ploeh blog danish software design

The code behind a lecture animation.

If you've seen my presentation Fractal Architecture, you may have wondered how I made the animation where a regular(ish) hexagonal grid emerges from adding more and more blobs to an area.

Like a few previous blog posts, today's article appears on Observable, which is where the animation and the code that creates it lives. Go there to read it.

If you have time, watch the animation evolve. Personally I find it quite mesmerising.

Encapsulation is only relevant for object-oriented programming, right?

The concept of encapsulation is closely related to object-oriented programming (OOP), and you rarely hear the word in discussions about (statically-typed) functional programming (FP). I will argue, however, that the notion is relevant in FP as well. Typically, it just appears with a different catchphrase.

Contracts #

I base my understanding of encapsulation on Object-Oriented Software Construction. I've tried to distil it in my Pluralsight course Encapsulation and SOLID.

In short, encapsulation denotes the distinction between an object's contract and its implementation. An object should fulfil its contract in such a way that client code doesn't need to know about its implementation.

Contracts, according to Bertrand Meyer, describe three properties of objects:

• Preconditions: What client code must fulfil in order to successfully interact with the object.
• Invariants: Statements about the object that are always true.
• Postconditions: Statements that are guaranteed to be true after a successful interaction between client code and object.

You can replace object with value and I'd argue that the same concerns are relevant in FP.

In OOP invariants often point to the properties of an object that are guaranteed to remain even in the face of state mutation. As you change the state of an object, the object should guarantee that its state remains valid. These are the properties (i.e. qualities, traits, attributes) that don't vary - i.e. are invariant.

An example would be helpful around here.

Table mutation #

Consider an object that models a table in a restaurant. You may, for example, be working on the Maître d' kata. In short, you may decide to model a table as being one of two kinds: Standard tables and communal tables. You can reserve seats at communal tables, but you still share the table with other people.

You may decide to model the problem in such a way that when you reserve the table, you change the state of the object. You may decide to describe the contract of Table objects like this:

• Preconditions
  • To create a Table object, you must supply a type (standard or communal).
  • To create a Table object, you must supply the size of the table, which is a measure of its capacity; i.e. how many people can sit at it.
  • The capacity must be a natural number. One (1) is the smallest valid capacity.
  • When reserving a table, you must supply a valid reservation.
  • When reserving a table, the reservation quantity must be less than or equal to the table's remaining capacity.
• Invariants
  • The table capacity doesn't change.
  • The table type doesn't change.
  • The number of remaining seats is never negative.
  • The number of remaining seats is never greater than the table's capacity.
• Postconditions
  • After reserving a table, the number of remaining seats can't be greater than the previous number of remaining seats minus the reservation quantity.

This list may be incomplete, and if you add more operations, you may have to elaborate on what that means to the contract.

In C# you may implement a Table class like this:

public sealed class Table
{
    private readonly List<Reservation> reservations;
 
    public Table(int capacity, TableType type)
    {
        if (capacity < 1)
            throw new ArgumentOutOfRangeException(
                nameof(capacity),
                $"Capacity must be greater than zero, but was: {capacity}.");
 
        reservations = new List<Reservation>();
        Capacity = capacity;
        Type = type;
        RemaingSeats = capacity;
    }
 
    public int Capacity { get; }
    public TableType Type { get; }
    public int RemaingSeats { get; private set; }
 
    public void Reserve(Reservation reservation)
    {
        if (RemaingSeats < reservation.Quantity)
            throw new InvalidOperationException(
                "The table has no remaining seats.");
 
        if (Type == TableType.Communal)
            RemaingSeats -= reservation.Quantity;
        else
            RemaingSeats = 0;
 
        reservations.Add(reservation);
    }
}

This class has good encapsulation because it makes sure to fulfil the contract. You can't put it in an invalid state.

Immutable Table #

Notice that two of the invariants for the above Table class is that the table can't change type or capacity. While OOP often revolves around state mutation, it seems reasonable that some data is immutable. A table doesn't all of a sudden change size.

In FP data is immutable. Data doesn't change. Thus, data has that invariant property.

If you consider the above contract, it still applies to FP. The specifics change, though. You'll no longer be dealing with Table objects, but rather Table data, and to make reservations, you call a function that returns a new Table value.

In F# you could model a Table like this:

type Table = private Standard of int * Reservation list | Communal of int * Reservation list
 
module Table =
    let standard capacity =
        if 0 < capacity
        then Some (Standard (capacity, []))
        else None
 
    let communal capacity =
        if 0 < capacity
        then Some (Communal (capacity, []))
        else None
        
    let remainingSeats = function
        | Standard (capacity, []) -> capacity
        | Standard _ -> 0
        | Communal (capacity, rs) -> capacity - List.sumBy (fun r -> r.Quantity) rs
 
    let reserve r t =
        match t with
        | Standard (capacity, []) when r.Quantity <= remainingSeats t ->
            Some (Standard (capacity, [r]))
        | Communal (capacity, rs) when r.Quantity <= remainingSeats t ->
            Some (Communal (capacity, r :: rs))
        | _ -> None

While you'll often hear fsharpers say that one should make illegal states unrepresentable, in practice you often have to rely on predicative data to enforce contracts. I've done this here by making the Table cases private. Code outside the module can't directly create Table data. Instead, it'll have to use one of two functions: Table.standard or Table.communal. These are functions that return Table option values.

That's the idiomatic way to model predicative data in statically typed FP. In Haskell such functions are called smart constructors.

Statically typed FP typically use Maybe (Option) or Either (Result) values to communicate failure, rather than throwing exceptions, but apart from that a smart constructor is just an object constructor.

The above F# Table API implements the same contract as the OOP version.

If you want to see a more elaborate example of modelling table and reservations in F#, see An F# implementation of the Maître d' kata.

Functional contracts in OOP languages #

You can adopt many FP concepts in OOP languages. My book Code That Fits in Your Head contains sample code in C# that implements an online restaurant reservation system. It includes a Table class that, at first glance, looks like the above C# class.

While it has the same contract, the book's Table class is implemented with the FP design principles in mind. Thus, it's an immutable class with this API:

public sealed class Table
{
    public static Table Standard(int seats)
 
    public static Table Communal(int seats)
 
    public int Capacity { get; }
 
    public int RemainingSeats { get; }
  
    public Table Reserve(Reservation reservation)
 
    public T Accept<T>(ITableVisitor<T> visitor)
 
    public override bool Equals(object? obj)
 
    public override int GetHashCode()
}

Notice that the Reserve method returns a Table object. That's the table with the reservation associated. The original Table instance remains unchanged.

The entire book is written in the Functional Core, Imperative Shell architecture, so all domain models are immutable objects with pure functions as methods.

The objects still have contracts. They have proper encapsulation.

Conclusion #

Functional programmers may not use the term encapsulation much, but that doesn't mean that they don't share that kind of concern. They often throw around the phrase make illegal states unrepresentable or talk about smart constructors or partial versus total functions. It's clear that they care about data modelling that prevents mistakes.

The object-oriented notion of encapsulation is ultimately about separating the affordances of an API from its implementation details. An object's contract is an abstract description of the properties (i.e. qualities, traits, or attributes) of the object.

Functional programmers care so much about the properties of data and functions that property-based testing is often the preferred way to perform automated testing.

Perhaps you can find a functional programmer who might be slightly offended if you suggest that he or she should consider encapsulation. If so, suggest instead that he or she considers the properties of functions and data.

Comments

#nullable enable
 
readonly record struct Reservation(int Quantity);
abstract record Table;
record StandardTable(int Capacity, Reservation? Reservation): Table;
record CommunalTable(int Capacity, ImmutableArray<Reservation> Reservations): Table;
 
static class TableModule
{
    public static StandardTable? Standard(int capacity) =>
        0 < capacity ? new StandardTable(capacity, null) : null;
 
    public static CommunalTable? Communal(int capacity) =>
        0 < capacity ? new CommunalTable(capacity, ImmutableArray<Reservation>.Empty) : null;
 
    public static int RemainingSeats(this Table table) => table switch
    {
        StandardTable { Reservation: null } t => t.Capacity,
        StandardTable => 0,
        CommunalTable t => t.Capacity - t.Reservations.Sum(r => r.Quantity)
    };
 
    public static Table? Reserve(this Table table, Reservation r) => table switch
    {
        StandardTable t when r.Quantity <= t.RemainingSeats() => t with { Reservation = r },
        CommunalTable t when r.Quantity <= t.RemainingSeats() => t with { Reservations = t.Reservations.Add(r) },
        _ => null,
    };
}

#nullable enable

using System.Collections.Immutable;

readonly record struct Reservation(int Quantity);
abstract record Table
{
    public abstract Table? Reserve(Reservation r);
    public abstract int RemainingSeats();

    public static Table? Standard(int capacity) => 
        capacity > 0 ? new StandardTable(capacity, null) : null;

    public static Table? Communal(int capacity) => 
        capacity > 0 ? new CommunalTable(
            capacity,
            ImmutableArray<Reservation>.Empty) : null;

    private record StandardTable(int Capacity, Reservation? Reservation) : Table
    {
        public override Table? Reserve(Reservation r) => RemainingSeats() switch
        {
            var seats when seats >= r.Quantity => this with { Reservation = r },
            _ => null,
        };

        public override int RemainingSeats() => Reservation switch
        {
            null => Capacity,
            _ => 0,
        };
    }

    private record CommunalTable(
        int Capacity, 
        ImmutableArray<Reservation> Reservations) : Table
    {
        public override Table? Reserve(Reservation r) => RemainingSeats() switch
        {
            var seats when seats >= r.Quantity =>
                this with { Reservations = Reservations.Add(r) },
            _ => null,
        };

        public override int RemainingSeats() => 
            Capacity - Reservations.Sum(r => r.Quantity);
    }
}
    

Favour Fakes over dynamic mocks.

For a while now, I've favoured Fakes over Stubs and Mocks. Using Fake Objects over other Test Doubles makes test suites more robust. I wrote the code base for my book Code That Fits in Your Head entirely with Fakes and the occasional Test Spy, and I rarely had to fix broken tests. No Moq, FakeItEasy, NSubstitute, nor Rhino Mocks. Just hand-written Test Doubles.

It recently occurred to me that a way to explain the problem with Mocks and Stubs is that they break encapsulation.

You'll see some examples soon, but first it's important to be explicit about terminology.

Terminology #

Words like Mocks, Stubs, as well as encapsulation, have different meanings to different people. They've fallen victim to semantic diffusion, if ever they were well-defined to begin with.

When I use the words Test Double, Fake, Mock, and Stub, I use them as they are defined in xUnit Test Patterns. I usually try to avoid the terms Mock and Stub since people use them vaguely and inconsistently. The terms Test Double and Fake fare better.

We do need, however, a name for those libraries that generate Test Doubles on the fly. In .NET, they are libraries like Moq, FakeItEasy, and so on, as listed above. Java has Mockito, EasyMock, JMockit, and possibly more like that.

What do we call such libraries? Most people call them mock libraries or dynamic mock libraries. Perhaps dynamic Test Double library would be more consistent with the xUnit Test Patterns vocabulary, but nobody calls them that. I'll call them dynamic mock libraries to at least emphasise the dynamic, on-the-fly object generation these libraries typically use.

Finally, it's important to define encapsulation. This is another concept where people may use the same word and yet mean different things.

I base my understanding of encapsulation on Object-Oriented Software Construction. I've tried to distil it in my Pluralsight course Encapsulation and SOLID.

In short, encapsulation denotes the distinction between an object's contract and its implementation. An object should fulfil its contract in such a way that client code doesn't need to know about its implementation.

Contracts, according to Meyer, describe three properties of objects:

• Preconditions: What client code must fulfil in order to successfully interact with the object.
• Invariants: Statements about the object that are always true.
• Postconditions: Statements that are guaranteed to be true after a successful interaction between client code and object.

As I'll demonstrate in this article, objects generated by dynamic mock libraries often break their contracts.

Create-and-read round-trip #

Consider the IReservationsRepository interface from Code That Fits in Your Head:

public interface IReservationsRepository
{
    Task Create(int restaurantId, Reservation reservation);
 
    Task<IReadOnlyCollection<Reservation>> ReadReservations(
        int restaurantId, DateTime min, DateTime max);
 
    Task<Reservation?> ReadReservation(int restaurantId, Guid id);
 
    Task Update(int restaurantId, Reservation reservation);
 
    Task Delete(int restaurantId, Guid id);
}

I already discussed some of the contract properties of this interface in an earlier article. Here, I want to highlight a certain interaction.

What is the contract of the Create method?

There are a few preconditions:

• The client must have a properly initialised IReservationsRepository object.
• The client must have a valid restaurantId.
• The client must have a valid reservation.

A client that fulfils these preconditions can successfully call and await the Create method. What are the invariants and postconditions?

I'll skip the invariants because they aren't relevant to the line of reasoning that I'm pursuing. One postcondition, however, is that the reservation passed to Create must now be 'in' the repository.

How does that manifest as part of the object's contract?

This implies that a client should be able to retrieve the reservation, either with ReadReservation or ReadReservations. This suggests a kind of property that Scott Wlaschin calls There and back again.

Picking ReadReservation for the verification step we now have a property: If client code successfully calls and awaits Create it should be able to use ReadReservation to retrieve the reservation it just saved. That's implied by the IReservationsRepository contract.

SQL implementation #

The 'real' implementation of IReservationsRepository used in production is an implementation that stores reservations in SQL Server. This class should obey the contract.

While it might be possible to write a true property-based test, running hundreds of randomly generated test cases against a real database is going to take time. Instead, I chose to only write a parametrised test:

[Theory]
[InlineData(Grandfather.Id, "2022-06-29 12:00", "e@example.gov", "Enigma", 1)]
[InlineData(Grandfather.Id, "2022-07-27 11:40", "c@example.com", "Carlie", 2)]
[InlineData(2, "2021-09-03 14:32", "bon@example.edu", "Jovi", 4)]
public async Task CreateAndReadRoundTrip(
    int restaurantId,
    string at,
    string email,
    string name,
    int quantity)
{
    var expected = new Reservation(
        Guid.NewGuid(),
        DateTime.Parse(at, CultureInfo.InvariantCulture),
        new Email(email),
        new Name(name),
        quantity);
    var connectionString = ConnectionStrings.Reservations;
    var sut = new SqlReservationsRepository(connectionString);
 
    await sut.Create(restaurantId, expected);
    var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
    Assert.Equal(expected, actual);
}

The part that we care about is the three last lines:

await sut.Create(restaurantId, expected);
var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
Assert.Equal(expected, actual);

First call Create and subsequently ReadReservation. The value created should equal the value retrieved, which is also the case. All tests pass.

Fake #

The Fake implementation is effectively an in-memory database, so we expect it to also fulfil the same contract. We can test it with an almost identical test:

[Theory]
[InlineData(RestApi.Grandfather.Id, "2022-06-29 12:00", "e@example.gov", "Enigma", 1)]
[InlineData(RestApi.Grandfather.Id, "2022-07-27 11:40", "c@example.com", "Carlie", 2)]
[InlineData(2, "2021-09-03 14:32", "bon@example.edu", "Jovi", 4)]
public async Task CreateAndReadRoundTrip(
    int restaurantId,
    string at,
    string email,
    string name,
    int quantity)
{
    var expected = new Reservation(
        Guid.NewGuid(),
        DateTime.Parse(at, CultureInfo.InvariantCulture),
        new Email(email),
        new Name(name),
        quantity);
    var sut = new FakeDatabase();
 
    await sut.Create(restaurantId, expected);
    var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
    Assert.Equal(expected, actual);
}

The only difference is that the sut is a different class instance. These test cases also all pass.

How is FakeDatabase implemented? That's not important, because it obeys the contract. FakeDatabase has good encapsulation, which makes it possible to use it without knowing anything about its internal implementation details. That, after all, is the point of encapsulation.

Dynamic mock #

How does a dynamic mock fare if subjected to the same test? Let's try with Moq 4.18.2 (and I'm not choosing Moq to single it out - I chose Moq because it's the dynamic mock library I used to love the most):

[Theory]
[InlineData(RestApi.Grandfather.Id, "2022-06-29 12:00", "e@example.gov", "Enigma", 1)]
[InlineData(RestApi.Grandfather.Id, "2022-07-27 11:40", "c@example.com", "Carlie", 2)]
[InlineData(2, "2021-09-03 14:32", "bon@example.edu", "Jovi", 4)]
public async Task CreateAndReadRoundTrip(
    int restaurantId,
    string at,
    string email,
    string name,
    int quantity)
{
    var expected = new Reservation(
        Guid.NewGuid(),
        DateTime.Parse(at, CultureInfo.InvariantCulture),
        new Email(email),
        new Name(name),
        quantity);
    var sut = new Mock<IReservationsRepository>().Object;
 
    await sut.Create(restaurantId, expected);
    var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
    Assert.Equal(expected, actual);
}

If you've worked a little with dynamic mock libraries, you will not be surprised to learn that all three tests fail. Here's one of the failure messages:

Ploeh.Samples.Restaurants.RestApi.Tests.MoqRepositoryTests.CreateAndReadRoundTrip(↩
    restaurantId: 1, at: "2022-06-29 12:00", email: "e@example.gov", name: "Enigma", quantity: 1)
 Source: MoqRepositoryTests.cs line 17
 Duration: 1 ms
 
Message: 
  Assert.Equal() Failure
  Expected: Reservation↩
            {↩
              At = 2022-06-29T12:00:00.0000000,↩
              Email = e@example.gov,↩
              Id = c9de4f95-3255-4e1f-a1d6-63591b58ff0c,↩
              Name = Enigma,↩
              Quantity = 1↩
            }
  Actual:   (null)
 
Stack Trace: 
  MoqRepositoryTests.CreateAndReadRoundTrip(↩
    Int32 restaurantId, String at, String email, String name, Int32 quantity) line 35
  --- End of stack trace from previous location where exception was thrown ---

(I've introduced line breaks and indicated them with the ↩ symbol to make the output more readable. I'll do that again later in the article.)

Not surprisingly, the return value of Create is null. You typically have to configure a dynamic mock in order to give it any sort of behaviour, and I didn't do that here. In that case, the dynamic mock returns the default value for the return type, which in this case correctly is null.

You may object that the above example is unfair. How can a dynamic mock know what to do? You have to configure it. That's the whole point of it.

Retrieval without creation #

Okay, let's set up the dynamic mock:

var dm = new Mock<IReservationsRepository>();
dm.Setup(r => r.ReadReservation(restaurantId, expected.Id)).ReturnsAsync(expected);
var sut = dm.Object;

These are the only lines I've changed from the previous listing of the test, which now passes.

A common criticism of dynamic-mock-heavy tests is that they mostly 'just test the mocks', and this is exactly what happens here.

You can make that more explicit by deleting the Create method call:

var dm = new Mock<IReservationsRepository>();
dm.Setup(r => r.ReadReservation(restaurantId, expected.Id)).ReturnsAsync(expected);
var sut = dm.Object;
 
var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
Assert.Equal(expected, actual);

The test still passes. Clearly it only tests the dynamic mock.

You may, again, demur that this is expected, and it doesn't demonstrate that dynamic mocks break encapsulation. Keep in mind, however, the nature of the contract: Upon successful completion of Create, the reservation is 'in' the repository and can later be retrieved, either with ReadReservation or ReadReservations.

This variation of the test no longer calls Create, yet ReadReservation still returns the expected value.

Do SqlReservationsRepository or FakeDatabase behave like that? No, they don't.

Try to delete the Create call from the test that exercises SqlReservationsRepository:

var sut = new SqlReservationsRepository(connectionString);
 
var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
Assert.Equal(expected, actual);

Hardly surprising, the test now fails because actual is null. The same happens if you delete the Create call from the test that exercises FakeDatabase:

var sut = new FakeDatabase();
 
var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
Assert.Equal(expected, actual);

Again, the assertion fails because actual is null.

The classes SqlReservationsRepository and FakeDatabase behave according to contract, while the dynamic mock doesn't.

Alternative retrieval #

There's another way in which the dynamic mock breaks encapsulation. Recall what the contract states: Upon successful completion of Create, the reservation is 'in' the repository and can later be retrieved, either with ReadReservation or ReadReservations.

In other words, it should be possible to change the interaction from Create followed by ReadReservation to Create followed by ReadReservations.

First, try it with SqlReservationsRepository:

await sut.Create(restaurantId, expected);
var min = expected.At.Date;
var max = min.AddDays(1);
var actual = await sut.ReadReservations(restaurantId, min, max);
 
Assert.Contains(expected, actual);

The test still passes, as expected.

Second, try the same change with FakeDatabase:

await sut.Create(restaurantId, expected);
var min = expected.At.Date;
var max = min.AddDays(1);
var actual = await sut.ReadReservations(restaurantId, min, max);
 
Assert.Contains(expected, actual);

Notice that this is the exact same code as in the SqlReservationsRepository test. That test also passes, as expected.

Third, try it with the dynamic mock:

await sut.Create(restaurantId, expected);
var min = expected.At.Date;
var max = min.AddDays(1);
var actual = await sut.ReadReservations(restaurantId, min, max);
 
Assert.Contains(expected, actual);

Same code, different sut, and the test fails. The dynamic mock breaks encapsulation. You'll have to go and fix the Setup of it to make the test pass again. That's not the case with SqlReservationsRepository or FakeDatabase.

Dynamic mocks break the SUT, not the tests #

Perhaps you're still not convinced that this is of practical interest. After all, Bertrand Meyer had limited success getting mainstream adoption of his thought on contract-based programming.

That dynamic mocks break encapsulation does, however, have real implications.

What if, instead of using FakeDatabase, I'd used dynamic mocks when testing my online restaurant reservation system? A test might have looked like this:

[Theory]
[InlineData(1049, 19, 00, "juliad@example.net", "Julia Domna", 5)]
[InlineData(1130, 18, 15, "x@example.com", "Xenia Ng", 9)]
[InlineData( 956, 16, 55, "kite@example.edu", null, 2)]
[InlineData( 433, 17, 30, "shli@example.org", "Shanghai Li", 5)]
public async Task PostValidReservationWhenDatabaseIsEmpty(
    int days,
    int hours,
    int minutes,
    string email,
    string name,
    int quantity)
{
    var at = DateTime.Now.Date + new TimeSpan(days, hours, minutes, 0);
    var dm = new Mock<IReservationsRepository>();
    dm.Setup(r => r.ReadReservations(Grandfather.Id, at.Date, at.Date.AddDays(1).AddTicks(-1)))
        .ReturnsAsync(Array.Empty<Reservation>());
    var sut = new ReservationsController(
        new SystemClock(),
        new InMemoryRestaurantDatabase(Grandfather.Restaurant),
        dm.Object);
    var expected = new Reservation(
        new Guid("B50DF5B1-F484-4D99-88F9-1915087AF568"),
        at,
        new Email(email),
        new Name(name ?? ""),
        quantity);
 
    await sut.Post(expected.ToDto());
 
    dm.Verify(r => r.Create(Grandfather.Id, expected));
}

This is yet another riff on the PostValidReservationWhenDatabaseIsEmpty test - the gift that keeps giving. I've previously discussed this test in other articles:

• Branching tests
• Waiting to happen
• Parametrised test primitive obsession code smell
• The Equivalence contravariant functor

Here I've replaced the FakeDatabase Test Double with a dynamic mock. (I am, again, using Moq, but keep in mind that the fallout of using a dynamic mock is unrelated to specific libraries.)

To go 'full dynamic mock' I should also have replaced SystemClock and InMemoryRestaurantDatabase with dynamic mocks, but that's not necessary to illustrate the point I wish to make.

This, and other tests, describe the desired outcome of making a reservation against the REST API. It's an interaction that looks like this:

POST /restaurants/90125/reservations?sig=aco7VV%2Bh5sA3RBtrN8zI8Y9kLKGC60Gm3SioZGosXVE%3D HTTP/1.1
content-type: application/json
{
  "at": "2022-12-12T20:00",
  "name": "Pearl Yvonne Gates",
  "email": "pearlygates@example.net",
  "quantity": 4
}

HTTP/1.1 201 Created
Content-Length: 151
Content-Type: application/json; charset=utf-8
Location: [...]/restaurants/90125/reservations/82e550b1690742368ea62d76e103b232?sig=fPY1fSr[...]
{
  "id": "82e550b1690742368ea62d76e103b232",
  "at": "2022-12-12T20:00:00.0000000",
  "email": "pearlygates@example.net",
  "name": "Pearl Yvonne Gates",
  "quantity": 4
}

What's of interest here is that the response includes the JSON representation of the resource that the interaction created. It's mostly a copy of the posted data, but enriched with a server-generated ID.

The code responsible for the database interaction looks like this:

private async Task<ActionResult> TryCreate(Restaurant restaurant, Reservation reservation)
{
    using var scope = new TransactionScope(TransactionScopeAsyncFlowOption.Enabled);
 
    var reservations = await Repository
        .ReadReservations(restaurant.Id, reservation.At)
        .ConfigureAwait(false);
    var now = Clock.GetCurrentDateTime();
    if (!restaurant.MaitreD.WillAccept(now, reservations, reservation))
        return NoTables500InternalServerError();
 
    await Repository.Create(restaurant.Id, reservation).ConfigureAwait(false);
 
    scope.Complete();
 
    return Reservation201Created(restaurant.Id, reservation);
}

The last line of code creates a 201 Created response with the reservation as content. Not shown in this snippet is the origin of the reservation parameter, but it's the input JSON document parsed to a Reservation object. Each Reservation object has an ID that the server creates when it's not supplied by the client.

The above TryCreate helper method contains all the database interaction code related to creating a new reservation. It first calls ReadReservations to retrieve the existing reservations. Subsequently, it calls Create if it decides to accept the reservation. The ReadReservations method is actually an internal extension method:

internal static Task<IReadOnlyCollection<Reservation>> ReadReservations(
    this IReservationsRepository repository,
    int restaurantId,
    DateTime date)
{
    var min = date.Date;
    var max = min.AddDays(1).AddTicks(-1);
    return repository.ReadReservations(restaurantId, min, max);
}

Notice how the dynamic-mock-based test has to replicate this internal implementation detail to the tick. If I ever decide to change this just one tick, the test is going to fail. That's already bad enough (and something that FakeDatabase gracefully handles), but not what I'm driving towards.

At the moment the TryCreate method echoes back the reservation. What if, however, you instead want to query the database and return the record that you got from the database? In this particular case, there's no reason to do that, but perhaps in other cases, something happens in the data layer that either enriches or normalises the data. So you make an innocuous change:

private async Task<ActionResult> TryCreate(Restaurant restaurant, Reservation reservation)
{
    using var scope = new TransactionScope(TransactionScopeAsyncFlowOption.Enabled);
 
    var reservations = await Repository
        .ReadReservations(restaurant.Id, reservation.At)
        .ConfigureAwait(false);
    var now = Clock.GetCurrentDateTime();
    if (!restaurant.MaitreD.WillAccept(now, reservations, reservation))
        return NoTables500InternalServerError();
 
    await Repository.Create(restaurant.Id, reservation).ConfigureAwait(false);
    var storedReservation = await Repository
        .ReadReservation(restaurant.Id, reservation.Id)
        .ConfigureAwait(false);
 
    scope.Complete();
 
    return Reservation201Created(restaurant.Id, storedReservation!);
}

Now, instead of echoing back reservation, the method calls ReadReservation to retrieve the (possibly enriched or normalised) storedReservation and returns that value. Since this value could, conceivably, be null, for now the method uses the ! operator to insist that this is not the case. A new test case might be warranted to cover the scenario where the query returns null.

This is perhaps a little less efficient because it implies an extra round-trip to the database, but it shouldn't change the behaviour of the system!

But when you run the test suite, that PostValidReservationWhenDatabaseIsEmpty test fails:

Ploeh.Samples.Restaurants.RestApi.Tests.ReservationsTests.PostValidReservationWhenDatabaseIsEmpty(↩
    days: 433, hours: 17, minutes: 30, email: "shli@example.org", name: "Shanghai Li", quantity: 5)↩
    [FAIL]
  System.NullReferenceException : Object reference not set to an instance of an object.
  Stack Trace:
    [...]\Restaurant.RestApi\ReservationsController.cs(94,0): at↩
      [...].RestApi.ReservationsController.Reservation201Created↩
      (Int32 restaurantId, Reservation r)
    [...]\Restaurant.RestApi\ReservationsController.cs(79,0): at↩
      [...].RestApi.ReservationsController.TryCreate↩
      (Restaurant restaurant, Reservation reservation)
    [...]\Restaurant.RestApi\ReservationsController.cs(57,0): at↩
      [...].RestApi.ReservationsController.Post↩
      (Int32 restaurantId, ReservationDto dto)
    [...]\Restaurant.RestApi.Tests\ReservationsTests.cs(73,0): at↩
      [...].RestApi.Tests.ReservationsTests.PostValidReservationWhenDatabaseIsEmpty↩
      (Int32 days, Int32 hours, Int32 minutes, String email, String name, Int32 quantity)
    --- End of stack trace from previous location where exception was thrown ---

Oh, the dreaded NullReferenceException! This happens because ReadReservation returns null, since the dynamic mock isn't configured.

The typical reaction that most people have is: Oh no, the tests broke!

I think, though, that this is the wrong perspective. The dynamic mock broke the System Under Test (SUT) because it passed an implementation of IReservationsRepository that breaks the contract. The test didn't 'break', because it was never correct from the outset.

Shotgun surgery #

When a test code base uses dynamic mocks, it tends to do so pervasively. Most tests create one or more dynamic mocks that they pass to their SUT. Most of these dynamic mocks break encapsulation, so when you refactor, the dynamic mocks break the SUT.

You'll typically need to revisit and 'fix' all the failing tests to accommodate the refactoring:

[Theory]
[InlineData(1049, 19, 00, "juliad@example.net", "Julia Domna", 5)]
[InlineData(1130, 18, 15, "x@example.com", "Xenia Ng", 9)]
[InlineData( 956, 16, 55, "kite@example.edu", null, 2)]
[InlineData( 433, 17, 30, "shli@example.org", "Shanghai Li", 5)]
public async Task PostValidReservationWhenDatabaseIsEmpty(
    int days,
    int hours,
    int minutes,
    string email,
    string name,
    int quantity)
{
    var at = DateTime.Now.Date + new TimeSpan(days, hours, minutes, 0);
    var expected = new Reservation(
        new Guid("B50DF5B1-F484-4D99-88F9-1915087AF568"),
        at,
        new Email(email),
        new Name(name ?? ""),
        quantity);
    var dm = new Mock<IReservationsRepository>();
    dm.Setup(r => r.ReadReservations(Grandfather.Id, at.Date, at.Date.AddDays(1).AddTicks(-1)))
        .ReturnsAsync(Array.Empty<Reservation>());
    dm.Setup(r => r.ReadReservation(Grandfather.Id, expected.Id)).ReturnsAsync(expected);
    var sut = new ReservationsController(
        new SystemClock(),
        new InMemoryRestaurantDatabase(Grandfather.Restaurant),
        dm.Object);
 
    await sut.Post(expected.ToDto());
 
    dm.Verify(r => r.Create(Grandfather.Id, expected));
}

The test now passes (until the next change in the SUT), but notice how top-heavy it becomes. That's a test code smell when using dynamic mocks. Everything has to happen in the Arrange phase.

You typically have many such tests that you need to edit. The name of this antipattern is Shotgun Surgery.

The implication is that refactoring by definition is impossible:

"to refactor, the essential precondition is [...] solid tests"

You need tests that don't break when you refactor. When you use dynamic mocks, tests tend to fail whenever you make changes in SUTs. Even though you have tests, they don't enable refactoring.

To add spite to injury, every time you edit existing tests, they become less trustworthy.

To address these problems, use Fakes instead of Mocks and Stubs. With the FakeDatabase the entire sample test suite for the online restaurant reservation system gracefully handles the change described above. No tests fail.

Spies #

If you spelunk the test code base for the book, you may also find this Test Double:

internal sealed class SpyPostOffice :
    Collection<SpyPostOffice.Observation>, IPostOffice
{
    public Task EmailReservationCreated(
        int restaurantId,
        Reservation reservation)
    {
        Add(new Observation(Event.Created, restaurantId, reservation));
        return Task.CompletedTask;
    }
 
    public Task EmailReservationDeleted(
        int restaurantId,
        Reservation reservation)
    {
        Add(new Observation(Event.Deleted, restaurantId, reservation));
        return Task.CompletedTask;
    }
 
    public Task EmailReservationUpdating(
        int restaurantId,
        Reservation reservation)
    {
        Add(new Observation(Event.Updating, restaurantId, reservation));
        return Task.CompletedTask;
    }
 
    public Task EmailReservationUpdated(
        int restaurantId,
        Reservation reservation)
    {
        Add(new Observation(Event.Updated, restaurantId, reservation));
        return Task.CompletedTask;
    }
 
    internal enum Event
    {
        Created = 0,
        Updating,
        Updated,
        Deleted
    }
 
    internal sealed class Observation
    {
        public Observation(
            Event @event,
            int restaurantId,
            Reservation reservation)
        {
            Event = @event;
            RestaurantId = restaurantId;
            Reservation = reservation;
        }
 
        public Event Event { get; }
        public int RestaurantId { get; }
        public Reservation Reservation { get; }
 
        public override bool Equals(object? obj)
        {
            return obj is Observation observation &&
                   Event == observation.Event &&
                   RestaurantId == observation.RestaurantId &&
                   EqualityComparer<Reservation>.Default.Equals(Reservation, observation.Reservation);
        }
 
        public override int GetHashCode()
        {
            return HashCode.Combine(Event, RestaurantId, Reservation);
        }
    }
}

As you can see, I've chosen to name this class with the Spy prefix, indicating that this is a Test Spy rather than a Fake Object. A Spy is a Test Double whose main purpose is to observe and record interactions. Does that break or realise encapsulation?

While I favour Fakes whenever possible, consider the interface that SpyPostOffice implements:

public interface IPostOffice
{
    Task EmailReservationCreated(int restaurantId, Reservation reservation);
 
    Task EmailReservationDeleted(int restaurantId, Reservation reservation);
 
    Task EmailReservationUpdating(int restaurantId, Reservation reservation);
 
    Task EmailReservationUpdated(int restaurantId, Reservation reservation);
}

This interface consist entirely of Commands. There's no way to query the interface to examine the state of the object. Thus, you can't check that postconditions hold exclusively via the interface. Instead, you need an additional retrieval interface to examine the posterior state of the object. The SpyPostOffice concrete class exposes such an interface.

In a sense, you can view SpyPostOffice as an in-memory message sink. It fulfils the contract.

Concurrency #

Perhaps you're still not convinced. You may argue, for example, that the (partial) contract that I stated is naive. Consider, again, the implications expressed as code:

await sut.Create(restaurantId, expected);
var actual = await sut.ReadReservation(restaurantId, expected.Id);
 
Assert.Equal(expected, actual);

You may argue that in the face of concurrency, another thread or process could be making changes to the reservation after Create, but before ReadReservation. Thus, you may argue, the contract I've stipulated is false. In a real system, we can't expect that to be the case.

I agree.

Concurrency makes things much harder. Even in that light, I think the above line of reasoning is appropriate, for two reasons.

First, I chose to model IReservationsRepository like I did because I didn't expect high contention on individual reservations. In other words, I don't expect two or more concurrent processes to attempt to modify the same reservation at the same time. Thus, I found it appropriate to model the Repository as

"a collection-like interface for accessing domain objects."

A collection-like interface implies both data retrieval and collection manipulation members. In low-contention scenarios like the reservation system, this turns out to be a useful model. As the aphorism goes, all models are wrong, but some models are useful. Treating IReservationsRepository as a collection accessed in a non-concurrent manner turned out to be useful in this code base.

Had I been more worried about data contention, a move towards CQRS seems promising. This leads to another object model, with different contracts.

Second, even in the face of concurrency, most unit test cases are implicitly running on a single thread. While they may run in parallel, each unit test exercises the SUT on a single thread. This implies that reads and writes against Test Doubles are serialised.

Even if concurrency is a real concern, you'd still expect that if only one thread is manipulating the Repository object, then what you Create you should be able to retrieve. The contract may be a little looser, but it'd still be a violation of the principle of least surprise if it was any different.

Conclusion #

In object-oriented programming, encapsulation is the notion of separating the affordances of an object from its implementation details. I find it most practical to think about this in terms of contracts, which again can be subdivided into sets of preconditions, invariants, and postconditions.

Polymorphic objects (like interfaces and base classes) come with contracts as well. When you replace 'real' implementations with Test Doubles, the Test Doubles should also fulfil the contracts. Fake objects do that; Test Spies may also fit that description.

When Test Doubles obey their contracts, you can refactor your SUT without breaking your test suite.

By default, however, dynamic mocks break encapsulation because they don't fulfil the objects' contracts. This leads to fragile tests.

Favour Fakes over dynamic mocks. You can read more about this way to write tests by following many of the links in this article, or by reading my book Code That Fits in Your Head.

Comments

A slightly less unrealistic example in C#.

This article is one of the examples that I promised in the earlier article The State pattern and the State monad. That article examines the relationship between the State design pattern and the State monad. It's deliberately abstract, so one or more examples are in order.

In the previous example you saw how to refactor Design Patterns' TCP connection example. That example is, unfortunately, hardly illuminating due to its nature, so a second example is warranted.

This second example shows how to refactor a stateful asynchronous message handler from the State pattern to the State monad.

Shipping policy #

Instead of inventing an example from scratch, I decided to use an NServiceBus saga tutorial as a foundation. Read on even if you don't know NServiceBus. You don't have to know anything about NServiceBus in order to follow along. I just thought that I'd embed the example code in a context that actually executes and does something, instead of faking it with a bunch of unit tests. Hopefully this will help make the example a bit more realistic and relatable.

The example is a simple demo of asynchronous message handling. In a web store shipping department, you should only ship an item once you've received the order and a billing confirmation. When working with asynchronous messaging, you can't, however, rely on message ordering, so perhaps the OrderBilled message arrives before the OrderPlaced message, and sometimes it's the other way around.

Only when you've received both messages may you ship the item.

It's a simple workflow, and you don't really need the State pattern. So much is clear from the sample code implementation:

public class ShippingPolicy : Saga<ShippingPolicyData>,
    IAmStartedByMessages<OrderBilled>,
    IAmStartedByMessages<OrderPlaced>
{
    static ILog log = LogManager.GetLogger<ShippingPolicy>();
 
    protected override void ConfigureHowToFindSaga(SagaPropertyMapper<ShippingPolicyData> mapper)
    {
        mapper.MapSaga(sagaData => sagaData.OrderId)
            .ToMessage<OrderPlaced>(message => message.OrderId)
            .ToMessage<OrderBilled>(message => message.OrderId);
    }
 
    public Task Handle(OrderPlaced message, IMessageHandlerContext context)
    {
        log.Info($"OrderPlaced message received.");
        Data.IsOrderPlaced = true;
        return ProcessOrder(context);
    }
 
    public Task Handle(OrderBilled message, IMessageHandlerContext context)
    {
        log.Info($"OrderBilled message received.");
        Data.IsOrderBilled = true;
        return ProcessOrder(context);
    }
 
    private async Task ProcessOrder(IMessageHandlerContext context)
    {
        if (Data.IsOrderPlaced && Data.IsOrderBilled)
        {
            await context.SendLocal(new ShipOrder() { OrderId = Data.OrderId });
            MarkAsComplete();
        }
    }
}

I don't expect you to be familiar with the NServiceBus API, so don't worry about the base class, the interfaces, or the ConfigureHowToFindSaga method. What you need to know is that this class handles two types of messages: OrderPlaced and OrderBilled. What the base class and the framework does is handling message correlation, hydration and dehydration, and so on.

For the purposes of this demo, all you need to know about the context object is that it enables you to send and publish messages. The code sample uses context.SendLocal to send a new ShipOrder Command.

Messages arrive asynchronously and conceptually with long wait times between them. You can't just rely on in-memory object state because a ShippingPolicy instance may receive one message and then risk that the server it's running on shuts down before the next message arrives. The NServiceBus framework handles message correlation and hydration and dehydration of state data. The latter is modelled by the ShippingPolicyData class:

public class ShippingPolicyData : ContainSagaData
{
    public string OrderId { get; set; }
    public bool IsOrderPlaced { get; set; }
    public bool IsOrderBilled { get; set; }
}

Notice that the above sample code inspects and manipulates the Data property defined by the Saga<ShippingPolicyData> base class.

When the ShippingPolicy methods are called by the NServiceBus framework, the Data is automatically populated. When you modify the Data, the state data is automatically persisted when the message handler shuts down to wait for the next message.

Characterisation tests #

While you can draw an explicit state diagram like the one above, the sample code doesn't explicitly model the various states as objects. Instead, it relies on reading and writing two Boolean values.

There's nothing wrong with this implementation. It's the simplest thing that could possibly work, so why make it more complicated?

In this article, I am going to make it more complicated. First, I'm going to refactor the above sample code to use the State design pattern, and then I'm going to refactor that code to use the State monad. From a perspective of maintainability, this isn't warranted, but on the other hand, I hope it's educational. The sample code is just complex enough to showcase the structures of the State pattern and the State monad, yet simple enough that the implementation logic doesn't get in the way.

Simplicity can be deceiving, however, and no refactoring is without risk.

"to refactor, the essential precondition is [...] solid tests"

I found it safest to first add a few Characterisation Tests to make sure I didn't introduce any errors as I changed the code. It did catch a few copy-paste goofs that I made, so adding tests turned out to be a good idea.

Testing NServiceBus message handlers isn't too hard. All the tests I wrote look similar, so one should be enough to give you an idea.

[Theory]
[InlineData("1337")]
[InlineData("baz")]
public async Task OrderPlacedAndBilled(string orderId)
{
    var sut = 
        new ShippingPolicy 
        {
            Data = new ShippingPolicyData { OrderId = orderId }
        };
    var ctx = new TestableMessageHandlerContext();
 
    await sut.Handle(new OrderPlaced { OrderId = orderId }, ctx);
    await sut.Handle(new OrderBilled { OrderId = orderId }, ctx);
 
    Assert.True(sut.Completed);
    var msg = Assert.Single(ctx.SentMessages.Containing<ShipOrder>());
    Assert.Equal(orderId, msg.Message.OrderId);
}

The tests use xUnit.net 2.4.2. When I downloaded the NServiceBus saga sample code it targeted .NET Framework 4.8, and I didn't bother to change the version.

While the NServiceBus framework will automatically hydrate and populate Data, in a unit test you have to remember to explicitly populate it. The TestableMessageHandlerContext class is a Test Spy that is part of NServiceBus testing API.

You'd think I was paid by Particular Software to write this article, but I'm not. All this is really just the introduction. You're excused if you've forgotten the topic of this article, but my goal is to show a State pattern example. Only now can we begin in earnest.

State pattern implementation #

Refactoring to the State pattern, I chose to let the ShippingPolicy class fill the role of the pattern's Context. Instead of a base class with virtual method, I used an interface to define the State object, as that's more Idiomatic in C#:

public interface IShippingState
{
    Task OrderPlaced(OrderPlaced message, IMessageHandlerContext context, ShippingPolicy policy);
 
    Task OrderBilled(OrderBilled message, IMessageHandlerContext context, ShippingPolicy policy);
}

The State pattern only shows examples where the State methods take a single argument: The Context. In this case, that's the ShippingPolicy. Careful! There's also a parameter called context! That's the NServiceBus context, and is an artefact of the original example. The two other parameters, message and context, are run-time values passed on from the ShippingPolicy's Handle methods:

public IShippingState State { get; internal set; }
 
public async Task Handle(OrderPlaced message, IMessageHandlerContext context)
{
    log.Info($"OrderPlaced message received.");
    Hydrate();
    await State.OrderPlaced(message, context, this);
    Dehydrate();
}
 
public async Task Handle(OrderBilled message, IMessageHandlerContext context)
{
    log.Info($"OrderBilled message received.");
    Hydrate();
    await State.OrderBilled(message, context, this);
    Dehydrate();
}

The Hydrate method isn't part of the State pattern, but finds an appropriate state based on Data:

private void Hydrate()
{
    if (!Data.IsOrderPlaced && !Data.IsOrderBilled)
        State = InitialShippingState.Instance;
    else if (Data.IsOrderPlaced && !Data.IsOrderBilled)
        State = AwaitingBillingState.Instance;
    else if (!Data.IsOrderPlaced && Data.IsOrderBilled)
        State = AwaitingPlacementState.Instance;
    else
        State = CompletedShippingState.Instance;
}

In more recent versions of C# you'd be able to use more succinct pattern matching, but since this code base is on .NET Framework 4.8 I'm constrained to C# 7.3 and this is as good as I cared to make it. It's not important to the topic of the State pattern, but I'm showing it in case you where wondering. It's typical that you need to translate between data that exists in the 'external world' and your object-oriented, polymorphic code, since at the boundaries, applications aren't object-oriented.

Likewise, the Dehydrate method translates the other way:

private void Dehydrate()
{
    if (State is AwaitingBillingState)
    {
        Data.IsOrderPlaced = true;
        Data.IsOrderBilled = false;
        return;
    }
 
    if (State is AwaitingPlacementState)
    {
        Data.IsOrderPlaced = false;
        Data.IsOrderBilled = true;
        return;
    }
 
    if (State is CompletedShippingState)
    {
        Data.IsOrderPlaced = true;
        Data.IsOrderBilled = true;
        return;
    }
 
    Data.IsOrderPlaced = false;
    Data.IsOrderBilled = false;
}

In any case, Hydrate and Dehydrate are distractions. The important part is that the ShippingPolicy (the State Context) now delegates execution to its State, which performs the actual work and updates the State.

Initial state #

The first time the saga runs, both Data.IsOrderPlaced and Data.IsOrderBilled are false, which means that the State is InitialShippingState:

public sealed class InitialShippingState : IShippingState
{
    public readonly static InitialShippingState Instance =
        new InitialShippingState();
 
    private InitialShippingState()
    {
    }
 
    public Task OrderPlaced(
        OrderPlaced message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        policy.State = AwaitingBillingState.Instance;
        return Task.CompletedTask;
    }
 
    public Task OrderBilled(
        OrderBilled message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        policy.State = AwaitingPlacementState.Instance;
        return Task.CompletedTask;
    }
}

As the above state transition diagram indicates, the only thing that each of the methods do is that they transition to the next appropriate state: AwaitingBillingState if the first event was OrderPlaced, and AwaitingPlacementState when the event was OrderBilled.

"State object are often Singletons"

Like in the previous example I've made all the State objects Singletons. It's not that important, but since they are all stateless, we might as well. At least, it's in the spirit of the book.

Awaiting billing #

AwaitingBillingState is another IShippingState implementation:

public sealed class AwaitingBillingState : IShippingState
{
    public readonly static IShippingState Instance =
        new AwaitingBillingState();
 
    private AwaitingBillingState()
    {
    }
 
    public Task OrderPlaced(
        OrderPlaced message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        return Task.CompletedTask;
    }
 
    public async Task OrderBilled(
        OrderBilled message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        await context.SendLocal(
            new ShipOrder() { OrderId = policy.Data.OrderId });
        policy.Complete();
        policy.State = CompletedShippingState.Instance;
    }
}

This State doesn't react to OrderPlaced because it assumes that an order has already been placed. It only reacts to an OrderBilled event. When that happens, all requirements have been fulfilled to ship the item, so it sends a ShipOrder Command, marks the saga as completed, and changes the State to CompletedShippingState.

The Complete method is a little wrapper method I had to add to the ShippingPolicy class, since MarkAsComplete is a protected method:

internal void Complete()
{
    MarkAsComplete();
}

The AwaitingPlacementState class is similar to AwaitingBillingState, except that it reacts to OrderPlaced rather than OrderBilled.

Terminal state #

The fourth and final state is the CompletedShippingState:

public sealed class CompletedShippingState : IShippingState
{
    public readonly static IShippingState Instance =
        new CompletedShippingState();
 
    private CompletedShippingState()
    {
    }
 
    public Task OrderPlaced(
        OrderPlaced message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        return Task.CompletedTask;
    }
 
    public Task OrderBilled(
        OrderBilled message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        return Task.CompletedTask;
    }
}

In this state, the saga is completed, so it ignores both events.

Move Commands to output #

The saga now uses the State pattern to manage state-specific behaviour as well as state transitions. To be clear, this complexity isn't warranted for the simple requirements. This is, after all, an example. All tests still pass, and smoke testing also indicates that everything still works as it's supposed to.

The goal of this article is now to refactor the State pattern implementation to pure functions. When the saga runs it has an observable side effect: It eventually sends a ShipOrder Command. During processing it also updates its internal state. Both of these are sources of impurity that we have to decouple from the decision logic.

I'll do this in several steps. The first impure action I'll address is the externally observable message transmission. A common functional-programming trick is to turn a side effect into a return value. So far, the IShippingState methods don't return anything. (This is strictly not true; they each return Task, but we can regard Task as 'asynchronous void'.) Thus, return values are still available as a communications channel.

Refactor the IShippingState methods to return Commands instead of actually sending them. Each method may send an arbitrary number of Commands, including none, so the return type has to be a collection:

public interface IShippingState
{
    IReadOnlyCollection<ICommand> OrderPlaced(
        OrderPlaced message,
        IMessageHandlerContext context,
        ShippingPolicy policy);
 
    IReadOnlyCollection<ICommand> OrderBilled(
        OrderBilled message,
        IMessageHandlerContext context,
        ShippingPolicy policy);
}

When you change the interface you also have to change all the implementing classes, including AwaitingBillingState:

public sealed class AwaitingBillingState : IShippingState
{
    public readonly static IShippingState Instance = new AwaitingBillingState();
 
    private AwaitingBillingState()
    {
    }
 
    public IReadOnlyCollection<ICommand> OrderPlaced(
        OrderPlaced message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        return Array.Empty<ICommand>();
    }
 
    public IReadOnlyCollection<ICommand> OrderBilled(
        OrderBilled message,
        IMessageHandlerContext context,
        ShippingPolicy policy)
    {
        policy.Complete();
        policy.State = CompletedShippingState.Instance;
        return new[] { new ShipOrder() { OrderId = policy.Data.OrderId } };
    }
}

In order to do nothing a method like OrderPlaced now has to return an empty collection of Commands. In order to 'send' a Command, OrderBilled now returns it instead of using the context to send it. The context is already redundant, but since I prefer to move in small steps, I'll remove it in a separate step.

It's now the responsibility of the ShippingPolicy class to do something with the Commands returned by the State:

public async Task Handle(OrderBilled message, IMessageHandlerContext context)
{
    log.Info($"OrderBilled message received.");
    Hydrate();
    var result = State.OrderBilled(message, context, this);
    await Interpret(result, context);
    Dehydrate();
}
 
private async Task Interpret(
    IReadOnlyCollection<ICommand> commands,
    IMessageHandlerContext context)
{
    foreach (var cmd in commands)
        await context.SendLocal(cmd);
}

In functional programming, you often run an interpreter over the instructions returned by a pure function. Here the interpreter is just a private helper method.

The IShippingState methods are no longer asynchronous. Now they just return collections. I consider that a simplification.

Remove context parameter #

The context parameter is now redundant, so remove it from the IShippingState interface:

public interface IShippingState
{
    IReadOnlyCollection<ICommand> OrderPlaced(OrderPlaced message, ShippingPolicy policy);
 
    IReadOnlyCollection<ICommand> OrderBilled(OrderBilled message, ShippingPolicy policy);
}

I used Visual Studio's built-in refactoring tools to remove the parameter, which automatically removed it from all the call sites and implementations.

This takes us part of the way towards implementing the states as pure functions, but there's still work to be done.

public IReadOnlyCollection<ICommand> OrderBilled(OrderBilled message, ShippingPolicy policy)
{
    policy.Complete();
    policy.State = CompletedShippingState.Instance;
    return new[] { new ShipOrder() { OrderId = policy.Data.OrderId } };
}

The above OrderBilled implementation calls policy.Complete to indicate that the saga has completed. That's another state mutation that must be eliminated to make this a pure function.

Return complex result #

How do you refactor from state mutation to pure function? You turn the mutation statement into an instruction, which is a value that you return. In this case you might want to return a Boolean value: True to complete the saga. False otherwise.

There seems to be a problem, though. The IShippingState methods already return data: They return a collection of Commands. How do we get around this conundrum?

Introduce a complex object:

public sealed class ShippingStateResult
{
    public ShippingStateResult(
        IReadOnlyCollection<ICommand> commands,
        bool completeSaga)
    {
        Commands = commands;
        CompleteSaga = completeSaga;
    }
 
    public IReadOnlyCollection<ICommand> Commands { get; }
    public bool CompleteSaga { get; }
 
    public override bool Equals(object obj)
    {
        return obj is ShippingStateResult result &&
               EqualityComparer<IReadOnlyCollection<ICommand>>.Default
                    .Equals(Commands, result.Commands) &&
               CompleteSaga == result.CompleteSaga;
    }
 
    public override int GetHashCode()
    {
        int hashCode = -1668187231;
        hashCode = hashCode * -1521134295 + EqualityComparer<IReadOnlyCollection<ICommand>>
            .Default.GetHashCode(Commands);
        hashCode = hashCode * -1521134295 + CompleteSaga.GetHashCode();
        return hashCode;
    }
}

That looks rather horrible, but most of the code is generated by Visual Studio. The only thing I wrote myself was the class declaration and the two read-only properties. I then used Visual Studio's Generate constructor and Generate Equals and GetHashCode Quick Actions to produce the rest of the code.

With more modern versions of C# I could have used a record, but as I've already mentioned, I'm on C# 7.3 here.

The IShippingState interface can now define its methods with this new return type:

public interface IShippingState
{
    ShippingStateResult OrderPlaced(OrderPlaced message, ShippingPolicy policy);
 
    ShippingStateResult OrderBilled(OrderBilled message, ShippingPolicy policy);
}

This change reminds me of the Introduce Parameter Object refactoring, but instead applied to the return value instead of input.

Implementers now have to return values of this new type:

public sealed class AwaitingBillingState : IShippingState
{
    public readonly static IShippingState Instance = new AwaitingBillingState();
 
    private AwaitingBillingState()
    {
    }
 
    public ShippingStateResult OrderPlaced(OrderPlaced message, ShippingPolicy policy)
    {
        return new ShippingStateResult(Array.Empty<ICommand>(), false);
    }
 
    public ShippingStateResult OrderBilled(OrderBilled message, ShippingPolicy policy)
    {
        policy.State = CompletedShippingState.Instance;
        return new ShippingStateResult(
            new[] { new ShipOrder() { OrderId = policy.Data.OrderId } },
            true);
    }
}

Moving a statement to an output value implies that the effect must happen somewhere else. It seems natural to put it in the ShippingPolicy class' Interpret method:

public async Task Handle(OrderBilled message, IMessageHandlerContext context)
{
    log.Info($"OrderBilled message received.");
    Hydrate();
    var result = State.OrderBilled(message, this);
    await Interpret(result, context);
    Dehydrate();
}
 
private async Task Interpret(ShippingStateResult result, IMessageHandlerContext context)
{
    foreach (var cmd in result.Commands)
        await context.SendLocal(cmd);
 
    if (result.CompleteSaga)
        MarkAsComplete();
}

Since Interpret is an instance method on the ShippingPolicy class I can now also delete the internal Complete method, since MarkAsComplete is already callable (it's a protected method defined by the Saga base class).

Use message data #

Have you noticed an odd thing about the code so far? It doesn't use any of the message data!

This is an artefact of the original code example. Refer back to the original ProcessOrder helper method. It uses neither OrderPlaced nor OrderBilled for anything. Instead, it pulls the OrderId from the saga's Data property. It can do that because NServiceBus makes sure that all OrderId values are correlated. It'll only instantiate a saga for which Data.OrderId matches OrderPlaced.OrderId or OrderBilled.OrderId. Thus, these values are guaranteed to be the same, and that's why ProcessOrder can get away with using Data.OrderId instead of the message data.

So far, through all refactorings, I've retained this detail, but it seems odd. It also couples the implementation methods to the ShippingPolicy class rather than the message classes. For these reasons, refactor the methods to use the message data instead. Here's the AwaitingBillingState implementation:

public ShippingStateResult OrderBilled(OrderBilled message, ShippingPolicy policy)
{
    policy.State = CompletedShippingState.Instance;
    return new ShippingStateResult(
        new[] { new ShipOrder() { OrderId = message.OrderId } },
        true);
}

Compare this version with the previous iteration, where it used policy.Data.OrderId instead of message.OrderId.

Now, the only reason to pass ShippingPolicy as a method parameter is to mutate policy.State. We'll get to that in due time, but first, there's another issue I'd like to address.

Immutable arguments #

Keep in mind that the overall goal of the exercise is to refactor the state machine to pure functions. For good measure, method parameters should be immutable as well. Consider a method like OrderBilled shown above in its most recent iteration. It mutates policy by setting policy.State. The long-term goal is to get rid of that statement.

The method doesn't mutate the other argument, message, but the OrderBilled class is actually mutable:

public class OrderBilled : IEvent
{
    public string OrderId { get; set; }
}

The same is true for the other message type, OrderPlaced.

For good measure, pure functions shouldn't take mutable arguments. You could argue that, since none of the implementation methods actually mutate the messages, it doesn't really matter. I am, however, enough of a neat freak that I don't like to leave such a loose strand dangling. I'd like to refactor the IShippingState API so that only immutable message data is passed as arguments.

In a situation like this, there are (at least) three options:

• Make the message types immutable. This would mean making OrderBilled and OrderPlaced immutable. These message types are by default mutable Data Transfer Objects (DTO), because NServiceBus needs to serialise and deserialise them to transmit them over durable queues. There are ways you can configure NServiceBus to use serialisation mechanisms that enable immutable records as messages, but for an example code base like this, I might be inclined to reach for an easier solution if one presents itself.
• Add an immutable 'mirror' class. This may often be a good idea if you have a rich domain model that you'd like to represent. You can see an example of that in Code That Fits in Your Head, where there's both a mutable ReservationDto class and an immutable Reservation Value Object. This makes sense if the invariants of the domain model are sufficiently stronger than the DTO. That hardly seems to be the case here, since both messages only contain an OrderId.
• Dissolve the DTO into its constituents and pass each as an argument. This doesn't work if the DTO is complex and nested, but here there's only a single constituent element, and that's the OrderId property.

The third option seems like the simplest solution, so refactor the IShippingState methods to take an orderId parameter instead of a message:

public interface IShippingState
{
    ShippingStateResult OrderPlaced(string orderId, ShippingPolicy policy);
 
    ShippingStateResult OrderBilled(string orderId, ShippingPolicy policy);
}

While this is the easiest of the three options given above, the refactoring doesn't hinge on this. It would work just as well with one of the two other options.

Implementations now look like this:

public ShippingStateResult OrderBilled(string orderId, ShippingPolicy policy)
{
    policy.State = CompletedShippingState.Instance;
    return new ShippingStateResult(
        new[] { new ShipOrder() { OrderId = orderId } },
        true);
}

The only impure action still lingering is the mutation of policy.State. Once we're rid of that, the API consists of pure functions.

Return state #

As outlined by the parent article, instead of mutating the caller's state, you can return the state as part of a tuple. This means that you no longer need to pass ShippingPolicy as a parameter:

public interface IShippingState
{
    Tuple<ShippingStateResult, IShippingState> OrderPlaced(string orderId);
 
    Tuple<ShippingStateResult, IShippingState> OrderBilled(string orderId);
}

Why not expand the ShippingStateResult class, or conversely, dissolve that class and instead return a triple (a three-tuple)? All of these are possible as alternatives, as they'd be isomorphic to this particular design. The reason I've chosen this particular return type is that it's the idiomatic implementation of the State monad: The result is the first element of a tuple, and the state is the second element. This means that you can use a standard, reusable State monad library to manipulate the values, as you'll see later.

An implementation now looks like this:

public sealed class AwaitingBillingState : IShippingState
{
    public readonly static IShippingState Instance = new AwaitingBillingState();
 
    private AwaitingBillingState()
    {
    }
 
    public Tuple<ShippingStateResult, IShippingState> OrderPlaced(string orderId)
    {
        return Tuple.Create(
            new ShippingStateResult(Array.Empty<ICommand>(), false),
            (IShippingState)this);
    }
 
    public Tuple<ShippingStateResult, IShippingState> OrderBilled(string orderId)
    {
        return Tuple.Create(
            new ShippingStateResult(
                new[] { new ShipOrder() { OrderId = orderId } },
                true),
            CompletedShippingState.Instance);
    }
}

Since the ShippingPolicy class that calls these methods now directly receives the state as part of the output, it no longer needs a mutable State property. Instead, it immediately handles the return value:

public async Task Handle(OrderPlaced message, IMessageHandlerContext context)
{
    log.Info($"OrderPlaced message received.");
    var state = Hydrate();
 
    var result = state.OrderPlaced(message.OrderId);
 
    await Interpret(result.Item1, context);
    Dehydrate(result.Item2);
}
 
public async Task Handle(OrderBilled message, IMessageHandlerContext context)
{
    log.Info($"OrderBilled message received.");
    var state = Hydrate();
 
    var result = state.OrderBilled(message.OrderId);
 
    await Interpret(result.Item1, context);
    Dehydrate(result.Item2);
}

Each Handle method is now an impureim sandwich.

Since the result is now a tuple, the Handle methods now have to pass the first element (result.Item1) to the Interpret helper method, and the second element (result.Item2) - the state - to Dehydrate. It's also possible to pattern match (or destructure) each of the elements directly; you'll see an example of that later.

Since the mutable State property is now gone, the Hydrate method returns the hydrated state:

private IShippingState Hydrate()
{
    if (!Data.IsOrderPlaced && !Data.IsOrderBilled)
        return InitialShippingState.Instance;
    else if (Data.IsOrderPlaced && !Data.IsOrderBilled)
        return AwaitingBillingState.Instance;
    else if (!Data.IsOrderPlaced && Data.IsOrderBilled)
        return AwaitingPlacementState.Instance;
    else
        return CompletedShippingState.Instance;
}

Likewise, the Dehydrate method takes the new state as an input parameter:

private void Dehydrate(IShippingState state)
{
    if (state is AwaitingBillingState)
    {
        Data.IsOrderPlaced = true;
        Data.IsOrderBilled = false;
        return;
    }
 
    if (state is AwaitingPlacementState)
    {
        Data.IsOrderPlaced = false;
        Data.IsOrderBilled = true;
        return;
    }
 
    if (state is CompletedShippingState)
    {
        Data.IsOrderPlaced = true;
        Data.IsOrderBilled = true;
        return;
    }
 
    Data.IsOrderPlaced = false;
    Data.IsOrderBilled = false;
}

Since each Handle method only calls a single State-valued method, they don't need the State monad machinery. This only becomes useful when you need to compose multiple State-based operations.

This might be useful in unit tests, so let's examine that next.

State monad #

In previous articles about the State monad you've seen it implemented based on an IState interface. I've also dropped hints here and there that you don't need the interface. Instead, you can implement the monad functions directly on State-valued functions. That's what I'm going to do here:

public static Func<S, Tuple<T1, S>> SelectMany<S, T, T1>(
    this Func<S, Tuple<T, S>> source,
    Func<T, Func<S, Tuple<T1, S>>> selector)
{
    return s =>
    {
        var tuple = source(s);
        var f = selector(tuple.Item1);
        return f(tuple.Item2);
    };
}

This SelectMany implementation works directly on another function, source. This function takes a state of type S as input and returns a tuple as a result. The first element is the result of type T, and the second element is the new state, still of type S. Compare that to the IState interface to convince yourself that these are just two representations of the same idea.

The return value is a new function with the same shape, but where the result type is T1 rather than T.

You can implement the special SelectMany overload that enables query syntax in the standard way.

The return function also mirrors the previous interface-based implementation:

public static Func<S, Tuple<T, S>> Return<S, T>(T x)
{
    return s => Tuple.Create(x, s);
}

You can also implement the standard Get, Put, and Modify functions, but we are not going to need them here. Try it as an exercise.

State-valued event handlers #

The IShippingState methods almost look like State values, but the arguments are in the wrong order. A State value is a function that takes state as input and returns a tuple. The methods on IShippingState, however, take orderId as input and return a tuple. The state is also present, but as the instance that exposes the methods. We have to flip the arguments:

public static Func<IShippingState, Tuple<ShippingStateResult, IShippingState>> Billed(
    this string orderId)
{
    return s => s.OrderBilled(orderId);
}
 
public static Func<IShippingState, Tuple<ShippingStateResult, IShippingState>> Placed(
    this string orderId)
{
    return s => s.OrderPlaced(orderId);
}

This is a typical example of how you have to turn things on their heads in functional programming, compared to object-oriented programming. These two methods convert OrderBilled and OrderPlaced to State monad values.

Testing state results #

A unit test demonstrates how this enables you to compose multiple stateful operations using query syntax:

[Theory]
[InlineData("90125")]
[InlineData("quux")]
public void StateResultExample(string orderId)
{
    var sf = from x in orderId.Placed()
             from y in orderId.Billed()
             select new[] { x, y };
 
    var (results, finalState) = sf(InitialShippingState.Instance);
 
    Assert.Equal(
        new[] { false, true },
        results.Select(r => r.CompleteSaga));
    Assert.Single(
        results
            .SelectMany(r => r.Commands)
            .OfType<ShipOrder>()
            .Select(msg => msg.OrderId),
        orderId);
    Assert.Equal(CompletedShippingState.Instance, finalState);
}

Keep in mind that a State monad value is a function. That's the reason I called the composition sf - for State Function. When you execute it with InitialShippingState as input it returns a tuple that the test immediately pattern matches (destructures) into its constituent elements.

The test then asserts that the results and finalState are as expected. The assertions against results are a bit awkward, since C# collections don't have structural equality. These assertions would have been simpler in F# or Haskell.

Testing with an interpreter #

While the Arrange and Act phases of the above test are simple, the Assertion phase seems awkward. Another testing strategy is to run a test-specific interpreter over the instructions returned as the State computation result:

[Theory]
[InlineData("1984")]
[InlineData("quuz")]
public void StateInterpretationExample(string orderId)
{
    var sf = from x in orderId.Placed()
             from y in orderId.Billed()
             select new[] { x, y };
 
    var (results, finalState) = sf(InitialShippingState.Instance);
 
    Assert.Equal(CompletedShippingState.Instance, finalState);
    var result = Interpret(results);
    Assert.True(result.CompleteSaga);
    Assert.Single(
        result.Commands.OfType<ShipOrder>().Select(msg => msg.OrderId),
        orderId);
}

It helps a little, but the assertions still have to work around the lack of structural equality of result.Commands.

Monoid #

The test-specific Interpret helper method is interesting in its own right, though:

private ShippingStateResult Interpret(IEnumerable<ShippingStateResult> results)
{
    var identity = new ShippingStateResult(Array.Empty<ICommand>(), false);
    ShippingStateResult Combine(ShippingStateResult x, ShippingStateResult y)
    {
        return new ShippingStateResult(
            x.Commands.Concat(y.Commands).ToArray(),
            x.CompleteSaga || y.CompleteSaga);
    }
    return results.Aggregate(identity, Combine);
}

It wasn't until I started implementing this helper method that I realised that ShippingStateResult gives rise to a monoid! Since monoids accumulate, you can start with the identity and use the binary operation (here called Combine) to Aggregate an arbitrary number of ShippingStateResult values into one.

The ShippingStateResult class is composed of two constituent values (a collection and a Boolean value), and since both of these give rise to one or more monoids, a tuple of those monoids itself gives rise to one or more monoids. The ShippingStateResult is isomorphic to a tuple, so this result carries over.

Should you move the Combine method and the identity value to the ShippingStateResult class itself. After all, putting them in a test-specific helper method smells a bit of Feature Envy.

This seems compelling, but it's not clear that arbitrary client code might need this particular monoid. After all, there are four monoids over Boolean values, and at least two over collections. That's eight possible combinations. Which one should ShippingStateResult expose as members?

The monoid used in Interpret combines the normal collection monoid with the any monoid. That seems appropriate in this case, but other clients might rather need the all monoid.

Without more usage examples, I decided to leave the code as an Interpret implementation detail for now.

In any case, I find it worth noting that by decoupling the state logic from the NServiceBus framework, it's possible to test it without running asynchronous workflows.

Conclusion #

In this article you saw how to implement an asynchronous messaging saga in three different ways. First, as a simple ad-hoc solution, second using the State pattern, and third implemented with the State monad. Both the State pattern and State monad implementations are meant exclusively to showcase these two techniques. The first solution using two Boolean flags is by far the simplest solution, and the one I'd use in a production system.

The point is that you can use the State monad if you need to write stateful computations. This may include finite state machines, as otherwise addressed by the State design pattern, but could also include other algorithms where you need to keep track of state.

Next: Postel's law as a profunctor.

On the net value of process and code quality.

Once upon a time there was a software company that had a special way of doing things. No other company had ever done things quite like that before, but the company had much success. In short time it rose to dominance in the market, outcompeting all serious competition. Some people disliked the company because of its business tactics and sheer size, but others admired it.

Even more wanted to be like it.

How did the company achieve its indisputable success? It looked as though it was really, really good at making software. How did they write such good software?

It turned out that the company had a special software development process.

Other software organisations, hoping to be able to be as successful, tried to copy the special process. The company was willing to share. Its employees wrote about the process. They gave conference presentations on their special sauce.

Which company do I have in mind, and what was the trick that made it so much better than its competition? Was it microservices? Monorepos? Kubernetes? DevOps? Serverless?

No, the company was Microsoft and the development process was called Microsoft Solutions Framework (MSF).

What?! do you say.

You've never heard of MSF?

That's hardly surprising. I doubt that MSF was in any way related to Microsoft's success.

Net profits #

These days, many people in technology consider Microsoft an embarrassing dinosaur. While you know that it's still around, does it really matter, these days?

You can't deny, however, that Microsoft made a lot of money in the Nineties. They still do.

What's the key to making a lot of money? Have a revenue larger than your costs.

I'm too lazy to look up the actual numbers, but clearly Microsoft had (and still has) a revenue vastly larger than its costs:

Compared to real, historic numbers, this may be exaggerated, but I'm trying to make a general point - not one that hinges on actual profit numbers of Microsoft, Apple, Amazon, Google, or any other tremendously profitable company. I'm also aware that real companies have costs that aren't directly related to software development: Marketing, operations, buildings, sales, etcetera. They also make money in other ways than from their software, mainly from investments of the profits.

The difference between the revenue and the cost is the profit or net value.

If the graph looks like the above, is managing cost the main cause of success? Hardly. The cost is almost a rounding error on the profits.

If so, is the technology or process key to such a company's success? Was it MSF that made Microsoft the wealthiest company in the world? Are two-pizza teams the only explanation of Amazon's success? Is Google the dominant search engine because the source code is organised in a monorepo?

I'd be surprised were that the case. Rather, I think that these companies were at the right place at the right time. While there were search engines before Google, Google was so much better that users quickly migrated. Google was also better at making money than earlier search engines like AltaVista or Yahoo! Likewise, Microsoft made more successful PC operating systems than the competition (which in the early Windows era consisted exclusively of OS/2) and better professional software (word processor, spreadsheet, etcetera). Amazon made a large-scale international web shop before anyone else. Apple made affordable computers with graphical user interfaces before other companies. Later, they introduced a smartphone at the right time.

All of this is simplified. For example, it's not really true that Apple made the first smartphone. When the iPhone was introduced, I already carried a Pocket PC Phone Edition device that could browse the internet, had email, phone, SMS, and so on. There were other precursors even earlier.

I'm not trying to explain away excellence of execution. These companies succeeded for a variety of reasons, including that they were good at what they were doing. Lots of companies, however, are good at what they are doing, and still they fail. Being at the right place at the right time matters. Once in a while, a company finds itself in such favourable circumstances that success is served on a silver platter. While good execution is important, it doesn't explain the magnitude of the success.

Bad execution is likely to eliminate you in the long run, but it doesn't follow logically that good execution guarantees success.

Perhaps the successful companies succeeded because of circumstances, and despite mediocre execution. As usual, you should be wary not to mistake correlation for causation.

Legacy code #

You should be sceptical of adopting processes or technology just because a Big Tech company uses it. Still, if that was all I had in mind, I could probably had said that shorter. I have another point to make.

I often encounter resistance to ideas about better software development on the grounds that the status quo is good enough. Put bluntly,

""legacy," [...] is condescending-engineer-speak for "actually makes money.""

To be clear, I have nothing against the author or the cited article, which discusses something (right-sizing VMs) that I know nothing about. The phrase, or variations thereof, however, is such a fit meme that it spreads. It strongly indicates that people who discuss code quality are wankers, while 'real programmers' produce code that makes money. I consider that a false dichotomy.

Most software organisations aren't in the fortunate situation that revenues are orders of magnitude greater than costs. Most software organisations can make a decent profit if they find a market and execute on a good idea. Perhaps the revenue starts at 'only' double the cost.

If you can consistently make the double of your costs, you'll be in business for a long time. As the above line chart indicates, however, is that if the costs rise faster than the revenue, you'll eventually hit a point when you start losing money.

The Big Tech companies aren't likely to run into that situation because their profit margins are so great, but normal companies are very much at risk.

The area between the revenue and the cost represents the profit. Thus, looking back, it may be true that a software system has been making money. This doesn't mean, however, that it will keep making money.

In the above chart, the cost eventually exceeds the revenue. If this cost is mainly driven by rising software development costs, then the company is in deep trouble.

I've worked with such a company. When I started with it, it was a thriving company with many employees, most of them developers or IT professionals. In the previous decade, it had turned a nice profit every year.

This all started to change around the time that I arrived. (I will, again, remind the reader that correlation does not imply causation.) One reason I was engaged was that the developers were stuck. Due to external market pressures they had to deliver a tremendous amount of new features, and they were stuck in analysis paralysis.

I helped them get unstuck, but as we started working on the new features, we discovered the size of the mess of the legacy code base.

I recall a conversation I later had with the CEO. He told me, after having discussed the situation with several key people: "I knew that we had a legacy code base... but I didn't know it was this bad!"

Revenue remained constant, but costs kept rising. Today, the company is no longer around.

This was a 100% digital service company. All revenue was ultimately based on software. The business idea was good, but the company couldn't keep up with competitors. As far as I can tell, it was undone by its legacy code base.

Conclusion #

Software should provide some kind of value. Usually profits, but sometimes savings, and occasionally wider concerns are in scope. It's reasonable and professional to consider value as you produce software. You should, however, be aware of a too myopic focus on immediate and past value.

Finding safety in past value is indulging in complacency. Legacy software can make money from day one, but that doesn't mean that it'll keep making money. The main problem with legacy code is that costs keep rising. When non-technical business stakeholders start to notice this, it may be too late.

The is one of many reasons I believe that we, software developers, have a responsibility to combat the mess. I don't think there's anything condescending about that attitude.

A C# example.

This article is one of the examples that I promised in the earlier article The State pattern and the State monad. That article examines the relationship between the State design pattern and the State monad. That article is deliberately abstract, so one or more examples are in order.

In this article, I show you how to start with the example from Design Patterns and refactor it to an immutable solution using pure functions.

The code shown here is available on GitHub.

TCP connection #

The example is a class that handles TCP connections. The book's example is in C++, while I'll show my C# interpretation.

A TCP connection can be in one of several states, so the TcpConnection class keeps an instance of the polymorphic TcpState, which implements the state and transitions between them.

TcpConnection plays the role of the State pattern's Context, and TcpState of the State.

public class TcpConnection
{
    public TcpState State { get; internal set; }
 
    public TcpConnection()
    {
        State = TcpClosed.Instance;
    }
 
    public void ActiveOpen()
    {
        State.ActiveOpen(this);
    }
 
    public void PassiveOpen()
    {
        State.PassiveOpen(this);
    }
 
    // More members that delegate to State follows...

The TcpConnection class' methods delegate to a corresponding method on TcpState, passing itself an argument. This gives the TcpState implementation an opportunity to change the TcpConnection's State property, which has an internal setter.

State #

This is the TcpState class:

public class TcpState
{
    public virtual void Transmit(TcpConnection connection, TcpOctetStream stream)
    {
    }
 
    public virtual void ActiveOpen(TcpConnection connection)
    {
    }
 
    public virtual void PassiveOpen(TcpConnection connection)
    {
    }
 
    public virtual void Close(TcpConnection connection)
    {
    }
 
    public virtual void Synchronize(TcpConnection connection)
    {
    }
 
    public virtual void Acknowledge(TcpConnection connection)
    {
    }
 
    public virtual void Send(TcpConnection connection)
    {
    }
}

I don't consider this entirely idiomatic C# code, but it seems closer to the book's C++ example. (It's been a couple of decades since I wrote C++, so I could be mistaken.) It doesn't matter in practice, but instead of a concrete class with no-op virtual methods, I would usually define an interface. I'll do that in the next example article.

The methods have the same names as the methods on TcpConnection, but the signatures are different. All the TcpState methods take a TcpConnection parameter, whereas the TcpConnection methods take no arguments.

While the TcpState methods don't do anything, various classes can inherit from the class and override some or all of them.

Connection closed #

The book shows implementations of three classes that inherit from TcpState, starting with TcpClosed. Here's my translation to C#:

public class TcpClosed : TcpState
{
    public static TcpState Instance = new TcpClosed();
 
    private TcpClosed()
    {
    }
 
    public override void ActiveOpen(TcpConnection connection)
    {
        // Send SYN, receive SYN, Ack, etc.
 
        connection.State = TcpEstablished.Instance;
    }
 
    public override void PassiveOpen(TcpConnection connection)
    {
        connection.State = TcpListen.Instance;
    }
}

This implementation overrides ActiveOpen and PassiveOpen. In both cases, after performing some work, they change connection.State.

"TCPState subclasses maintain no local state, so they can be shared, and only one instance of each is required. The unique instance of TCPState subclass is obtained by the static Instance operation. [...]

"This make each TCPState subclass a Singleton [...]."

I've maintained that property of each subclass in my C# code, even though it has no impact on the structure of the State pattern.

The other subclasses #

The next subclass, TcpEstablished, is cast in the same mould:

public class TcpEstablished : TcpState
{
    public static TcpState Instance = new TcpEstablished();
 
    private TcpEstablished()
    {
    }
 
    public override void Close(TcpConnection connection)
    {
        // send FIN, receive ACK of FIN
 
        connection.State = TcpListen.Instance;
    }
 
    public override void Transmit(
        TcpConnection connection,
        TcpOctetStream stream)
    {
        connection.ProcessOctet(stream);
    }
}

As is TcpListen:

public class TcpListen : TcpState
{
    public static TcpState Instance = new TcpListen();
 
    private TcpListen()
    {
    }
 
    public override void Send(TcpConnection connection)
    {
        // Send SYN, receive SYN, ACK, etc.
 
        connection.State = TcpEstablished.Instance;
    }
}

I admit that I find these examples a bit anaemic, since there's really no logic going on. None of the overrides change state conditionally, which would be possible and make the examples a little more interesting. If you're interested in an example where this happens, see my article Tennis kata using the State pattern.

Refactor to pure functions #

There's only one obvious source of impurity in the example: The literal State mutation of TcpConnection:

public TcpState State { get; internal set; }

While client code can't set the State property, subclasses can, and they do. After all, it's how the State pattern works.

It's quite a stretch to claim that if we can only get rid of that property setter then all else will be pure. After all, who knows what all those comments actually imply:

// Send SYN, receive SYN, ACK, etc.

To be honest, we must imagine that I/O takes place here. This means that even though it's possible to refactor away from mutating the State property, these implementations are not really going to be pure functions.

I could try to imagine what that SYN and ACK would look like, but it would be unfounded and hypothetical. I'm not going to do that here. Instead, that's the reason I'm going to publish a second article with a more realistic and complex example. When it comes to the present example, I'm going to proceed with the unreasonable assumption that the comments hide no nondeterministic behaviour or side effects.

As outlined in the article that compares the State pattern and the State monad, you can refactor state mutation to a pure function by instead returning the new state. Usually, you'd have to return a tuple, because you'd also need to return the 'original' return value. Here, however, the 'return type' of all methods is void, so this isn't necessary.

void is isomorphic to unit, so strictly speaking you could refactor to a return type like Tuple<Unit, TcpConnection>, but that is isomorphic to TcpConnection. (If you need to understand why that is, try writing two functions: One that converts a Tuple<Unit, TcpConnection> to a TcpConnection, and another that converts a TcpConnection to a Tuple<Unit, TcpConnection>.)

There's no reason to make things more complicated than they have to be, so I'm going to use the simplest representation: TcpConnection. Thus, you can get rid of the State mutation by instead returning a new TcpConnection from all methods:

public class TcpConnection
{
    public TcpState State { get; }
 
    public TcpConnection()
    {
        State = TcpClosed.Instance;
    }
 
    private TcpConnection(TcpState state)
    {
        State = state;
    }
 
    public TcpConnection ActiveOpen()
    {
        return new TcpConnection(State.ActiveOpen(this));
    }
 
    public TcpConnection PassiveOpen()
    {
        return new TcpConnection(State.PassiveOpen(this));
    }
 
    // More members that delegate to State follows...

The State property no longer has a setter; there's only a public getter. In order to 'change' the state, code must return a new TcpConnection object with the new state. To facilitate that, you'll need to add a constructor overload that takes the new state as an input. Here I made it private, but making it more accessible is not prohibited.

This implies, however, that the TcpState methods also return values instead of mutating state. The base class now looks like this:

public class TcpState
{
    public virtual TcpState Transmit(TcpConnection connection, TcpOctetStream stream)
    {
        return this;
    }
 
    public virtual TcpState ActiveOpen(TcpConnection connection)
    {
        return this;
    }
 
    public virtual TcpState PassiveOpen(TcpConnection connection)
    {
        return this;
    }
 
    // And so on...

Again, all the methods previously 'returned' void, so while, according to the State monad, you should strictly speaking return Tuple<Unit, TcpState>, this simplifies to TcpState.

Individual subclasses now do their work and return other TcpState implementations. I'm not going to tire you with all the example subclasses, so here's just TcpEstablished:

public class TcpEstablished : TcpState
{
    public static TcpState Instance = new TcpEstablished();
 
    private TcpEstablished()
    {
    }
 
    public override TcpState Close(TcpConnection connection)
    {
        // send FIN, receive ACK of FIN
 
        return TcpListen.Instance;
    }
 
    public override TcpState Transmit(
        TcpConnection connection,
        TcpOctetStream stream)
    {
        TcpConnection newConnection = connection.ProcessOctet(stream);
        return newConnection.State;
    }
}

The trickiest implementation is Transmit, since ProcessOctet returns a TcpConnection while the Transmit method has to return a TcpState. Fortunately, the Transmit method can achieve that goal by returning newConnection.State. It feels a bit roundabout, but highlights a point I made in the previous article: The TcpConnection and TcpState classes are isomorphic - or, they would be if we made the TcpConnection constructor overload public. Thus, the TcpConnection class is redundant and might be deleted.

Conclusion #

This article shows how to refactor the TCP connection sample code from Design Patterns to pure functions.

If it feels as though something's missing there's a good reason for that. The example, as given, is degenerate because all methods 'return' void, and we don't really know what the actual implementation code (all that Send SYN, receive SYN, ACK, etc.) looks like. This means that we actually don't have to make use of the State monad, because we can get away with endomorphisms. All methods on TcpConnection are really functions that take TcpConnection as input (the instance itself) and return TcpConnection. If you want to see a more realistic example showcasing that perspective, see my article From State tennis to endomorphism.

Even though the example is degenerate, I wanted to show it because otherwise you might wonder how the book's example code fares when exposed to the State monad. To be clear, because of the nature of the example, the State monad never becomes necessary. Thus, we need a second example.

Next: Refactoring a saga from the State pattern to the State monad.

FAQ: How do I convince my manager to let me refactor?

This question frequently comes up. Developers want to refactor, but are under the impression that managers or other stakeholders will not let them.

Sometimes people ask me how to convince their managers to get permission to refactor. I can't answer that. I don't know how to convince other people. That's not my métier.

I also believe that professional programmers should make their own decisions. You don't ask permission to add three lines to a file, or create a new class. Why do you feel that you have to ask permission to refactor?

Does refactoring take time? #

In Code That Fits in Your Head I tell the following story:

"I once led an effort to refactor towards deeper insight. My colleague and I had identified that the key to implementing a new feature would require changing a fundamental class in our code base.

"While such an insight rarely arrives at an opportune time, we wanted to make the change, and our manager allowed it.

"A week later, our code still didn’t compile.

"I’d hoped that I could make the change to the class in question and then lean on the compiler to identify the call sites that needed modification. The problem was that there was an abundance of compilation errors, and fixing them wasn’t a simple question of search-and-replace.

"My manager finally took me aside to let me know that he wasn’t satisfied with the situation. I could only concur.

"After a mild dressing down, he allowed me to continue the work, and a few more days of heroic effort saw the work completed.

"That’s a failure I don’t intend to repeat."

There's a couple of points to this story. Yes, I did ask for permission before refactoring. I expected the process to take time, and I felt that making such a choice of prioritisation should involve my manager. While this manager trusted me, I felt a moral obligation to be transparent about the work I was doing. I didn't consider it professional to take a week out of the calendar and work on one thing while the rest of the organisation was expecting me to be working on something else.

So I can understand why developers feel that they have to ask permission to refactor. After all, refactoring takes time... Doesn't it?

Small steps #

This may unearth the underlying assumption that prevents developers from refactoring: The notion that refactoring takes time.

As I wrote in Code That Fits in Your Head, that was a failure I didn't intend to repeat. I've never again asked permission to refactor, because I've never since allowed myself to be in a situation where refactoring would take significant time.

The reason I tell the story in the book is that I use it to motivate using the Strangler pattern at the code level. The book proceeds to show an example of that.

Migrating code to a new API by allowing the old and the new to coexist for a while is only one of many techniques for taking smaller steps. Another is the use of feature flags, a technique that I also show in the book. Martin Fowler's Refactoring is literally an entire book about how to improve code bases in small, controlled steps.

Follow the red-green-refactor checklist and commit after each green and refactor step. Move in small steps and use Git tactically.

I'm beginning to realise, though, that moving in small steps is a skill that must be explicitly learned. This may seem obvious once posited, but it may also be helpful to explicitly state it.

Whenever I've had a chance to talk to other software professionals and thought leaders, they agree. As far as I can tell, universities and coding boot camps don't teach this skill, and if (like me) you're autodidact, you probably haven't learned it either. After all, few people insist that this is an important skill. It may, however, be one of the most important programming skills you can learn.

Make it work, then make it right #

When should you refactor? As the boy scout rule suggests: All the time.

You can, specifically, do it after implementing a new feature. As Kent Beck perhaps said or wrote: Make it work, then make it right.

How long does it take to make it right?

Perhaps you think that it takes as much time as it does to make it work.

Perhaps you think that making it right takes even more time.

If this is how much time making the code right takes, I can understand why you feel that you need to ask your manager. That's what I did, those many years ago. But what if the proportions are more like this?

Do you still feel that you need to ask for permission to refactor?

Writing code so that the team can keep a sustainable pace is your job. It's not something you should have to ask for permission to do.

"Any fool can write code that a computer can understand. Good programmers write code that humans can understand."

Making the code right is not always a huge endeavour. It can be, if you've already made a mess of it, but if it's in good condition, keeping it that way doesn't have to take much extra effort. It's part of the ongoing design process that programming is.

How do you know what right is? Doesn't this make-it-work-make-it-right mentality lead to speculative generality?

No-one expects you to be able to predict the future, so don't try. Making it right means making the code good in the current context. Use good names, remove duplication, get rid of code smells, keep methods small and complexity low. Refactor if you exceed a threshold.

Make code easy to change #

The purpose of keeping code in a good condition is to make future changes as easy as possible. If you can't predict the future, however, then how do you know how to factor the code?

Another Kent Beck aphorism suggests a tactic:

"for each desired change, make the change easy (warning: this may be hard), then make the easy change"

In other words, when you know what you need to accomplish, first refactor the code so that it becomes easier to achieve the goal, and only then write the code to do that.

Should you ask permission to refactor in such a case? Only if you sincerely believe that you can complete the entire task significantly faster without first improving the code. How likely is that? If the code base is already a mess, how easy is it to make changes? Not easy, and granted: That will also be true for refactoring. The difference between first refactoring and not refactoring, however, is that if you refactor, you leave the code in a better state. If you don't, you leave it in a worse state.

These decisions compound.

But what if, as Kent Beck implies, refactoring is hard? Then the situation might look like this:

Should you ask for permission to refactor? I don't think so. While refactoring in this diagram is most of the work, it makes the change easy. Thus, once you're done refactoring, you make the easy change. The total amount of time this takes may turn out to be quicker than if you hadn't refactored (compare this figure to the previous figure: they're to scale). You also leave the code base in a better state so that future changes may be easier.

Conclusion #

There are lots of opportunities for refactoring. Every time you see something that could be improved, why not improve it? The fact that you're already looking at a piece of code suggests that it's somehow relevant to your current task. If it takes ten, fifteen minutes to improve it, why not do it? What if it takes an hour?

Most people think nothing of spending hours in meetings without asking their managers. If this is true, you can also decide to use a couple of hours improving code. They're likely as well spent as the meeting hours.

The key, however, is to be able to perform opportunistic refactoring. You can't do that if you can only move in day-long iterations; if hours, or days, go by when you can't compile, or when most tests fail.

On the other hand, if you're able to incrementally improve the code base in one-minute, or fifteen-minute, steps, then you can improve the code base every time an occasion arrives.

This is a skill that you need to learn. You're not born with the ability to improve in small steps. You'll have to practice - for example by doing katas. One customer of mine told me that they found Kent Beck's TCR a great way to teach that skill.

You can refactor in small steps. It's part of software engineering. Usually, you don't need to ask for permission.

Comments

Refactoring to a universal abstraction.

Despite my best efforts, no code base I write is perfect. This is also true for the code base that accompanies Code That Fits in Your Head.

One (among several) warts that has annoyed me for long is this:

[HttpPost("restaurants/{restaurantId}/reservations")]
public async Task<ActionResult> Post(
    int restaurantId,
    ReservationDto dto)
{
    if (dto is null)
        throw new ArgumentNullException(nameof(dto));
 
    var id = dto.ParseId() ?? Guid.NewGuid();
    Reservation? reservation = dto.Validate(id);
    if (reservation is null)
        return new BadRequestResult();
 
    // More code follows...

Passing id to Validate annoys me. Why does Validate need an id?

When you see it in context, it may makes some sort of sense, but in isolation, it seems arbitrary:

internal Reservation? Validate(Guid id)

Why does the method need an id? Doesn't ReservationDto have an Id?

Abstraction, broken #

Yes, indeed, ReservationDto has an Id property:

public string? Id { get; set; }

Then why do callers have to pass an id argument? Doesn't Validate use the Id property? It's almost as though the Validate method begs you to read the implementing code:

internal Reservation? Validate(Guid id)
{
    if (!DateTime.TryParse(At, out var d))
        return null;
    if (Email is null)
        return null;
    if (Quantity < 1)
        return null;
 
    return new Reservation(
        id,
        d,
        new Email(Email),
        new Name(Name ?? ""),
        Quantity);
}

Indeed, the method doesn't use the Id property. Reading the code may not be of much help, but at least we learn that id is passed to the Reservation constructor. It's still not clear why the method isn't trying to parse the Id property, like it's doing with At.

I'll return to the motivation in a moment, but first I'd like to dwell on the problems of this design.

It's a typical example of ad-hoc design. I had a set of behaviours I needed to implement, and in order to avoid code duplication, I came up with a method that seemed to solve the problem.

And indeed, the Validate method does solve the problem of code duplication. It also passes all tests. It could be worse.

It could also be better.

The problem with an ad-hoc design like this is that the motivation is unclear. As a reader, you feel that you're missing the full picture. Perhaps you feel compelled to read the implementation code to gain a better understanding. Perhaps you look for other call sites. Perhaps you search the Git history to find a helpful comment. Perhaps you ask a colleague.

It slows you down. Worst of all, it may leave you apprehensive of refactoring. If you feel that there's something you don't fully understand, you may decide to leave the API alone, instead of improving it.

It's one of the many ways that code slowly rots.

What's missing here is a proper abstraction.

Motivation #

I recently hit upon a design that I like better. Before I describe it, however, you need to understand the problem I was trying to solve.

The code base for the book is a restaurant reservation REST API, and I was evolving the code as I wrote it. I wanted the code base (and its Git history) to be as realistic as possible. In a real-world situation, you don't always know all requirements up front, or even if you do, they may change.

At one point I decided that a REST client could supply a GUID when making a new reservation. On the other hand, I had lots of existing tests (and a deployed system) that accepted reservations without IDs. In order to not break compatibility, I decided to use the ID if it was supplied with the DTO, and otherwise create one. (I later explored an API without explicit IDs, but that's a different story.)

The id is a JSON property, however, so there's no guarantee that it's properly formatted. Thus, the need to first parse it:

var id = dto.ParseId() ?? Guid.NewGuid();

To make matters even more complicated, when you PUT a reservation, the ID is actually part of the resource address, which means that even if it's present in the JSON document, that value should be ignored:

[HttpPut("restaurants/{restaurantId}/reservations/{id}")]
public async Task<ActionResult> Put(
    int restaurantId,
    string id,
    ReservationDto dto)
{
    if (dto is null)
        throw new ArgumentNullException(nameof(dto));
    if (!Guid.TryParse(id, out var rid))
        return new NotFoundResult();
 
    Reservation? reservation = dto.Validate(rid);
    if (reservation is null)
        return new BadRequestResult();
 
    // More code follows...

Notice that this Put implementation exclusively considers the resource address id parameter. Recall that the Validate method ignores the dto's Id property.

This is knowledge about implementation details that leaks through to the calling code. As a client developer, you need to know and keep this knowledge in your head while you write your own code. That's not really code that fits in your head.

As I usually put it: If you have to read the code, it implies that encapsulation is broken.

At the time, however, I couldn't think of a better alternative, and since the problem is still fairly small and localised, I decided to move on. After all, perfect is the enemy of good.

Why don't you just..? #

Is there a better way? Perhaps you think that you've spotted an obvious improvement. Why don't I just try to parse dto.Id and then create a Guid.NewGuid() if parsing fails? Like this:

internal Reservation? Validate()
{
    if (!Guid.TryParse(Id, out var id))
        id = Guid.NewGuid();
    if (!DateTime.TryParse(At, out var d))
        return null;
    if (Email is null)
        return null;
    if (Quantity < 1)
        return null;
 
    return new Reservation(
        id,
        d,
        new Email(Email),
        new Name(Name ?? ""),
        Quantity);
}

The short answer is: Because it doesn't work.

It may work for Get, but then Put doesn't have a way to tell the Validate method which ID to use.

Or rather: That's not entirely true, because this is possible:

dto.Id = id;
Reservation? reservation = dto.Validate();

This does suggest an even better way. Before we go there, however, there's another reason I don't like this particular variation: It makes Validate impure.

Why care? you may ask.

I always end up regretting making an otherwise potentially pure function non-deterministic. Sooner or later, it turns out to have been a bad decision, regardless of how alluring it initially looked. I recently gave an example of that.

When weighing the advantages and disadvantages, I preferred passing id explicitly rather than relying on Guid.NewGuid() inside Validate.

First monoid #

One of the reasons I find universal abstractions beneficial is that you only have to learn them once. As Felienne Hermans writes in The Programmer's Brain our working memory juggles a combination of ephemeral data and knowledge from our long-term memory. The better you can leverage existing knowledge, the easier it is to read code.

Which universal abstraction enables you to choose from a prioritised list of candidates? The First monoid!

In C# with nullable reference types the null-coalescing operator ?? already implements the desired functionality. (If you're using another language or an older version of C#, you can instead use Maybe.)

Once I got that idea I was able to simplify the API.

Parsing and coalescing DTOs #

Instead of that odd Validate method which isn't quite a validator and not quite a parser, this insight suggests to parse, don't validate:

internal Reservation? TryParse()
{
    if (!Guid.TryParse(Id, out var id))
        return null;
    if (!DateTime.TryParse(At, out var d))
        return null;
    if (Email is null)
        return null;
    if (Quantity < 1)
        return null;
 
    return new Reservation(
        id,
        d,
        new Email(Email),
        new Name(Name ?? ""),
        Quantity);
}

This function only returns a parsed Reservation object when the Id is present and well-formed. What about the cases where the Id is absent?

The calling ReservationsController can deal with that:

Reservation? candidate1 = dto.TryParse();
dto.Id = Guid.NewGuid().ToString("N");
Reservation? candidate2 = dto.TryParse();
Reservation? reservation = candidate1 ?? candidate2;
if (reservation is null)
    return new BadRequestResult();

First try to parse the dto, then explicitly overwrite its Id property with a new Guid, and then try to parse it again. Finally, pick the first of these that aren't null, using the null-coalescing ?? operator.

This API also works consistently in the Put method:

dto.Id = id;
Reservation? reservation = dto.TryParse();
if (reservation is null)
    return new BadRequestResult();

Why is this better? I consider it better because the TryParse function should be a familiar abstraction. Once you've seen a couple of those, you know that a well-behaved parser either returns a valid object, or nothing. You don't have to go and read the implementation of TryParse to (correctly) guess that. Thus, encapsulation is maintained.

Where does mutation go? #

The ReservationsController mutates the dto and relies on the impure Guid.NewGuid() method. Why is that okay when it wasn't okay to do this inside of Validate?

This is because the code base follows the functional core, imperative shell architecture. Specifically, Controllers make up the imperative shell, so I consider it appropriate to put impure actions there. After all, they have to go somewhere.

This means that the TryParse function remains pure.

Conclusion #

Sometimes a good API design can elude you for a long time. When that happens, I move on with the best solution I can think of in the moment. As it often happens, though, ad-hoc abstractions leave me unsatisfied, so I'm always happy to improve such code later, if possible.

In this article, you saw an example of an ad-hoc API design that represented the best I could produce at the time. Later, it dawned on me that an implementation based on a universal abstraction would be possible. In this case, the universal abstraction was null coalescing (which is a specialisation of the monoid abstraction).

I like universal abstractions because, once you know them, you can trust that they work in well-understood ways. You don't have to waste time reading implementation code in order to learn whether it's safe to call a method in a particular way.

This saves time when you have to work with the code, because, after all, we spend more time reading code than writing it.

Comments

The names are the same. Is there a connection? An article for object-oriented programmers.

This article is part of a series of articles about specific design patterns and their category theory counterparts. In this article I compare the State design pattern to the State monad.

Since the design pattern and the monad share the name State you'd think that they might be isomorphic, but it's not quite that easy. I find it more likely that the name is an example of parallel evolution. Monads were discovered by Eugenio Moggi in the early nineties, and Design Patterns is from 1994. That's close enough in time that I find it more likely that whoever came up with the names found them independently. State, after all, is hardly an exotic word.

Thus, it's possible that the choice of the same name is coincidental. If this is true (which is only my conjecture), does the State pattern have anything in common with the State monad? I find that the answer is a tentative yes. The State design pattern describes an open polymorphic stateful computation. That kind of computation can also be described with the State monad.

This article contains a significant amount of code, and it's all quite abstract. It examines the abstract shape of the pattern, so there's little prior intuition on which to build an understanding. While later articles will show more concrete examples, if you want to follow along, you can use the GitHub repository.

Shape #

Design Patterns is a little vague when it comes to representing the essential form of the pattern. What one can deduce from the diagram in the Structure section describing the pattern, you have an abstract State class with a Handle method like this:

public virtual void Handle(Context context)
{
}

This, however, doesn't capture all scenarios. What if you need to pass more arguments to the method? What if the method returns a result? What if there's more than one method?

Taking into account all those concerns, you might arrive at a more generalised description of the State pattern where an abstract State class might define methods like these:

public abstract Out1 Handle1(Context context, In1 in1);
 
public abstract Out2 Handle2(Context context, In2 in2);

There might be an arbitrary number of Handle methods, from Handle1 to HandleN, each with their own input and return types.

The idea behind the State pattern is that clients don't interact directly with State objects. Instead, they interact with a Context object that delegates operations to a State object, passing itself as an argument:

public Out1 Request1(In1 in1)
{
    return State.Handle1(this, in1);
}
 
public Out2 Request2(In2 in2)
{
    return State.Handle2(this, in2);
}

Classes that derive from the abstract State may then mutate context.State.

public override Out2 Handle2(Context context, In2 in2)
{
    if (in2 == In2.Epsilon)
        context.State = new ConcreteStateB();
 
    return Out2.Eta;
}

Clients interact with the Context object and aren't aware of this internal machinery:

var actual = ctx.Request2(in2);

With such state mutation going on, is it possible to refactor to a design that uses immutable data and pure functions?

State pair #

When you have a void method that mutates state, you can refactor it to a pure function by leaving the existing state unchanged and instead returning the new state. What do you do, however, when the method in question already returns a value?

This is the case with the generalised HandleN methods, above.

One way to resolve this problem is to introduce a more complex type to return. To avoid too much duplication or boilerplate code, you could make it a generic type:

public sealed class StatePair<T>
{
    public StatePair(T value, State state)
    {
        Value = value;
        State = state;
    }
 
    public T Value { get; }
    public State State { get; }
 
    public override bool Equals(object obj)
    {
        return obj is StatePair<T> result &&
               EqualityComparer<T>.Default.Equals(Value, result.Value) &&
               EqualityComparer<State>.Default.Equals(State, result.State);
    }
 
    public override int GetHashCode()
    {
        return HashCode.Combine(Value, State);
    }
}

This enables you to change the signatures of the Handle methods:

public abstract StatePair<Out1> Handle1(Context context, In1 in1);
 
public abstract StatePair<Out2> Handle2(Context context, In2 in2);

This refactoring is always possible. Even if the original return type of a method was void, you can use a unit type as a replacement for void. While redundant but consistent, a method could return StatePair<Unit>.

Generic pair #

The above StatePair type is so coupled to a particular State class that it's not reusable. If you had more than one implementation of the State pattern in your code base, you'd have to duplicate that effort. That seems wasteful, so why not make the type generic in the state dimension as well?

public sealed class StatePair<TState, T>
{
    public StatePair(T value, TState state)
    {
        Value = value;
        State = state;
    }
 
    public T Value { get; }
    public TState State { get; }
 
    public override bool Equals(object obj)
    {
        return obj is StatePair<TState, T> pair &&
               EqualityComparer<T>.Default.Equals(Value, pair.Value) &&
               EqualityComparer<TState>.Default.Equals(State, pair.State);
    }
 
    public override int GetHashCode()
    {
        return HashCode.Combine(Value, State);
    }
}

When you do that then clearly you'd also need to modify the Handle methods accordingly:

public abstract StatePair<State, Out1> Handle1(Context context, In1 in1);
 
public abstract StatePair<State, Out2> Handle2(Context context, In2 in2);

Notice that, as is the case with the State functor, the type declares the type with TState before T, while the constructor takes T before TState. While odd and potentially confusing, I've done this to stay consistent with my previous articles, which again do this to stay consistent with prior art (mainly Haskell).

With StatePair you can make the methods pure.

Pure functions #

Since Handle methods can now return a new state instead of mutating objects, they can be pure functions. Here's an example:

public override StatePair<State, Out2> Handle2(Context context, In2 in2)
{
    if (in2 == In2.Epsilon)
        return new StatePair<State, Out2>(Out2.Eta, new ConcreteStateB());
 
    return new StatePair<State, Out2>(Out2.Eta, this);
}

The same is true for Context:

public StatePair<Context, Out1> Request1(In1 in1)
{
    var pair = State.Handle1(this, in1);
    return new StatePair<Context, Out1>(pair.Value, new Context(pair.State));
}
 
public StatePair<Context, Out2> Request2(In2 in2)
{
    var pair = State.Handle2(this, in2);
    return new StatePair<Context, Out2>(pair.Value, new Context(pair.State));
}

Does this begin to look familiar?

Monad #

The StatePair class is nothing but a glorified tuple. Armed with that knowledge, you can introduce a variation of the IState interface I used to introduce the State functor:

public interface IState<TState, T>
{
    StatePair<TState, T> Run(TState state);
}

This variation uses the explicit StatePair class as the return type of Run, rather than a more anonymous tuple. These representations are isomorphic. (That might be a good exercise: Write functions that convert from one to the other, and vice versa.)

You can write the usual Select and SelectMany implementations to make IState a functor and monad. Since I have already shown these in previous articles, I'm also going to skip those. (Again, it might be a good exercise to implement them if you're in doubt of how they work.)

You can now, for example, use C# query syntax to run the same computation multiple times:

IState<Context, (Out1 a, Out1 b)> s =
    from a in in1.Request1()
    from b in in1.Request1()
    select (a, b);
StatePair<Context, (Out1 a, Out1 b)> t = s.Run(ctx);

This example calls Request1 twice, and collects both return values in a tuple. Running the computation with a Context will produce both a result (the two outputs a and b) as well as the 'current' Context (state).

Request1 is a State-valued extension method on In1:

public static IState<Context, Out1> Request1(this In1 in1)
{
    return
        from ctx in Get<Context>()
        let p = ctx.Request1(in1)
        from _ in Put(p.State)
        select p.Value;
}

Notice the abstraction level in play. This extension method doesn't return a StatePair, but rather an IState computation, defined by using the State monad's Get and Put functions. Since the computation is running with a Context state, the computation can Get a ctx object and call its Request1 method. This method returns a pair p. The computation can then Put the pair's State (here, a Context object) and return the pair's Value.

This stateful computation is composed from the building blocks of the State monad, including query syntax supported by SelectMany, Get, and Put.

This does, however, still feel unsatisfactory. After all, you have to know enough of the details of the State monad to know that ctx.Request1 returns a pair of which you must remember to Put the State. Would it be possible to also express the underlying Handle methods as stateful computations?

StatePair bifunctor #

The StatePair class is isomorphic to a pair (a two-tuple), and we know that a pair gives rise to a bifunctor:

public StatePair<TState1, T1> SelectBoth<TState1, T1>(
    Func<T, T1> selectValue,
    Func<TState, TState1> selectState)
{
    return new StatePair<TState1, T1>(
        selectValue(Value),
        selectState(State));
}

You can use SelectBoth to implement both Select and SelectState. In the following we're only going to need SelectState:

public StatePair<TState1, T> SelectState<TState1>(Func<TState, TState1> selectState)
{
    return SelectBoth(x => x, selectState);
}

This enables us to slightly simplify the Context methods:

public StatePair<Context, Out1> Request1(In1 in1)
{
    return State.Handle1(this, in1).SelectState(s => new Context(s));
}
 
public StatePair<Context, Out2> Request2(In2 in2)
{
    return State.Handle2(this, in2).SelectState(s => new Context(s));
}

Keep in mind that Handle1 returns a StatePair<State, Out1>, Handle2 returns StatePair<State, Out2>, and so on. While Request1 calls Handle1, it must return a StatePair<Context, Out1> rather than a StatePair<State, Out1>. Since StatePair is a bifunctor, the Request1 method can use SelectState to map the State to a Context.

Unfortunately, this doesn't seem to move us much closer to being able to express the underlying functions as stateful computations. It does, however, set up the code so that the next change is a little easier to follow.

State computations #

Is it possible to express the Handle methods on State as IState computations? One option is to write another extension method:

public static IState<State, Out1> Request1S(this In1 in1)
{
    return
        from s in Get<State>()
        let ctx = new Context(s)
        let p = s.Handle1(ctx, in1)
        from _ in Put(p.State)
        select p.Value;
}

I had to add an S suffix to the name, since it only differs from the above Request1 extension method on its return type, and C# doesn't allow method overloading on return types.

You can add a similar Request2S extension method. It feels like boilerplate code, but enables us to express the Context methods in terms of running stateful computations:

public StatePair<Context, Out1> Request1(In1 in1)
{
    return in1.Request1S().Run(State).SelectState(s => new Context(s));
}
 
public StatePair<Context, Out2> Request2(In2 in2)
{
    return in2.Request2S().Run(State).SelectState(s => new Context(s));
}

This still isn't entirely satisfactory, since the return types of these Request methods are state pairs, and not IState values. The above Request1S function, however, contains a clue about how to proceed. Notice how it can create a Context object from the underlying State, and convert that Context object back to a State object. That's a generalizable idea.

Invariant functor #

While it's possible to map the TState dimension of the state pair, it seems harder to do it on IState<TState, T>. A tuple, after all, is covariant in both dimensions. The State monad, on the other hand, is neither co- nor contravariant in the state dimension. You can deduce this with positional variance analysis (which I've learned from Thinking with Types). In short, this is because TState appears as both input and output in StatePair<TState, T> Run(TState state) - it's neither co- nor contravariant, but rather invariant.

What little option is left us, then, is to make IState an invariant functor in the state dimension:

public static IState<TState1, T> SelectState<TState, TState1, T>(
    this IState<TState, T> state,
    Func<TState, TState1> forward,
    Func<TState1, TState> back)
{
    return
        from s1 in Get<TState1>()
        let s = back(s1)
        let p = state.Run(s)
        from _ in Put(forward(p.State))
        select p.Value;
}

Given an IState<TState, T> the SelectState function enables us to turn it into a IState<TState1, T>. This is, however, only possible if you can translate both forward and back between two representations. When we have two such translations, we can produce a new computation that runs in TState1 by first using Get to retrieve a TState1 value from the new environment, translate it back to TState, which enables the expression to Run the state. Then translate the resulting p.State forward and Put it. Finally, return the Value.

As Sandy Maguire explains:

"... an invariant type T allows you to map from a to b if and only if a and b are isomorphic. [...] an isomorphism between a and b means they're already the same thing to begin with."

This may seem limiting, but is enough in this case. The Context class is only a wrapper of a State object:

public Context(State state)
{
    State = state;
}
 
public State State { get; }

If you have a State object, you can create a Context object via the Context constructor. On the other hand, if you have a Context object, you can get the wrapped State object by reading the State property.

The first improvement this offers is simplification of the Request1 extension method:

public static IState<Context, Out1> Request1(this In1 in1)
{
    return in1.Request1S().SelectState(s => new Context(s), ctx => ctx.State);
}

Recall that Request1S returns a IState<State, Out1>. Since a two-way translation between State and Context exists, SelectState can translate IState<State, Out1> to IState<Context, Out1>.

The same applies to the equivalent Request2 extension method.

This, again, enables us to rewrite the Context methods:

public StatePair<Context, Out1> Request1(In1 in1)
{
    return in1.Request1().Run(this);
}
 
public StatePair<Context, Out2> Request2(In2 in2)
{
    return in2.Request2().Run(this);
}

While this may seem like an insignificant change, one result has been gained: This last refactoring pushed the Run call to the right. It's now clear that each expression is a stateful computation, and that the only role that the Request methods play is to Run the computations.

This illustrates that the Request methods can be decomposed into two decoupled steps:

1. A stateful computation expression
2. Running the expression

Eliminating the Context #

A reasonable next refactoring might be to remove the context parameter from each of the Handle methods. After all, this parameter is a remnant of the State design pattern. Its original purpose was to enable State implementers to mutate the context by changing its State.

After refactoring to immutable functions, the context parameter no longer needs to be there - for that reason. Do we need it for other reasons? Does it carry other information that a State implementer might need?

In the form that the code now has, it doesn't. Even if it did, we could consider moving that data to the other input parameter: In1, In2, etcetera.

Therefore, it seems sensible to remove the context parameter from the State methods:

public abstract StatePair<State, Out1> Handle1(In1 in1);
 
public abstract StatePair<State, Out2> Handle2(In2 in2);

This also means that a function like Request1S becomes simpler:

public static IState<State, Out1> Request1S(this In1 in1)
{
    return
        from s in Get<State>()
        let p = s.Handle1(in1)
        from _ in Put(p.State)
        select p.Value;
}

Since Context and State are isomorphic, you can rewrite all callers of Context to instead use State, like the above example:

IState<State, (Out1 a, Out1 b)> s =
    from a in in1.Request1()
    from b in in1.Request1()
    select (a, b);
var t = s.Run(csa);

Do this consistently, and you can eventually delete the Context class.

Further possible refactorings #

With the Context class gone, you're left with the abstract State class and its implementers:

public abstract class State
{
    public abstract StatePair<State, Out1> Handle1(In1 in1);
 
    public abstract StatePair<State, Out2> Handle2(In2 in2);
}

One further change worth considering might be to change the abstract base class to an interface.

In this article, I've considered the general case where the State class supports an arbitrary number of independent state transitions, symbolised by the methods Handle1 and Handle2. With an arbitrary number of such state transitions, you would have additional methods up to HandleN for N independent state transitions.

At the other extreme, you may have just a single polymorphic state transition function. My intuition tells me that that's more likely to be the case than one would think at first.

Relationship between pattern and monad #

You can view the State design pattern as a combination of two common practices in object-oriented programming: Mutation and polymorphism.

The patterns in Design Patterns rely heavily on mutation of object state. Most other 'good' object-oriented code tends to do likewise.

Proper object-oriented code also makes good use of polymorphism. Again, refer to Design Patterns or a book like Refactoring for copious examples.

I view the State pattern as the intersection of these two common practices. The problem to solve is this:

"Allow an object to alter its behavior when its internal state changes."

The State pattern achieves that goal by having an inner polymorphic object (State) wrapped by an container object (Context). The State objects can mutate the Context, which enables them to replace themselves with other states.

While functional programming also has notions of polymorphism, a pure function can't mutate state. Instead, a pure function must return a new state, leaving the old state unmodified. If there's nothing else to return, you can model such state-changing behaviour as an endomorphism. The article From State tennis to endomorphism gives a quite literal example of that.

Sometimes, however, an object-oriented method does more than one thing: It both mutates state and returns a value. (This, by the way, violates the Command Query Separation principle.) The State monad is the functional way of doing that: Return both the result and the new state.

Essentially, you replace mutation with the State monad.

From a functional perspective, then, we can view the State pattern as the intersection of polymorphism and the State monad.

Examples #

This article is both long and abstract. Some examples might be helpful, so I'll give a few in separate articles:

• Refactoring the TCP State pattern example to pure functions
• Refactoring a saga from the State pattern to the State monad

Conclusion #

You can view the State design pattern as the intersection of polymorphism and mutation. Both are object-oriented staples. The pattern uses polymorphism to model state, and mutation to change from one polymorphic state to another.

In functional programming pure functions can't mutate state. You can often design around that problem, but if all else fails, the State monad offers a general-purpose alternative to both return a value and change object state. Thus, you can view the functional equivalent of the State pattern as the intersection of polymorphism and the State monad.

Next: Refactoring the TCP State pattern example to pure functions.

An article (also) for object-oriented programmers.

This article is part of a series of articles about invariant functors. An invariant functor is a functor that is neither covariant nor contravariant. See the series introduction for more details. The previous article described how you can view an endomorphism as an invariant functor. This article generalises that result.

Endomorphism as a natural transformation #

An endomorphism is a function whose domain and codomain is the same. In C# you'd denote the type as Func<T, T>, in F# as 'a -> 'a, and in Haskell as a -> a. T, 'a, and a all symbolise generic types - the notation is just different, depending on the language.

A 'naked' value is isomorphic to the Identity functor. You can wrap a value of the type a in Identity a, and if you have an Identity a, you can extract the a value.

An endomorphism is thus isomorphic to a function from Identity to Identity. In C#, you might denote that as Func<Identity<T>, Identity<T>>, and in Haskell as Identity a -> Identity a.

In fact, you can lift any function to an Identity-valued function:

Prelude Data.Functor.Identity> :t \f -> Identity . f . runIdentity
\f -> Identity . f . runIdentity
  :: (b -> a) -> Identity b -> Identity a

While this is a general result that allows a and b to differ, when a ~ b this describes an endomorphism.

Since Identity is a functor, a function Identity a -> Identity a is a natural transformation.

The identity function (id in F# and Haskell; x => x in C#) is the only one possible entirely general endomorphism. You can use the natural-transformation package to make it explicit that this is a natural transformation:

idNT :: Identity :~> Identity
idNT = NT $ Identity . id . runIdentity

The point, so far, is that you can view an endomorphism as a natural transformation.

Since an endomorphism forms an invariant functor, this suggests a promising line of inquiry.

Natural transformations as invariant functors #

Are all natural transformations invariant functors?

Yes, they are. In Haskell, you can implement it like this:

instance (Functor f, Functor g) => Invariant (NT f g) where
  invmap f g (NT h) = NT $ fmap f . h . fmap g

Here, I chose to define NT from scratch, rather than relying on the natural-transformation package.

newtype NT f g a = NT { unNT :: f a -> g a }

Notice how the implementation (fmap f . h . fmap g) looks like a generalisation of the endomorphism implementation of invmap (f . h . g). Instead of pre-composing with g, the generalisation pre-composes with fmap g, and instead of post-composing with f, it post-composes with fmap f.

Using the same kind of diagram as in the previous article, this composition now looks like this:

I've used thicker arrows to indicate that each one potentially involves 'more work'. Each is a mapping from a functor to a functor. For the List functor, for example, the arrow implies zero to many values being mapped. Thus, 'more data' moves 'through' each arrow, and for that reason I thought it made sense to depict them as being thicker. This 'more data' view is not always correct. For example, for the Maybe functor, the amount of data transported though each arrow is zero or one, which rather suggests a thinner arrow. For something like the State functor or the Reader functor, there's really no data in the strictest sense moving through the arrows, but rather functions (which are also, however, a kind of data). Thus, don't take this metaphor of the thicker arrows literally. I did, however, wish to highlight that there's something 'more' going on.

The diagram shows a natural transformation h from some functor F to another functor G. It transports objects of the type a. If a and b are isomorphic, you can map that natural transformation to one that transports objects of the type b.

Compared to endomorphisms, where you need to, say, map b to a, you now need to map F b to F a. If g maps b to a, then fmap g maps F b to F a. The same line of argument applies to fmap f.

In C# you can implement the same behaviour as follows. Assume that you have a natural transformation H from the functor F to the functor G:

public Func<F<A>, G<A>> H { get; }

You can now implement a non-standard Select overload (as described in the introductory article) that maps a natural transformation FToG<A> to a natural transformation FToG<B>:

public FToG<B> Select<B>(Func<A, B> aToB, Func<B, A> bToA)
{
    return new FToG<B>(fb => H(fb.Select(bToA)).Select(aToB));
}

The implementation looks more imperative than in Haskell, but the idea is the same. First it uses Select on F in order to translate fb (of the type F<B>) to an F<A>. It then uses H to transform the F<A> to an G<A>. Finally, now that it has a G<A>, it can use Select on that functor to map to a G<B>.

Note that there's two different functors (F and G) in play, so the two Select methods are different. This is also true in the Haskell code. fmap g need not be the same as fmap f.

Identity law #

As in the previous article, I'll set out to prove the two laws for invariant functors, starting with the identity law. Again, I'll use equational reasoning with the notation that Bartosz Milewski uses. Here's the proof that the invmap instance obeys the identity law:

  invmap id id (NT h)
= { definition of invmap }
  NT $ fmap id . h . fmap id
= { first functor law }
  NT $ id . h . id
= { eta expansion }
  NT $ (\x -> (id . h . id) x)
= { definition of (.) }
  NT $ (\x -> id(h(id(x))))
= { defintion of id }
  NT $ (\x -> h(x))
= { eta reduction }
  NT h
= { definition of id }
  id (NT h)

I'll leave it here without further comment. The Haskell type system is so expressive and abstract that it makes little sense to try to translate these findings to C# or F# in the abstract. Instead, you'll see some more concrete examples later.

Composition law #

As with the identity law, I'll offer a proof for the composition law for the Haskell instance:

  invmap f2 f2' $ invmap f1 f1' (NT h)
= { definition of invmap }
  invmap f2 f2' $ NT $ fmap f1 . h . fmap f1'
= { defintion of ($) }
  invmap f2 f2' (NT (fmap f1 . h . fmap f1'))
= { definition of invmap }
  NT $ fmap f2 . (fmap f1 . h . fmap f1') . fmap f2'
= { associativity of composition (.) }
  NT $ (fmap f2 . fmap f1) . h . (fmap f1' . fmap f2')
= { second functor law }
  NT $ fmap (f2 . f1) . h . fmap (f1' . f2')
= { definition of invmap }
  invmap (f2 . f1) (f1' . f2') (NT h)

Unless I've made a mistake, these two proofs should demonstrate that all natural transformations can be turned into an invariant functor - in Haskell, at least, but I'll conjecture that that result carries over to other languages like F# and C# as long as one stays within the confines of pure functions.

The State functor as a natural transformation #

I'll be honest and admit that my motivation for embarking on this exegesis was because I'd come to the realisation that you can think about the State functor as a natural transformation. Recall that State is usually defined like this:

newtype State s a = State { runState :: s -> (a, s) }

You can easily establish that this definition of State is isomorphic with a natural transformation from the Identity functor to the tuple functor:

stateToNT :: State s a -> NT Identity ((,) a) s
stateToNT (State h) = NT $ h . runIdentity
 
ntToState :: NT Identity ((,) a) s -> State s a
ntToState (NT h) = State $ h . Identity

Notice that this is a natural transformation in s - not in a.

Since I've already established that natural transformations form invariant functors, this also applies to the State monad.

State mapping #

My point with all of this isn't really to insist that anyone makes actual use of all this machinery, but rather that this line of reasoning helps to identify a capability. We now know that it's possible to translate a State s a value to a State t a value if s is isomorphic to t.

As an example, imagine that you have some State-valued function that attempts to find the maximum value based on various criteria. Such a pickMax function may have the type State (Max Integer) String where the state type (Max Integer) is used to keep track of the maximum value found while examining candidates.

You could conceivably turn such a function around to instead look for the minimum by mapping the state to a Min value instead:

pickMin :: State (Min Integer) String
pickMin = ntToState $ invmap (Min . getMax) (Max . getMin) $ stateToNT pickMax

You can use getMax to extract the underlying Integer from the Max Integer and then Min to turn it into a Min Integer value, and vice versa. Max Integer and Min Integer are isomorphic.

In C#, you can implement a similar method. The code shown here extends the code shown in The State functor. I chose to call the method SelectState so as to not make things too confusing. The State functor already comes with a Select method that maps T to T1 - that's the 'normal', covariant functor implementation. The new method is the invariant functor implementation that maps the state S to S1:

public static IState<S1, T> SelectState<T, S, S1>(
    this IState<S, T> state,
    Func<S, S1> sToS1,
    Func<S1, S> s1ToS)
{
    return new InvariantStateMapper<T, S, S1>(state, sToS1, s1ToS);
}
 
private class InvariantStateMapper<T, S, S1> : IState<S1, T>
{
    private readonly IState<S, T> state;
    private readonly Func<S, S1> sToS1;
    private readonly Func<S1, S> s1ToS;
 
    public InvariantStateMapper(
        IState<S, T> state,
        Func<S, S1> sToS1,
        Func<S1, S> s1ToS)
    {
        this.state = state;
        this.sToS1 = sToS1;
        this.s1ToS = s1ToS;
    }
 
    public Tuple<T, S1> Run(S1 s1)
    {
        return state.Run(s1ToS(s1)).Select(sToS1);
    }
}

As usual when working in C# with interfaces instead of higher-order functions, there's some ceremony to be expected. The only interesting line of code is the Run implementation.

It starts by calling s1ToS in order to translate the s1 parameter into an S value. This enables it to call Run on state. The result is a tuple with the type Tuple<T, S>. It's necessary to translate the S to S1 with sToS1. You could do that by extracting the value from the tuple, mapping it, and returning a new tuple. Since a tuple gives rise to a functor (two, actually) I instead used the Select method I'd already defined on it.

Notice how similar the implementation is to the implementation of the endomorphism invariant functor. The only difference is that when translating back from S to S1, this happens inside a Select mapping. This is as predicted by the general implementation of invariant functors for natural transformations.

In a future article, you'll see an example of SelectState in action.

Other natural transformations #

As the natural transformations article outlines, there are infinitely many natural transformations. Each one gives rise to an invariant functor.

It might be a good exercise to try to implement a few of them as invariant functors. If you want to do it in C#, you could, for example, start with the safe head natural transformation.

If you want to stick to interfaces, you could define one like this:

public interface ISafeHead<T>
{
    Maybe<T> TryFirst(IEnumerable<T> ts);
}

The exercise is now to define and implement a method like this:

public static ISafeHead<T1> Select<T, T1>(
    this ISafeHead<T> source,
    Func<T, T1> tToT1,
    Func<T1, T> t1ToT)
{
    // Implementation goes here...
}

The implementation, once you get the handle of it, is entirely automatable. After all, in Haskell it's possible to do it once and for all, as shown above.

Conclusion #

A natural transformation forms an invariant functor. This may not be the most exciting result ever, because invariant functors are limited in use. They only work when translating between types that are already isomorphic. Still, I did find a use for this result when I was working with the relationship between the State design pattern and the State monad.

Next: Functors as invariant functors.

Comments

type (~>) f g = forall a. f a -> g a
 
-- Use the natural transformation twice, for different types
convertLists :: ([] ~> g) -> (g Int, g Bool)
convertLists nt = (nt [1,2], nt [True])
 
newtype NT f g a = NT (f a -> g a)
 
-- Does not type check, does not work; not a natural transformation
convertLists2 :: NT [] g a -> (g Int, g Bool)
convertLists2 (NT f) = (f [1,2], f [True])

* Couldn't match type `a' with `Int'
  `a' is a rigid type variable bound by
    the type signature for:
      convertLists2 :: forall (g :: * -> *) a.
                       NT [] g a -> (g Int, g Bool)
  Expected type: g Int
    Actual type: g a
* In the expression: f [1, 2]
  In the expression: (f [1, 2], f [True])
  In an equation for `convertLists2':
      convertLists2 (NT f) = (f [1, 2], f [True])