Expressing a Relationship between Multiple Types in Elm

Elm’s type system is sufficiently sophisticated that you’ll often want to make fine-grained distinctions between roughly similar types. In a recent project, for instance, we ended up with a separate type for a Mother and a Child.¹ Now, a Mother is a little different than a Child. Most obviously, mothers have children, whereas (at least, in our data model) children do not. So, it was nice for them to be separate types. In fact, there were certain operations which could be done on a Mother but not a Child (and vice versa). So it was nice to be able to enforce that at the type level.

Yet, a Mother and a Child clearly have a lot in common as well. For this reason, it sometimes felt natural to write functions that could accept either. So, in those cases, it was a little awkward for them to be separate types. Something was needed to express a relationship between the two types.

What alternatives are available to do this sort of thing in Elm? Which did we end up choosing? For answers to these questions, and more, read on!

Our Data Model

Before proceeding further, here’s a little excerpt from our data model, to get us started. Of course, some of this would have been a little different had we chosen a different approach, so we’ll explore that as well. But this will give you a sense of the kind of data we were working with. (I’ve simplified things a bit, compared with the actual app).

    type Gender
        = Female
        | Male

    type alias Child =
        { name : String
        , avatarUrl : Maybe String
        , motherId : MotherId
        , birthDate : NominalDate
        , gender : Gender
        }

    type alias Mother =
        { name : String
        , avatarUrl : Maybe String
        , children : List ChildId
        , birthDate : NominalDate
        }

    type MotherId =
        MotherId Int

    type ChildId =
        ChildId Int

You’ll notice that each Child has a reference not to a Mother, but to a MotherId. Similarly, each Mother has a list of ChildId, not a list of Child. The reasons we do things this way are a little subtle – perhaps they deserve a blog post of their own someday. (Amongst other things, it keeps the client data model closer to the data model on the backend, which makes JSON encoding and decoding simpler). However, it does mean that we need some kind of “container” type in order to get actual children and mothers. In our case, the relevant parts of that type looked something like this (again, I’ve simplified a little bit compared to the actual app):

    type alias Container =
        { mothers : EveryDict MotherId Mother
        , children : EveryDict ChildId Child
        , motherMeasurements : EveryDict MotherId MotherMeasurements
        , childMeasurements : EveryDict ChildId ChildMeasurements
        }

    type alias MotherMeasurements =
        { familyPlanningMethod : List FamilyPlanningMethod
        }

    type alias ChildMeasurements =
        { height : List Height
        , weight : List Weight
        , photo : List Photo
        }

Now, what are all these “measurements”? They were the main point of the app we were working on – we were collecting and displaying those measurements (and a few others I’ve omitted for the sake of simplicity).

Note that these measurements are themselves an example of related types. You could, for instance, say that ChildMeasurements is to Child as MotherMeasurements is to Mother. Furthermore, we needed another couple of related types to represent the various measurements at the data level (rather than just the type level)…something like:²

    type ChildActivity
        = TakePhoto
        | MeasureHeight
        | MeasureWeight

    type MotherActivity
        = RecordFamilyPlanningMethod

Now, these types are all reasonably sensible on their own. However, there is clearly some kind of relationship amongst them. You could even imagine giving names to some of those relationships:

• Child and Mother could both be a kind of Person.
• ChildMeasurements and MotherMeasurements could both be a kind of Measurement.
• ChildActivty and MotherActivity could both be a kind of Activity.

But how can we express those kind of relationships in Elm’s type system? Or, to put it another way, how might you fill in the gaps in this pseudo-code:

    type Person = ???

    type Measurement = ???

    type Activity = ???

To evaluate the available alternatives, you’ll need to know a little more about the sort of work that we wanted to do with these types – in other words, the functions we wanted to be able to write. In pseudo-code, here are some example function signatures that we ended up needing. (You can probably form an intuition about why we’d want most of these things, and we’ll discuss some of them in more detail below).

    getAllActivities : Person -> List Activity

    getAvatarUrl : Person -> Maybe String

    getBirthDate : Person -> NominalDate

    getChildren : PersonId -> Container -> List ChildId

    getMotherId : PersonId -> Container -> Maybe MotherId

    getName : Person -> String

    hasPendingActivity : PersonId -> Activity -> Container -> Bool

    iconClass : Person -> String

    getMeasurements : PersonId -> Container -> Measurements

So, what approaches are possible? I can think of four:

1. Tagged types
2. Type classes
3. Just don’t do it
4. Extensible records

Tagged Types

If what we want is to define a type that can either by a Child or a Mother, the simplest way of doing it is via a tagged type (sometimes referred to as a sum type, union type, or algebraic data type). That is the most basic way in which we can define something which might be one sort of thing or another sort of thing. So, a Person could be defined in this way:

    type Person
        = Mother Mother
        | Child Child

    type PersonId
        = PersonIdMother MotherId
        | PersonIdChild ChildId

What we have here is a kind of “wrapper” type (Person), which can be one of two things (either a Child or a Mother). To identify which it is, we re-use the words Child and Mother as “tags” which identify, for a particular Person, what sort of person it is.³

Now, this will no doubt be very familiar to you, and it is certainly the first thing you ought to think about when expressing this kind of relationship between types. It is the simplest approach, and often fits the bill admirably. Consider, for instance, how we might implement a few of the functions we sketched above:

    getAvatarUrl : Person -> Maybe String
    getAvatarUrl person =
        case person of
            Child child ->
                child.avatarUrl

            Mother mother ->
                mother.avatarUrl

    iconClass : Person -> String
    iconClass person =
        case person of
            Child _ ->
                "child"

            Mother _ ->
                "mother"

    getMotherId : PersonId -> Container -> Maybe MotherId
    getMotherId personId container =
        case personId of
            PersonIdChild id ->
                EveryDict.get id container.children
                    |> Maybe.map .motherId

            PersonIdMother id ->
                Just id

    getChildren : PersonId -> Container -> List ChildId
    getChildren personId container =
        getMotherId personId container
            |> Maybe.andThen (\id -> EveryDict.get id container.mothers)
            |> Maybe.map .children
            |> Maybe.withDefault []

That all works very well, so far. However, this approach turned out to have some pitfalls in our app, especially when we started implementing functions which depended on additional related types. Consider how one might express those other types:

    type Measurements
        = MotherMeasurements MotherMeasurements
        | ChildMeasurements ChildMeasurements

    type Activity
        = MotherActivity MotherActivity
        | ChildActivity ChildActivity

So far, so good, and some additional functions can be implemented in a perfectly reasonable way, e.g.:

    getAllActivities : Person -> List Activity
    getAllActivities person =
        case person of
            Mother _ ->
                List.map MotherActivity
                    [ RecordFamilyPlanningMethod ]

            Child _ ->
                List.map ChildActivity
                    [ TakePhoto
                    , MeasureHeight
                    , MeasureWeight
                    ]

However, we start to run into some trouble when implementing functions that depend on multiple related types. Consider how we might implement hasPendingActivity. The original implementation looked something roughly like this (simplified a little compared to the actual app):

    hasPendingActivity : PersonId -> Activity -> Container -> Bool
    hasPendingActivity personId activity container =
        case ( personId, activity ) of
            ( PersonIdMother id, MotherActivity motherActivity ) ->
                hasPendingMotherActivity id motherActivity container

            ( PersonIdChild id, ChildActivity childActivity ) ->
                hasPendingChildActivity id childActivity container

            _ ->
                -- Hmm. If we get here, we've got a mis-match between the
                -- personId type and the activity type ... one is suitable for
                -- a mother, but the other is suitable for a child. So, what
                -- answer should we give?
                Debug.crash "Mismatched parameters"

Now, whenever you’re writing code and you think to yourself “we shouldn’t get here”, that’s a clue that you haven’t structured your types quite as well as you might. Ideally, you should be able to prove to the compiler that you can’t get there, so you don’t have to write the code at all. Or, you should at least be able to prove to yourself that you can’t get there, even if it’s hard to convince the compiler (that’s one reasonable case for Debug.crash in production code). However, in this case we can do neither. It’s perfectly possible to call the function with a mis-match between the PersonId and the Activity, so we have to figure out what answer to give in that case.

You might be thinking that it would be perfectly reasonable to answer False instead of using Debug.crash. After all, a Mother presumably doesn’t have a pending ChildActivity. Yet there are a couple of problems with this. Calling the function with these mis-matched parameters presumably indicates a bug of some kind in your program logic. It would be better to prevent this bug with appropriately designed types, rather than acting as though there were some reasonable way to continue. Furthermore, what happens if you apply a not to the result of calling hasPendingActivity? All of a sudden, it doesn’t seem so reasonable to have returned False to a non-sensible question.

Now, I suppose one option to deal with this would be to change the signature of hasPendingActivity to return a Maybe (or a Result)…something like:

    hasPendingActivity : PersonId -> Activity -> Container -> Maybe Bool

That way, we could return Nothing in cases where there is a mismatch between our parameters. This would be technically correct at some level, but is really ugly. Perhaps we can do better!

Type Classes

What if we conceived of the Person type not as a “wrapper” for Child and Mother, but instead as a set of requirements that we must fulfill in order to deal with a type as a person? In Elm, we could express those requirements in the form of a record, along these lines (with some omissions):

    type alias Person p =
        { getAllActivities : p -> List Activity
        , getAvatarUrl : p -> Maybe String
        , getBirthDate : p -> NominalDate
        , getName : p -> String
        , iconClass : p -> String
        }

In effect, we’re saying that any type (here, represented as p) can be a Person, so long as you provide an implementation for each of the indicated functions. So, we need to fill in the record for Child and for Mother, something like this:

    childPerson : Person Child
    childPerson =
        { getAllActivities =
            always <|
                List.map ChildActivity
                    [ TakePhoto
                    , MeasureHeight
                    , MeasureWeight
                    ]
        , getAvatarUrl = .avatarUrl
        , getBirthDate = .birthDate
        , getName = .name
        , iconClass = always "child"
        }


    motherPerson : Person Mother
    motherPerson =
        { getAllActivities =
            always <|
                List.map MotherActivity
                    [ RecordFamilyPlanningMethod
                    ]
        , getAvatarUrl = .avatarUrl
        , getBirthDate = .birthDate
        , getName = .name
        , iconClass = always "mother"
        }

So Person now describes a class of types (or, perhaps, a “typeclass”) with certain capabilities. If we’re writing a function that needs to make use of one of those capabilities, we no longer have to specify exactly which type it takes. Instead, we can ask for any type that has the capability we need.

Consider, for instance, a function to view a person. In our first attempt at this, with a tagged type for Person, a simple version might look something like this.

    viewPerson : Person -> Html a
    viewPerson person =
        div []
            [ h4 [] [ text <| getName person ]
            , getAvatarUrl person
                |> maybeViewImage (iconClass person)
            ]

Using Person as a typeclass instead would look something like this:⁴

    viewPerson : Person p -> p -> Html a
    viewPerson personConfig person =
        div []
            [ h4 [] [ text <| personConfig.getName person ]
            , personConfig.getAvatarUrl person
                |> maybeViewImage (personConfig.iconClass person)
            ]

This leads to a corresponding difference in how you would call the two functions. In our previous case, assuming you knew you had a Child, you’d need to wrap it up as a Person…something like viewPerson (Child child). Using typeclasses, you can simply supply the child itself, along with the implementation which allows you to treat a child as a person…something like viewPerson childPerson child.

Now, so far, we haven’t actually gained a lot by using Person as a typeclass instead of a tagged type – it’s just an alternate idiom, so far. The compelling advantage comes when dealing with additional related types. Consider something like getAllActivities and hasPendingActivity. Instead of dealing with a wrapped Activity type, they can now deal directly with the exact type that expresses the activities which are relevant to this kind of person. This can be expressed in Elm as additional type parameters to the Person record, along these lines:

    type alias Person p a id m =
        { getAllActivities : p -> List a
        , getAvatarUrl : p -> Maybe String
        , getBirthDate : p -> NominalDate
        , getChildren : id -> Container -> List ChildId
        , getMotherId : id -> Container -> Maybe MotherId
        , getName : p -> String
        , hasPendingActivity : id -> a -> Container -> Bool
        , iconClass : p -> String
        , getMeasurements : id -> Container -> m
        }

You might call this a “multi-parameter type class”, if you were so inclined.

Adding these additional type parameters neatly solves our difficulty with implementing hasPendingActivity, since we can now depend on getting an activity of the appropriate type – the compiler will complain if we don’t. So, we can do something like:

    motherConfig : Person Mother MotherActivity MotherId MotherMeasurements
    motherConfig =
        { hasPendingActivity = hasPendingMotherActivity
        , ...
        }

    childConfig : Person Child ChildActivity ChildId ChildMeasurements
    childConfig
        { hasPendingActivity = hasPendingChildActivity
        , ...
        }

    hasPendingChildActivity : ChildId -> ChildActivity -> Container -> Bool
    hasPendingChildActivity childId childActivity container =
        ...

    hasPendingMotherActivity : MotherId -> MotherActivity -> Container -> Bool
    hasPendingMotherActivity motherId motherActivity container =
        ...

There can no longer be any mismatches between the id and the activity supplied to hasPendingActivity, since the compiler is aware of all the related types and will complain if any of them are wrong.

So, while you might have heard that Elm lacks typeclasses, my own experience is that I use them (at least somewhere) in pretty much every app. You can also find examples of this technique in packages such as elm-sortable-table, where the Config data msg in view : Config data msg -> State -> List data -> Html msg is a kind of typeclass.

There are a few limitations of typeclasses in Elm which I should mention. One is that you must explicitly mention the typeclass implementation when you call a function that requires one. So, for instance, to call the viewPerson function sketched above, you need to explicitly refer to the typeclass…something like viewPerson childConfig child, or viewPerson motherConfig mother. In some languages, the compiler can deduce that if you’re supplying a child to viewPerson, you must want to use the childConfig, so you don’t have to mention it explicitly. That is a convenience, but it is often confusing to try to follow the compiler’s reasoning about which typeclass instance it will deduce. It may not be such a terrible thing to just say which one you want. Saying which typeclass you want also makes it easy to construct typeclasses at run-time, which is occasionally handy, and is more convoluted (but not impossible) in languages like Haskell.

A bigger difficulty is Elm’s lack of higher-kinded polymorphism. What this means is that type parameters cannot be used as wrappers – they can only be wrapped. So, in the example above, we have to be specific about the List in List p. The p can be a parameter, but we have to make a definite choice about List – you must always choose concrete “container” types. So, there are some relationships between types that you won’t be able to model accurately. However, that still leaves a lot of room for this technique to be useful.

Finally, there are cases in which you really do want a tagged type. Consider a case where you might want to include both children and mothers in the same list.

• You can say List p, but that is either a list of all mothers, or all children, not a list that can include both.

• You could do something fancy with existential types (or rank-n types), but Elm doesn’t have those.

So, if you need a list that can include both mothers and children, you’re pretty much going to need a tagged type. In our app, it turned out that we didn’t need that for mothers and children, but there were cases in which we wanted lists of activities. So, in addition to the Person record, we also had a tagged type for activities.

    type Activity
        = MotherActivity MotherActivity
        | ChildActivity ChildActivity

Once you have that, constructing a List Activity is straightforward. We also added something to Person so that we could convert (when necessary) from its generic activity type to the more concrete Activity, along these lines:

    type alias Person p a id m =
        { ...
        , wrapActivity : a -> Activity
        }

    childConfig : Person Child ChildActivity ChildId ChildMeasurements
    childConfig =
        { ...
        , wrapActivity = ChildActivity
        }

    motherConfig : Person Mother MotherActivity MotherId MotherMeasurements
    motherConfig =
        { ...
        , wrapActivity = MotherActivity
        }

This allows you to use both approaches (tagged types and typeclasses) together, in cases where you need both. However, it is often the case that just one or the other approach is fine on its own.

Just Don’t Do It

A question which may have occurred to some readers by now is whether we have really gained anything by expressing a relationship between Mother and Child (whether by tagged types or typeclasses). What if we didn’t bother? What if we just let mothers be mothers and children be children, without bothering with unifying types? After all, when writing Elm code, the right answer to some of our impulses is “just don’t do it” – especially when the impulse is towards greater abstraction.

Consider the hasPendingActivity function I’ve sketched above. No matter how we structure things, we still need the more concrete hasPendingChildActivity and hasPendingMotherActivity anyway. So, what exactly do we gain by also having the more abstract version at our disposal?

One way of addressing this question is to look at the viewPerson function which I sketched out above:

    -- With tagged types
    viewperson : person -> html a
    viewperson person =
        div []
            [ h4 [] [ text <| getname person ]
            , getavatarurl person
                |> maybeviewimage (iconclass person)
            ]

    -- With type classes
    viewPerson : Person p -> p -> Html a
    viewPerson personConfig person =
        div []
            [ h4 [] [ text <| personConfig.getName person ]
            , personConfig.getAvatarUrl person
                |> maybeViewImage (personConfig.iconClass person)
            ]

What if we didn’t have a Person type at all – just Mother and Child. Then, we’d end up with something like this:

    viewMother : Mother -> Html a
    viewMother mother =
        div []
            [ h4 [] [ text mother.name ]
            , maybeViewImage "mother" mother.avatarUrl
            ]

    viewChild : Child -> Html a
    viewChild child =
        div []
            [ h4 [] [ text child.name ]
            , maybeViewImage "child" child.avatarUrl
            ]

I suppose it’s true that we’re repeating ourselves a little bit here. However, if our view function really were this simple, it would be obviously better to repeat ourselves rather than engage in the complexity of constructing a type class. That is, you wouldn’t want to use type classes to avoid this little bit of repetition – the repetition would be less painful (and, fewer lines of code) than the type classes.

Of course, in our real app, the view function was much more complex than this. It’s always difficulty writing about programming techniques that only make sense in the presence of complexity, since it would be tedious, and distracting, to actually provide all the complexity. But, consider the following sort of pseduo-code that is somewhat typical:

    viewMother : Mother -> Html a
    viewMother mother =
        let
            nameBlock =
                viewName mother.name

            imageBlock =
                maybeViewImage "mother" mother.avatarUrl

            part3 =
                ...

            part4 =
                ...

            part5 =
                ...

            part6 =
                ...
        in
        div []
            [ nameBlock
            , imageBlock
            , part3
            , part4
            , part5
            , part6
            ]

Now, suppose you want to be able to view a Child in a roughly similar way, while avoiding as much code repetition as is reasonable. One way is to generalize the whole function, using tagged types or type classes (the approaches we’ve considered so far). But that’s not the first technique I’d actually reach for. The first technique I’d reach for is generalizing the parts of the function. So, you could imagine something like this for viewChild:

    viewChild : Child -> Html a
    viewChild child =
        let
            nameBlock =
                viewName child.name

            imageBlock =
                maybeViewImage "child" child.avatarUrl

            part3 =
                ...

            part4 =
                ...

            part5 =
                ...

            part6 =
                ...
        in
        div []
            [ nameBlock
            , imageBlock
            , part3
            , part4
            , part5
            , part6
            ]

Here, we’re identifying multiple “helper” functions, like viewName and maybeViewImage, which we can re-use inside our two distinct functions, rather than trying to create a single, master function. Now, this does leave some repetition in viewChild and viewMother. However, the guts of the logic is not repeated, since it is broken out into multiple functions that both viewChild and viewMother can call. Depending on what kind of computation goes into part3, part4, part5 and part6, we may have many more opportunities to create additional helper functions.

Why is this often a preferable approach? One reason is that the helper functions often make a great deal of sense in their own right – you’d probably want to create them anyway. One of the main questions I ask myself when structuring code is: how can I structure this in a way that I can be confident that it’s finished – that I won’t have to revisit it? That is a lot easier to do for viewNameBlock than it is for viewMother. Well, I suppose you might want to change the way the name is viewed at some point. But it’s a small, well-defined function that you may be able to just leave alone for quite a while. That’s the kind of function I like.

The other reason is that the similarities between viewChild and viewMother may not be as profound as you initially thought. What if the product manager comes back to you tomorrow, humble developer, and says that children ought to be viewed in a subtly different way than mothers? (They are known to do such things). If you’ve created a viewPerson function that handles both mothers and children, you can deal with that by creating some sort of configuration in your Person type – for instance, something like the iconClass I use above. However, if you have to do too much of that, your viewPerson function can become convoluted and tricky to understand. It might have been better to break out a bunch of helper functions, so that you can make more comprehensible changes in separate viewChild and viewMother functions.

Now, in the case of the app I was working on, I was pretty confident that the view for children was going to stay structurally similar to the view for mothers, as we continued to develop the app. So, it seemed worthwhile to construct a unified viewPerson function using type classes. But, you can never be entirely sure – you have to rely on an intuition as to which techniques best fit which situation. After all, you can’t really sketch out each approach in detail and see which is actually nicer – it would take too long! (Unless you’re writing a blog post!). Instead, you need to think about the app’s requirements now, and what they are likely to become, and make the best choice you can.

Extensible Records

Finally, I should at least mention one option which wasn’t suitable for our example, but which could be interesting in some cases: extensible records.

When you have two related types that are both “record” types, and they share some field definitions in common, it is possible to use Elm’s record syntax to work with just those fields. Consider a getName function which we want to use with both Mother and Child. Both types have a field defined as name : String. So, we could define a getName function like this:

    getName : { a | name : String } -> String
    getName thingWithAName =
        thingWithAName.name

    -- Or, more succintly
    getName2 : { a | name : String } -> String
    getName2 =
        .name

Either of those functions can be called with a Mother or a Child, because both a Mother and a Child have the required name field. (The a type parameter tells the compiler that the argument can have other fields as well, in addition to name).

Now, as getName2 suggests, you don’t really even need to define getName, since Elm will magically build it for you if you say .name. But, this can get more interesting where two types share multiple fields. It becomes possible to define a type that expresses all the fields that the two types have in common. For instance, you could imagine a Person type that contains the fields that Child and Mother have in common:

    type alias Person a =
        { a
            | name : String
            , avatarUrl : Maybe String
            , birthDate : NominalDate
        }

Then, you could almost write the simplest version of our viewPerson function in a way that will accept either a Child or a Mother as an argument.

    viewPerson : Person a -> Html b
    viewPerson person =
        div []
            [ h4 [] [ text person.name ]
            , maybeViewImage "?" person.avatarUrl
            ]

This can be a useful technique in simple cases. However, even our simplest version of viewPerson isn’t quite simple enough. We want to associate a different iconClass with mothers and children, for use in maybeViewIamge. Extensible records don’t, by themselves, provide a mechanism for doing that. So, you’ll often need more complex techniques than extensible records. However, in cases where extensible records are sufficient, they are very convenient.

Notes