private const string alphaNumericCharacters =
    "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
 
public static Generator<string> AlphaNumericString =
    new Generator<string>(r =>
    {
        var length = r.Next(25); // Arbitrarily chosen max length
        var chars = new char[length];
        for (int i = 0; i < length; i++)
        {
            var idx = r.Next(alphaNumericCharacters.Length);
            chars[i] = alphaNumericCharacters[idx];
        }
        return new string(chars);
    });

This Generator<string> can generate a random string with alphanumeric characters. It randomly picks a length between 0 and 24, and fills it with randomly selected alphanumeric characters. The maximum length of 24 is arbitrarily chosen. The generated string may be empty.

Notice that the argument passed to the constructor is a function. It's not evaluated at initialisation, but only if Generate is called.

The r argument is the Random object passed to Generate.

Another useful general-purpose building block is a generator that can use a single-object generator to create many objects:

public static Generator<IEnumerable<T>> Many<T>(Generator<T> generator)
{
    return new Generator<IEnumerable<T>>(r =>
    {
        var length = r.Next(25); // Arbitrarily chosen max length
        var elements = new List<T>();
        for (int i = 0; i < length; i++)
            elements.Add(generator.Generate(r));
        return elements;
    });
}

This method takes a Generator<T> as input, and uses it to generate zero or more T objects. Again, the maximum length of 24 is arbitrarily chosen. It could have been a method argument, but in order to keep the example simple, I hard-coded it.

Domain-specific generators #

From such general-purpose building blocks, you can define custom generators for your domain model. This enables you to use such generators in your unit tests.

In order to generate post codes, you can combine the AlphaNumericString and the Many generators:

public static Generator<PostCode> PostCode =
    new Generator<PostCode>(r => 
    {
        var postCodes = Many(AlphaNumericString).Generate(r);
        return new PostCode(postCodes.ToArray());
    });

The PostCode class is part of your domain model; it takes an array of strings as input to its constructor. The PostCode generator uses the AlphaNumericString generator as input to the Many method. This generates zero or many alphanumeric strings, which you can pass to the PostCode constructor.

This, in turn, gives you all the building blocks you need to generate Address objects:

public static Generator<Address> Address =
    new Generator<Address>(r =>
    {
        var street = AlphaNumericString.Generate(r);
        var city = AlphaNumericString.Generate(r);
        var postCode = PostCode.Generate(r);
        return new Address(street, city, postCode);
    });

This Generator<Address> uses the AlphaNumericString generator to generate street and city strings. It uses the PostCode generator to generate a PostCode object. All these objects are passed to the Address constructor.

Keep in mind that all of this logic is defined in lazily evaluated functions. Only when you invoke the Generate method on a generator does the code execute.

Generating values #

You can now write tests similar to the tests shown in the article series about Test Data Builders. If, for example, you need an address in Paris, you can generate it like this:

var rnd = new Random();
var address = Gen.Address.Select(a => a.WithCity("Paris")).Generate(rnd);

Gen.Address is the Address generator shown above; I put all those generators in a static class called Gen. If you don't modify it, Gen.Address will generate a random Address object, but by using Select, you can pin the city to Paris.

You can also start with one type of generator and use Select to map to another type of generator, like this:

var rnd = new Random();
var address = Gen.PostCode
    .Select(pc => new Address("Rue Morgue", "Paris", pc))
    .Generate(rnd);

You use Gen.PostCode as the initial generator, and then Select a new Address in Rue Morgue, Paris, with a randomly generated post code.

Functor #

Such a Test Data Generator is a functor. One way to see that is to use query syntax instead of the fluent API:

var rnd = new Random();
var address =
    (from a in Gen.Address select a.WithCity("Paris")).Generate(rnd);

Likewise, you can also translate the Rue Morgue generator to query syntax:

var address = (
    from pc in Gen.PostCode
    select new Address("Rue Morgue", "Paris", pc)).Generate(rnd);

This is, however, awkward, because you have to enclose the query expression in brackets in order to be able to invoke the Generate method. Alternatively, you can separate the query from the generation, like this:

var g = from a in Gen.Address select a.WithCity("Paris");
var rnd = new Random();
var address = g.Generate(rnd);

Or this:

var g =
    from pc in Gen.PostCode
    select new Address("Rue Morgue", "Paris", pc);
var rnd = new Random();
var address = g.Generate(rnd);

You'd probably still prefer the fluent API over this syntax. The reason I show this alternative is to demonstrate that the functor gives you the ability to separate the definition of data generation from the actual generation. In order to emphasise this point, I defined the g variables before creating the Random object rnd.

Property-based testing #

The above Generator<T> is only a crude example of a Test Data Generator. In order to demonstrate how such a generator is a functor, I left out several useful features. Still, this should have given you a sense for how the Generator<T> class itself, as well as such general-purpose building blocks as Many and AlphaNumericString, could be packaged in a reusable library.

The examples above show how to use a generator to create a single random object. You could, however, easily generate many (say, 100) random objects, and run unit tests for each object created. This is the idea behind property-based testing.

There's more to property-based testing than generation of random values, but the implementations I've seen are all based on Test Data Generators as functors (and monads).

FsCheck #

FsCheck is an open source F# library for property-based testing. It defines a Gen functor (and monad) that you can use to generate Address values, just like the above examples:

let! address = Gen.address |> Gen.map (fun a -> { a with City = "Paris"} )

Here, Gen.address is a Gen<Address> value. By itself, it'll generate random Address values, but by using Gen.map, you can pin the city to Paris.

The map function corresponds to the C# Select method. In functional programming, map is the most common name, although Haskell calls the function fmap; the Select name is, in fact, the odd man out.

Likewise, you can map from one generator type to another:

let! address =
    Gen.postCode
    |> Gen.map (fun pc ->
        { Street = "Rue Morgue"; City = "Paris"; PostCode = pc })

This example uses Gen.postCode as the initial generator. This is, as the name implies, a Gen<PostCode> value. For every random PostCode value generated, map turns it into an address in Rue Morgue, Paris.

There's more going on here than I'd like to cover in this article. The use of let! syntax actually requires Gen<'a> to be a monad (which it is), but that's a topic for another day. Both of these examples are contained in a computation expression, and the implication of that is that the address values represent a multitude of randomly generated Address values.

Hedgehog #

Hedgehog is another open source F# library for property-based testing. With Hedgehog, the Address code examples look like this:

let! address = Gen.address |> Gen.map (fun a -> { a with City = "Paris"} )

And:

let! address =
    Gen.postCode
    |> Gen.map (fun pc ->
        { Street = "Rue Morgue"; City = "Paris"; PostCode = pc })

Did you notice something?

This is literally the same syntax as FsCheck! This isn't because Hedgehog is copying FsCheck, but because both are based on the same underlying abstraction: functor (and monad). There are other parts of the API where Hedgehog differs from FsCheck, but their generators are similar.

This is one of the most important advantages of using well-known abstractions like functors. Once you understand such an abstraction, it's easy to learn a new library. With professional experience with FsCheck, it only took me a few minutes to figure out how to use Hedgehog.

Summary #

Functors are well-defined objects from category theory. It may seem abstract, and far removed from 'real' programming, but it's extraordinarily useful. Many category theory abstractions can be applied to a host of different situations. Once you've learned what a functor is, you'll find it easy to learn to use new libraries that build on that abstraction.

In this article you saw a sketch of how the functor abstraction can be used to model Test Data Generators. Contrary to Test Data Builders, which turned out to be a redundant abstraction, a Test Data Generator is truly useful.

Many years ago, I had the idea to create a Test Data Generator for unit testing purposes. I called it AutoFixture, and although it's had some success, the API isn't as clean as it could be. Back then, I didn't know about functors, so I had to invent an API for AutoFixture. This API is proprietary to AutoFixture, so anyone learning AutoFixture must learn this particular API, and its abstractions. It would have been so much easier for all involved if I had designed AutoFixture as a functor instead.

Comments

We don't need no steenkin' Test Data Builders!

This is the fifth and final in a series of articles about the relationship between the Test Data Builder design pattern, and the identity functor. In the previous article, you learned why a Builder functor adds little value. In this article, you'll see what to do instead.

From Identity to naked values #

While you can define Test Data Builders with Haskell's Identity functor, it adds little value:

Identity address = fmap (\a -> a { city = "Paris" }) addressBuilder

That's nothing but an overly complicated way to create a data value from another data value. You can simplify the code from the previous article. First, instead of calling them 'Builders', we should be honest and name them as the default values they are:

defaultPostCode :: PostCode
defaultPostCode = PostCode []
 
defaultAddress :: Address
defaultAddress  = Address { street = "", city = "", postCode = defaultPostCode }

defaultPostCode is nothing but an empty PostCode value, and defaultAddress is an Address value with empty constituent values. Notice that defaultAddress uses defaultPostCode for the postCode value.

If you need a value in Paris, you can simply write it like this:

address = defaultAddress { city = "Paris" }

Likewise, if you need a more specific address, but you don't care about the post code, you can write it like this:

address' =
  Address { street = "Rue Morgue", city = "Paris", postCode = defaultPostCode }

Notice how much simpler this is. There's no need to call fmap in order to pull the 'underlying value' out of the functor, transform it, and put it back in the functor. Haskell's 'copy and update' syntax gives you this ability for free. It's built into the language.

Building F# values #

Haskell isn't the only language with 'copy and update' syntax. F# has it as well, and in fact, it's from the F# documentation that I've taken the 'copy and update' term.

The code corresponding to the above Haskell code looks like this in F#:

let defaultPostCode = PostCode []
let defaultAddress = { Street = ""; City = ""; PostCode = defaultPostCode }
 
let address = { defaultAddress with City = "Paris" }
let address' =
    { Street = "Rue Morgue"; City = "Paris"; PostCode = defaultPostCode }

The syntax is a little different, but the concepts are the same. F# adds the keyword with to 'copy and update' expressions, which translates easily back to C# fluent interfaces.

Building C# objects #

In a previous article, you saw how to refactor your domain model to a model of Value Objects with fluent interfaces.

In your unit tests, you can define natural default values for testing purposes:

public static class Natural
{
    public static PostCode PostCode = new PostCode();
    public static Address Address = new Address("", "", PostCode);
    public static InvoiceLine InvoiceLine =
        new InvoiceLine("", PoundsShillingsPence.Zero);
    public static Recipient Recipient = new Recipient("", Address);
    public static Invoice Invoice = new Invoice(Recipient, new InvoiceLine[0]);
}

This static Natural class is a test-specific container of 'good' default values. Notice how, once more, the Address value uses the PostCode value to fill in the PostCode property of the default Address value.

With these default test values, and the fluent interface of your domain model, you can easily build a test address in Paris:

var address = Natural.Address.WithCity("Paris");

Because Natural.Address is an Address object, you can use its WithCity method to build a test address in Paris, and where all other constituent values remain the default values.

Likewise, you can create an address on Rue Morgue, but with a default post code:

var address = new Address("Rue Morgue", "Paris", Natural.PostCode);

Here, you can simply create a new Address object, but with Natural.PostCode as the post code value.

Conclusion #

Using a fluent domain model obviates the need for Test Data Builders. There's a tendency among functional programmers to overbearingly state that design patterns are nothing but recipes to overcome deficiencies in particular programming languages or paradigms. If you believe such a claim, at least it ought to go both ways, but at the conclusion of this article series, I hope I've been able to demonstrate that this is true for the Test Data Builder pattern. You only need it for 'classic', mutable, object-oriented domain models.

1. For mutable object models, use Test Data Builders.
2. Consider, however, modelling your domain with Value Objects and 'copy and update' instance methods.
3. Even better, consider using a programming language with built-in 'copy and update' expressions.

public class Invoice
{
    public Recipient Recipient { get; }
    public IReadOnlyCollection<InvoiceLine> Lines { get; }
 
    public Invoice(
        Recipient recipient,
        IReadOnlyCollection<InvoiceLine> lines)
    {
        if (recipient == null)
            throw new ArgumentNullException(nameof(recipient));
        if (lines == null)
            throw new ArgumentNullException(nameof(lines));
 
        this.Recipient = recipient;
        this.Lines = lines;
    }
 
    public Invoice WithRecipient(Recipient newRecipient)
    {
        return new Invoice(newRecipient, this.Lines);
    }
 
    public Invoice WithLines(IReadOnlyCollection<InvoiceLine> newLines)
    {
        return new Invoice(this.Recipient, newLines);
    }
 
    public override bool Equals(object obj)
    {
        var other = obj as Invoice;
        if (other == null)
            return base.Equals(obj);
 
        return object.Equals(this.Recipient, other.Recipient)
            && Enumerable.SequenceEqual(
                this.Lines.OrderBy(l => l.Name),
                other.Lines.OrderBy(l => l.Name));
    }
 
    public override int GetHashCode()
    {
        return
            this.Recipient.GetHashCode() ^
            this.Lines.GetHashCode();
    }
}

That may seem like quite a maintenance burden (and it is), but consider that it has the same degree of complexity and overhead as defining a Test Data Builder for each domain object. At least, by putting this extra code in your domain model, you make all of that API (all the With[...] methods, and the structural equality) available to other production code. In my experience, that's a better return of investment than isolating such useful features only to test code.

Still, once you've tried using a language like F# or Haskell, where 'copy and update' expressions come with the language, you realise how much redundant code you're writing in C# or Java. The Test Data Builder design pattern truly is a recipe that addresses deficiencies in particular languages.

Next: The Test Data Generator functor.

Comments

In which the Builder functor turns out to be nothing but the Identity functor in disguise.

This is the fourth in a series of articles about the relationship between the Test Data Builder design pattern, and the identity functor. In the previous article, you saw how a generic Test Data Builder can be modelled as a functor.

You may, however, be excused if you're slightly underwhelmed. Modelling a Test Data Builder as a functor doesn't seem to add much value.

Haskell's Identity functor #

In the previous article, you saw the Builder functor implemented in various languages, including Haskell:

newtype Builder a = Builder a deriving (Show, Eq)
 
instance Functor Builder where
  fmap f (Builder a) = Builder $ f a

The fmap implementation is literally a one-liner: pattern match the value a out of the Builder, call f with a, and package the result in a new Builder value.

For many trivial functors, it turns out that the Glasgow Haskell Compiler (GHC) can automatically implement fmap with a language extension:

{-# LANGUAGE DeriveFunctor #-}
module Builder where
 
newtype Builder a = Builder a deriving (Show, Eq, Functor)

Notice the DeriveFunctor language extension. This enables the compiler to automatically implement fmap by adding Functor to the deriving list.

Perhaps we should take this as a hint. If the compiler can automatically make Builder a Functor, perhaps it doesn't add that much value.

This particular Builder is equivalent to Haskell's built-in Identity functor. Identity is a 'no-op' functor, if you will. While it's a functor, it doesn't 'do' anything. It's similar to the Null Object design pattern, in the sense that the only value it adds is that it enables you to turn any naked value into a functor. This can occasionally be useful if you need to pass a functor to an API.

PostCode and Address builders #

You can rewrite the previous PostCode and Address Test Data Builders as Identity values:

postCodeBuilder :: Identity PostCode
postCodeBuilder = Identity $ PostCode []
 
addressBuilder :: Identity Address
addressBuilder  =
  Identity Address { street = "", city = "", postCode = pc }
  where Identity pc = postCodeBuilder

As in the previous examples, postCodeBuilder is nothing but a 'good' default PostCode value. This time, it's turned into an Identity value, instead of a Builder value. The same is true for addressBuilder - notice that it uses postCodeBuilder for the postCode value.

This enables you to build an address in Paris, like previous examples:

Identity address = fmap (\a -> a { city = "Paris" }) addressBuilder

This builds an address with city bound to "Paris", but with all other values still at their default values:

Address {street = "", city = "Paris", postCode = PostCode []}

You can also build an address from an Identity of a different generic type:

Identity address' = fmap newAddress postCodeBuilder
  where newAddress pc =
          Address { street = "Rue Morgue", city = "Paris", postCode = pc }

Notice that this example uses postCodeBuilder as an origin, but creates a new Address value. In this expression, newAddress is a local function that takes a PostCode value as input, and returns an Address value as output.

Summary #

Neither F# nor C# comes with a built-in identity functor, but it'd be as trivial to create them as the code you've already seen. In the previous article, you saw how to define a Builder<'a> type in F#. All you have to do is to change its name to Identity<'a>, and you have the identity functor. You can perform a similar rename for the C# code in the previous articles.

Since the Identity functor doesn't really 'do' anything, there's no reason to use it for building test values. In the next article, you'll see how to discard the functor and in the process make your code simpler.

Next: Test data without Builders.

The Test Data Builder design pattern as a functor.

This is the third in a series of articles about the relationship between the Test Data Builder design pattern, and the identity functor. The previous article introduced this generic Builder class:

public class Builder<T>
{
    private readonly T item;
 
    public Builder(T item)
    {
        if (item == null)
            throw new ArgumentNullException(nameof(item));
 
        this.item = item;
    }
 
    public Builder<T1> Select<T1>(Func<T, T1> f)
    {
        var newItem = f(this.item);
        return new Builder<T1>(newItem);
    }
 
    public T Build()
    {
        return this.item;
    }
 
    public override bool Equals(object obj)
    {
        var other = obj as Builder<T>;
        if (other == null)
            return base.Equals(obj);
 
        return object.Equals(this.item, other.item);
    }
 
    public override int GetHashCode()
    {
        return this.item.GetHashCode();
    }
}

The workhorse is the Select method. As I previously promised to explain, there's a reason I chose that particular name.

Query syntax #

C# comes with a small DSL normally known as query syntax. People mostly think of it in relation to ORMs such as Entity Framework, but it's a general-purpose language feature. Still, most developers probably associate it with the IEnumerable<T> interface, but it's more general than that. In fact, any type that comes with a Select method with a compatible signature supports query syntax.

I deliberately designed the Builder's Select method to support query syntax:

Address address = from a in Builder.Address
                  select a.WithCity("Paris");

Builder.Address is a Builder<Address> object that contains a 'good' default Address value. Since Builder<T> has a compatible Select method, you can 'query it'. In this example, you use the WithCity method to explicitly pin the Address object's City property, while all the other Address values remain the default values.

There's an extra bit (pun intended) of compiler magic at work. Did you wonder how a Builder<Address> automatically turns into an Address value? After all, address is of the type Address, not Builder<Address>.

I specifically added an implicit conversion so that I didn't have to surround the query expression with brackets in order to call the Build method:

public static implicit operator T(Builder<T> b)
{
    return b.item;
}

This conversion is defined on Builder<T>. It's the reason I explicitly use the type name when I declare the address variable above, instead of using the var keyword. Declaring the type forces the implicit conversion.

You can also use query syntax to map one constructed Builder type into another (and ultimately to the value it contains):

Address address =
    from pc in Builder.PostCode
    select new Address("Rue Morgue", "Paris", pc);

This expression starts with a Builder<PostCode> object, transforms it into a Builder<Address> object, and then finally uses the implicit conversion to turn the Builder<Address> into an Address object.

Even a more complex 'query' looks almost palatable:

Invoice invoice =
    from i in Builder.Invoice
    select i.WithRecipient(
        from r in Builder.Recipient
        select r.WithAddress(Builder.Address.WithNoPostCode()));

Again, the implicit type conversion makes the syntax much cleaner.

Functor #

Isn't it amazing that the C# designers were able to come up with such a generally useful language feature? It certainly is a nice piece of work, but it's based on a an existing body of knowledge.

A type like Builder<T> with a suitable Select method is a functor. This is a term from category theory, but I'll try to avoid turning this article into a category theory lecture. Likewise, I'm not going to talk specifically about monads here, although it's a closely related topic. A functor is a mapping between categories; it maps an object from one category into an object of another category.

Although I've never seen Microsoft explicitly acknowledge the connection to functors and monads, it's clear that it's there. One of the principal designers of LINQ was Erik Meijer, who definitely knows his way around category theory and functional programming. A functor is a simple, but widely applicable abstraction.

In order to be a functor, a type must have an associated mapping. In C#'s query syntax, this is a method named Select, but more often it's called map.

Haskell Builder #

In Haskell, the mapping is called fmap, and you can define the Builder functor like this:

newtype Builder a = Builder a deriving (Show, Eq)
 
instance Functor Builder where
  fmap f (Builder a) = Builder $ f a

Notice how terse the definition is, compared to the C# version. Despite the difference in size, they accomplish the same goal. The first line of code defines the Builder type, complete with structural equality (Eq) and the ability to convert a Builder value to a string (Show).

This Builder type is explicitly defined as a Functor in the second expression, where the fmap function is implemented. The code is similar to the Select method in the above C# example: f is a function that takes the generic type a (corresponding to T in the C# example) as input, and returns a value of the generic type b (corresponding to T1 in the C# example). The mapping pulls the underlying value out of the input Builder, calls f with that value, and puts the return value into a new Builder.

In Haskell, a functor is part of the language itself, so Builder is explicitly declared to be a Functor instance.

If you define some default Builder values, corresponding to the above Builder.Address, you can use them to build addresses in the same way:

Builder address = fmap (\a -> a { city = "Paris" }) addressBuilder

Here, addressBuilder is a Builder Address value, corresponding to the C# Builder.Address value. \a -> a { city = "Paris" } is a lambda expression that takes an Address value as input, and return a similar value as output, only with city explicitly bound to "Paris".

F# example #

Unlike Haskell, F# doesn't treat functors as an explicit construct, but you can still define a Builder functor:

type Builder<'a> = Builder of 'a
 
module Builder =
    // ('a -> 'b) -> Builder<'a> -> Builder<'b>
    let map f (Builder x) = Builder (f x)

You can see how similar this is to the Haskell example. In F#, it's common to define a module with the same name as a generic type. This example defines a generic Builder<'a> type and a supporting Builder module. Normally, a module would contain other functions, in addition to map.

Just like in C# and Haskell, you can build an address in Paris with a predefined Builder value as a start:

let (Builder address) =
    addressBuilder |> Builder.map (fun a -> { a with City = "Paris" })

Again, addressBuilder is a Builder<Address> that contains a 'default' Address (test) value. You use Builder.map with a lambda expression to map the default value into a new Address value where City is bound to "Paris".

Functor laws #

In order to be a proper functor, an object must obey two simple laws. It's not enough that a mapping function exists, it must also obey the laws. While that sounds uncomfortably like mathematics, the laws are simple and intuitive.

The first law is that when the mapping returns the input, the functor returned is also the input functor. There's only one (generic) function that returns its input unmodified. It's called the identity function (often abbreviated id).

Here's an example test case that illustrates the first functor law for the C# Builder<T>:

[Fact]
public void BuilderObeysFirstFunctorLaw()
{
    Func<int, int> id = x => x;
    var sut = new Builder<int>(42);
 
    var actual = sut.Select(id);
 
    Assert.Equal(sut, actual);
}

The .NET Base Class Library doesn't come with a built-in identity function, so the test case first defines it as id. Normally, the identity function would be defined as a function that takes a value of the generic type T as input, and returns the same value (still of type T) as output. This test is only an example for the type int, so it also defines the identity function as constrained to int.

The test creates a new Builder<int> with the value 42, and calls Select with id. Since the first functor law says that mapping with the identity function must return the input functor, the expected value is the sut variable.

This test is only an example of the first functor law. It doesn't prove that Builder<T> obeys the law for all generic types (T) and for all values. It only proves that it holds for the integer 42. You get the idea, though, I'm sure.

The second functor law says that if you chain two functions to make a third function, and map your functor using that third function, the result should be equal to the result you get if you chain two mappings made out of those two functions. Here's an example:

[Fact]
public void BuilderObeysSecondFunctorLaw()
{
    Func<int, string> g = i => i.ToString();
    Func<string, string> f = s => new string(s.Reverse().ToArray());
    var sut = new Builder<int>(1337);
 
    var actual = sut.Select(i => f(g(i)));
 
    var expected = sut.Select(g).Select(f);
    Assert.Equal(expected, actual);
}

This test case (which is, again, only an example) first defines two functions, f and g. It then creates a new Builder<int> and calls Select with the combined function f(g). This returns the actual result, which is a Builder<string>.

This result should be equal to first calling Select with g (which returns a Builder<string>), and then calling Select with f (which returns another Builder<string>). These two Builder objects should be equal to each other, which they are.

Both these tests compare an expected Builder to an actual Builder, which is the reason that Builder<T> overrides Equals in order to have structural equality. In Haskell, the above Builder type has structural equality because it uses the default instance of Eq, and in F#, Builder<'a> has structural equality because that's the default equality for the immutable F# data types.

We can't easily talk about the functor laws without being able to talk about functor values being (or not being) equal to each other, so structural equality is an important element in the discussion.

Summary #

You can define a Test Data Builder as a functor by defining a generic Builder type with a Select method. In order to be a proper functor, it must also obey the functor laws, but these laws are quite natural; you almost have to go out of your way in order to violate them.

A functor is a well-known abstraction. Instead of trying to come up with a half-baked, ad-hoc abstraction, modelling an API based on already known and understood abstractions such as functors will make the API easier to learn. Everyone who knows what a functor is, will automatically have a good understanding of the API. Even if you didn't know about functors until now, you only have to learn about them once.

This can often be beneficial, but for Test Data Builders, it turns out to be a red herring. The Builder functor is nothing but the Identity functor in disguise.

Next: Builder as Identity.

Comments

var invoice = DefaultTestObjects.Invoice
    .WithRecipient(DefaultTestObjects.Recipient
        .WithAddress(DefaultTestObjects.Address
            .WithNoPostCode()
            .WithCity("Paris"))
    .WithDate(new DateTimeOffset(2017, 8, 29)));

This article presents a generalised Test Data Builder.

This is the second in a series of articles about the relationship between the Test Data Builder design pattern, and the identity functor. The previous article was a review of the Test Data Builder pattern.

Boilerplate #

While the Test Data Builder is an incredibly versatile and useful design pattern, it has a problem. In languages like C# and Java, it's difficult to generalise. This leads to an excess of boilerplate code.

Expanding on Nat Pryce's original example, an InvoiceBuilder is composed of other builders:

public class InvoiceBuilder
{
    private Recipient recipient;
    private IReadOnlyCollection<InvoiceLine> lines;
 
    public InvoiceBuilder()
    {
        this.recipient = new RecipientBuilder().Build();
        this.lines = new List<InvoiceLine> { new InvoiceLineBuilder().Build() };
    }
 
    public InvoiceBuilder WithRecipient(Recipient newRecipient)
    {
        this.recipient = newRecipient;
        return this;
    }
 
    public InvoiceBuilder WithInvoiceLines(
        IReadOnlyCollection<InvoiceLine> newLines)
    {
        this.lines = newLines;
        return this;
    }
 
    public Invoice Build()
    {
        return new Invoice(recipient, lines);
    }
}

In order to create a Recipient, a RecipientBuilder is used. Likewise, in order to create a single InvoiceLine, an InvoiceLineBuilder is used. This pattern repeats in the RecipientBuilder:

public class RecipientBuilder
{
    private string name;
    private Address address;
 
    public RecipientBuilder()
    {
        this.name = "";
        this.address = new AddressBuilder().Build();
    }
 
    public RecipientBuilder WithName(string newName)
    {
        this.name = newName;
        return this;
    }
 
    public RecipientBuilder WithAddress(Address newAddress)
    {
        this.address = newAddress;
        return this;
    }
 
    public Recipient Build()
    {
        return new Recipient(this.name, this.address);
    }
}

In order to create an Address object, an AddressBuilder is used.

Generalisation attempts #

You can describe the pattern in a completely automatable manner:

1. For each domain class, create a corresponding Builder class.
2. For each class field or property in the domain class, define a corresponding field or property in the Builder.
3. In the Builder's constructor, initialise each field or property with a 'good' default value.
   • If the field is a primitive value, such as a string or integer, hard-code an appropriate value.
   • If the field is a complex domain type, use that type's corresponding Builder to create the default value.
4. For each class field or property, add a With[...] method that changes the field and returns the Builder itself.
5. Add a Build method that returns a new instance of the domain class with the constituent values collected so far.

People have already done that. After having written individual Test Data Builders for a couple of months, I got tired of it and wrote AutoFixture. It uses Reflection to build objects at run-time, but I've also witnessed attempts to automate Test Data Builders via automated code generation.

AutoFixture has been moderately successful, but some people find its API difficult to learn. Correspondingly, code generation comes with its own issues.

In languages like C# or Java, it's difficult to identify a better generalisation.

Generic Builder #

Instead of trying to automate the Test Data Builder pattern, you can pursue a different strategy. At first, it doesn't look all that promising, but if you soldier on, it'll reveal meaningful insights.

As an alternative to replicating the Test Data Builder pattern exactly, you can define a single generically typed Builder class:

public class Builder<T>
{
    private readonly T item;
 
    public Builder(T item)
    {
        if (item == null)
            throw new ArgumentNullException(nameof(item));
 
        this.item = item;
    }
 
    public Builder<T1> Select<T1>(Func<T, T1> f)
    {
        var newItem = f(this.item);
        return new Builder<T1>(newItem);
    }
 
    public T Build()
    {
        return this.item;
    }
 
    public override bool Equals(object obj)
    {
        var other = obj as Builder<T>;
        if (other == null)
            return base.Equals(obj);
 
        return object.Equals(this.item, other.item);
    }
 
    public override int GetHashCode()
    {
        return this.item.GetHashCode();
    }
}

The Builder<T> class reduces the Test Data Builder design patterns to the essentials:

• A constructor that initialises the Builder with default data.
• A single fluent interface Select method, which returns a new Builder object.
• A Build method, which returns the built object.

This example of a generic Builder class overrides Equals (and, therefore, also GetHashCode). It doesn't have to do that, but there's a good reason to do this that we'll also come back to later.

It doesn't seem particularly useful, and a first attempt at using it seems to confirm such scepticism:

var address = Build.Address().Select(a =>
{
    a.City = "Paris";
    return a;
}).Build();

This example first uses Build.Address() to create an initial Builder object with appropriate defaults. This static method is defined on the static Build class:

public static Builder<Address> Address()
{
    return new Builder<Address>(new Address("", "", PostCode().Build()));
}

Contrary to Builder<T>, which is a reusable, general-purpose class, the static Build class is an example of a collection of Test Utility Methods specific to the domain model you're testing. Notice how the Build.Address() method uses Build.PostCode().Build() to create a default value for the initial Address object's post code.

The above example passes a C# code block to the Select method. It takes the a (Address) object as input, specifically mutates its City property, and returns it. This syntax is crude, but works. It may look acceptable when pinning a single City property, but it quickly becomes awkward:

var invoice = Build.Invoice().Select(i =>
    {
        i.Recipient = Build.Recipient().Select(r =>
        {
            r.Address = Build.Address().WithNoPostCode().Build();
            return r;
        }).Build();
        return i;
    }).Build();

Not only is it difficult to get right when writing such nested statements, it's also hard to read. You can, however, correct that problem, as you'll see in a little while.

Before we commence on making the code prettier, you may have noticed that the Select method returns a Builder with a different generic type argument than it contains. The Select method on a Builder<T> object has the signature public Builder<T1> Select<T1>(Func<T, T1> f). Until now, however, all the examples you've seen return the input object. In those examples, T is the same as T1. For completeness' sake, here's an example of a proper change of type:

var address = Build.PostCode()
    .Select(pc => new Address("Rue Morgue", "Paris", pc))
    .Build();

This example uses a Builder<PostCode> to create a new Address object. Plugging in the types, T becomes PostCode, and T1 becomes Address.

Perhaps you noticed that this example looks a little better than the previous examples. Instead of having to supply a C# code block, with return statement and all, this call to Select passes a proper (lambda) expression.

Expressions from extensions #

It'd be nice if you could use expressions, instead of full code blocks, with the Select method. As a first step, you could write some test-specific extension methods for your domain model, like this:

public static Address WithCity(this Address address, string newCity)
{
    address.City = newCity;
    return address;
}

This is same code as one of the code blocks above, only refactored to a named extension method. It simplifies use of the generic Builder, though:

var address = Build.Address().Select(a => a.WithCity("Paris")).Build();

That looks good in such a simple example, but unfortunately isn't much of an improvement when it comes to a more complex case:

var invoice =
    Build.Invoice()
        .Select(i => i
            .WithRecipient(Build.Recipient()
                .Select(r => r
                    .WithAddress(Build.Address()
                        .WithNoPostCode()
                        .Build()))
                .Build()))
        .Build();

If, at this point, you're tempted to give up on the overall strategy with a single generic Builder, you'd be excused. It will, however, turn out to be beneficial to carry on. There are more obstacles, but eventually, things will start to fall into place.

Copy and update #

The above WithCity extension method mutates the input object, which can lead to surprising behaviour. While it's a common way to implement fluent interfaces in object-oriented languages, nothing prevents you from making the code saner. Instead of mutating the input object, create a new object with the single value changed:

public static Address WithCity(this Address address, string newCity)
{
    return new Address(address.Street, newCity, address.PostCode);
}

Some people will immediately be concerned about the performance implications of doing this, but you're not one of those people, are you?

Granted, there's allocation and garbage collection overhead by creating new objects like this, but I'd digress if I started to discuss this here. In most cases, the impact is insignificant.

Fluent domain model #

Using extension methods enables you to use a more elegant syntax with the Select method, but there's still some maintenance overhead. If, for now, we accept such maintenance overhead, you could ask: given that we have to define and maintain all those With[...] methods, why limit them to your test code?

Would there be any harm in defining them as proper methods on your domain model?

public Address WithCity(string newCity)
{
    return new Address(this.Street, newCity, this.PostCode);
}

The above example shows the WithCity method as an instance method on the Address class. Here's the entire Address class, refactored to an immutable class:

public class Address
{
    public string Street { get; }
    public string City { get; }
    public PostCode PostCode { get; }
 
    public Address(string street, string city, PostCode postCode)
    {
        if (street == null)
            throw new ArgumentNullException(nameof(street));
        if (city == null)
            throw new ArgumentNullException(nameof(city));
        if (postCode == null)
            throw new ArgumentNullException(nameof(postCode));
 
        this.Street = street;
        this.City = city;
        this.PostCode = postCode;
    }
 
    public Address WithStreet(string newStreet)
    {
        return new Address(newStreet, this.City, this.PostCode);
    }
 
    public Address WithCity(string newCity)
    {
        return new Address(this.Street, newCity, this.PostCode);
    }
 
    public Address WithPostCode(PostCode newPostCode)
    {
        return new Address(this.Street, this.City, newPostCode);
    }
 
    public override bool Equals(object obj)
    {
        var other = obj as Address;
        if (other == null)
            return base.Equals(obj);
 
        return object.Equals(this.Street, other.Street)
            && object.Equals(this.City, other.City)
            && object.Equals(this.PostCode, other.PostCode);
    }
 
    public override int GetHashCode()
    {
        return
            this.Street.GetHashCode() ^
            this.City.GetHashCode() ^
            this.PostCode.GetHashCode();
    }
}

Technically, you could introduce instance methods like WithCity even if you kept the class itself mutable, but once you start down that path, it makes sense to make the class immutable. As Eric Evans recommends in Domain-Driven Design, modelling your domain with (immutable) Value Objects has many benefits. Such objects should also have structural equality, which is the reason that this version of Address also overrides Equals and GetHashCode.

While it looks like more work in a language like C# or Java, there are many benefits to be derived from modelling your domain with Value Objects. As an interim result, then, observe that working with unit testing (in this case a general-purpose Test Data Builder) has prompted a better design of the System Under Test.

You may still think that this seems unnecessarily verbose, and I'd agree. This is one of the many reasons I prefer languages like F# and Haskell over C# or Java. The former have such a copy and update feature built-in. Here's an F# example of updating an Address record with a specific city:

let address = { a with City = "Paris" }

This capability is built into the language. You don't have to add or maintain any code in order to be able to write code like that. Notice, even, how with is a keyword. I'm not sure about the etymology of the word with used in this context, but I find the similarity compelling.

In Haskell, it looks similar:

address = a { city = "Paris" }

In other words, domain models created from immutable Value Objects are laborious in some languages, but that only suggests a deficiency in such a language.

Default Builders as values #

Now that the domain model is immutable, you can define default builders as values. Previously, to start building e.g. an Address value, you had to call the Build.Address() method. When the domain model was mutable, containing a single default value inside of a Builder would enable tests to mutate that default value. Now that domain classes are immutable, this is no longer a concern, and you can instead define test-specific default builders as values:

public static class Builder
{
    public readonly static Builder<Address> Address;
    public readonly static Builder<Invoice> Invoice;
    public readonly static Builder<InvoiceLine> InvoiceLine;
    public readonly static Builder<PostCode> PostCode;
    public readonly static Builder<PoundsShillingsPence> PoundsShillingsPence;
    public readonly static Builder<Recipient> Recipient;
 
    static Builder()
    {
        PoundsShillingsPence = new Builder<PoundsShillingsPence>(
            DomainModel.PoundsShillingsPence.Zero);
        PostCode = new Builder<PostCode>(new PostCode());
        Address =
            new Builder<Address>(new Address("", "", PostCode.Build()));
        Recipient =
            new Builder<Recipient>(new Recipient("", Address.Build()));
        Invoice = new Builder<Invoice>(
            new Invoice(Recipient.Build(), new List<InvoiceLine>()));
        InvoiceLine = new Builder<InvoiceLine>(
            new InvoiceLine("", PoundsShillingsPence.Build()));
    }
 
    public static Builder<Address> WithNoPostCode(this Builder<Address> b)
    {
        return b.Select(a => a.WithPostCode(new PostCode()));
    }
}

This enables you to write expressions like this:

var address = Builder.Address.Select(a => a.WithCity("Paris")).Build();

To be clear: such a static Builder class is a Test Utility API specific to your unit tests. It would often be defined in a completely different file than the Builder<T> class, perhaps even in separate libraries.

Summary #

Instead of trying to automate Test Data Builders to the letter of the original design pattern description, you can define a single, reusable, generic Builder<T> class. It enables you to achieve some of the expressivity of Test Data Builders.

If you still don't find this strategy's prospects fertile, I understand. We're not done, though. In the next article, you'll see why Select is an appropriate name for the Builder's most important method, and how it relates to good abstractions.

Next: The Builder functor.

Comments

var address = new Address { City = "Paris" };

var defaultAddress =
    new Address { Street = "", PostCode = new DomainModel.PostCode(), City = "" };
var address = defaultAddress { City = "Paris" };

A brief recap of the Test Data Builder design pattern with examples in C#.

This is the first in a series of articles about the relationship between the Test Data Builder design pattern, and the identity functor.

In 2007 Nat Pryce described the Test Data Builder design pattern. The original article is easy to read, but in case you don't want to read it, here's a quick summary, with some of Nat Pryce's examples translated to C#.

The purpose of a Test Data Builder is to make it easy to create input data (or objects) for unit tests. Imagine, for example, that for a particular test case, you need an address in Paris; no other values matter. With a Test Data Builder, you can write an expression that gives you such a value:

var address = new AddressBuilder().WithCity("Paris").Build();

The address object explicity has a City value of "Paris". Any other values are default values defined by AddressBuilder. The values are there, but when they're unimportant to a particular test case, you don't have to specify them. To paraphrase Robert C. Martin, this eliminates the irrelevant, and amplifies the essentials of the test.

Address Builder #

An AddressBuilder could look like this:

public class AddressBuilder
{
    private string street;
    private string city;
    private PostCode postCode;
 
    public AddressBuilder()
    {
        this.street = "";
        this.city = "";
        this.postCode = new PostCodeBuilder().Build();
    }
 
    public AddressBuilder WithStreet(string newStreet)
    {
        this.street = newStreet;
        return this;
    }
 
    public AddressBuilder WithCity(string newCity)
    {
        this.city = newCity;
        return this;
    }
 
    public AddressBuilder WithPostCode(PostCode newPostCode)
    {
        this.postCode = newPostCode;
        return this;
    }
 
    public AddressBuilder WithNoPostcode()
    {
        this.postCode = new PostCode();
        return this;
    }
 
    public Address Build()
    {
        return new Address(this.street, this.city, this.postCode);
    }
}

The Address class is simpler than the Builder:

public class Address
{
    public string Street { get; set; }
    public string City { get; set; }
    public PostCode PostCode { get; set; }
 
    public Address(string street, string city, PostCode postCode)
    {
        this.Street = street;
        this.City = city;
        this.PostCode = postCode;
    }
}

Clearly, this class could contain some behaviour, but in order to keep the example as simple as possible, it's only a simple Data Transfer Object.

Composition #

Given that AddressBuilder is more complicated than Address itself, the benefit of the pattern may seem obscure, but one of the benefits is that Test Data Builders easily compose:

var invoice = new InvoiceBuilder()
    .WithRecipient(new RecipientBuilder()
        .WithAddress(new AddressBuilder()
            .WithNoPostcode()
            .Build())
        .Build())
    .Build();

Perhaps that looks verbose, but in general, the alternative is worse. If you didn't have a Test Utility Method, you'd have to fill in all the required data for the object:

var invoice = new Invoice(
    new Recipient("Sherlock Holmes",
        new Address("221b Baker Street",
                    "London",
                    new PostCode())),
    new List<InvoiceLine> {
        new InvoiceLine("Deerstalker Hat",
            new PoundsShillingsPence(0, 3, 10)),
        new InvoiceLine("Tweed Cape",
            new PoundsShillingsPence(0, 4, 12))});

Here, the important detail drowns in data. The post code is empty because the PostCode constructor is called without arguments. This hardly jumps out when you see it. Such code neither eliminates the irrelevant, nor amplifies the essential.

Summary #

Test Data Builders are useful because they are good abstractions. They enable you to write unit tests that you can trust.

The disadvantage, as you shall see, is that in languages like C# and Java, much boilerplate code is required.

Next: Generalised Test Data Builder.

Comments

var address = new {
		    City = "Paris"
		  }.ActLike<IAddress>();
			

var address = new {
		    City = "Paris", 
		    PostCode = new {
				      ISO = "FR"
				   }.ActLike<IPostCode>()
		  }.ActLike<IAddress>();
			

public interface IAddress
{
    string City { get; set; }
}

public interface IAddress
{
    string City { get; }
    string Street { get; }
    IPostCode PostCode { get; }
}

var address = new {
		    City = "Paris"
		  }.ActLike<IAddress>();

The Test Data Builder unit testing design pattern is closely related to the identity functor.

The Test Data Builder design pattern is a valuable technique for managing data for unit testing. It enables you to express test cases in such a way that the important parts of the test case stands out in your code, while the unimportant parts disappear. It perfectly fits Robert C. Martin's definition of an abstraction:

"Abstraction is the elimination of the irrelevant and the amplification of the essential"

1. Test Data Builders in C#
2. Generalised Test Data Builder
3. The Builder functor
4. Builder as Identity
5. Test data without Builders
6. (The Test Data Generator functor)

• How to make your code easier to use in unit tests.
• What a functor is.
• How Test Data Builders generalise.
• Why Test Data Builders are composable.

For readers wondering if this is 'yet another monad tutorial', it's not; it's a functor tutorial.

Next: Test Data Builders in C#.