NOTE: this tutorial assumes you are already familiar with monads. If not,
I would recommend learning about monads first.
Why monad transformers?
Let’s say we have functions with the following signatures:
Imagine we are building an app and this is an API we are given to access specific user’s data.
These functions take user’s id and go into the world to perform an IO action - e.g. a
network request, or read from the disk. Also, an IO action can fail if e.g.
there was no network connection available - that is why Maybe is in the return type.
With that, we want to implement the following function:
This function tries to fetch all the data for the specific user (name, surname and age) and if
any piece of this data couldn’t be obtained it will declare itself as failed by returning
Nothing within IO monad.
This is how we would go about implementing fetchUsersData:
And this would work! The only not so nice thing is that we have this “staircasing” typical when
nesting multiple Maybes. We would normally solve this by running things within a Maybe monad,
but this time we are in IO monad so we can’t do that!
To generalize the problem, it occurs when we have one monad within
another (Maybe within IO here) and would like to access “powers” of the inner monad to make
our code nicer.
This is a common case when using monads in Haskell and exactly what monad transformers are set to
solve - making it possible to user “powers” of one monad within another monad. In this case, we
would like to extend IO’s capabilities with Maybe’s power to exit the computation early.
A monad transformer makes a new monad out of an existing monad, such that computations of
the old monad may be embedded in the new one.
And then there is a typeclass MonadTrans which every monad transfomer has to implement, which means
monad transformer is actually a type. Monad transformer is a monad as well.
Here is how it looks like in our case, where we want to extend IO with Maybe capabilities:
MaybeT m a is a monad transformer version of Maybe a. There is only that extra m which stands
for an “inner” monad that will be expanded with Maybe capabilities.
Regarding the named field of MaybeT (runMaybeT), here’s another bit from the documentation:
Each monad transformer also comes with an operation runXXXT to unwrap the transformer, exposing a computation of the inner monad.
If we wrapped IO within MaybeT and then couldn’t get it back again that would be a problem,
since the function we are implementing needs to return IO (Maybe (String, String, Int)).
From this we can generalize and conclude that a monad transformer has:
one additional type parameter (compared to its monad counterpart) - an inner monad that is being
expanded with capabilities of the outer monad
runXXXT function/field which returns the original, “inner” monad
What does it mean “monads don’t compose”?
If you have been learning about monad transformers, odds are you came across this statement. I did
too, and often it was the first thing discussed when talking about monad transformers. But I
couldn’t understand what does it mean to “compose” monads nor why it is a problem if that cannot be
As you also probably know and as we saw in the example with Maybe, each monad has its monad
transformer counterpart (Maybe and MaybeT, Either and EitherT, …). Each of these monad
transformer counterparts had to be manually and separately implemented by somebody.
That is exactly what the statement in question (monad composition) challenges - why do we have to
do so much work, do we really need to implement xxxT version of each monad? It would be awesome
if we could somehow automate this.
And that is where composing monads would come in handy. Monad composition is creating a new type
which is parametrized by (any) two monads and is then also itself a monad. It would look like this:
This is the general case of the example above, where m1 and m2 were IO and Maybe,
respectively (one monad wrapped in another).
Now the main question here is can we implement the following:
If we could, that would mean MonadComposition m1 m2 is also a monad. Meaning that we solved
the general case of composing any two monads! If that was true, we wouldn’t need to bother
with implementing MaybeT, EitherT, ReaderT separately - MonadComposition would cover all
of that for us automatically!
But as you reckon, that is not the case. It is not possible to make MonadComposition m1 m2 an
instance of Monad typeclass. It can be proved and it is not trivial. From the intuitive
perspective, we can understand that we need more information, the general case is not covering it.
If the “outer” monad is Maybe, we need to implement what MaybeT will do in terms of Nothing
and Just x, which means we need the specifics.
So that is it! Now you know what “monads don’t compose” means and why it is important.
We used it as an example in the introduction, but let’s now officially take look at it.
The MaybeT monad transformer extends a monad with the ability to exit the computation without returning a value.
A sequence of actions produces a value only if all the actions in the sequence do. If one exits, the rest of the sequence is skipped and the composite action exits.
Here is the type definition:
m being an arbitrary monad composed with Maybe monad. Let’s now see it in action with our example from the beginning:
We can see from the types this works. We don’t end on the left hand side of <- anymore with Maybe a which we then have to
unpack (leading to the staircasing we saw before), but we get a directly.
But what actually happens behind the curtains? Let’s see how MaybeT implements Monad typeclass:
We can see that actually here MaybeT does the heavy lifting for us, what we previously did
manually (staircasing example) - it operates within m (IO in the example) and gets to Maybe a
and then does that “manual” check whether it is Nothing or not.
We said monad transformers are all about combining the powers of two or more monads. With our
MaybeT IO a example we’ve shown how we can get Maybe’s power and make sure that the whole computation is
short-circuited to Nothing if some sub-computation failed. But what if we wanted to do
some IO stuff, e.g. print Fetching data...?
This is why we have lift, which is the only function of MonadTrans typeclass:
Argument monad is the “inner” monad (IO in our example) and constructed monad is the actual
monad transformer (MaybeT in our case).
So this is the function that allows us to “lift” the inner monad’s computation
into the monad transformer’s realm, hence the name. It allows us to do this:
lift here does exactly what it says in its signature, takes IO () and lifts it into MaybeT IO () so we can
call this printing action within MaybeT monad.
It is also maybe interesting to see how MaybeT implements lift:
In the case of printing from above, IO () would come in, liftM Just would produce IO (Just ()) and then MaybeT data constructor would create an instance of MaybeT IO () type.
Phew, we just went through our first monad transformer! Let’s now take a look at another one - ExceptT.
ExceptT is a monad transformer version of Either and is very similar to MaybeT, just as Either is similar to Maybe.
The only difference is that in the case of the failure the exception that is thrown actually contains a value (additional error data) rather than just Nothing.
Here is the type definition:
So let’s just quickly go through the analogous example - let’s assume we are given following API functions:
And we want to implement:
If we try do to it without ExceptT monad transformer, we’ll again bump into the staircasing issue:
Now let’s try with ExceptT:
Nice! Let’s also take a look at how ExceptT implements Monad:
And that’s it! This is almost exactly the same as MaybeT, the only difference being the error message that Either brings with itself.
This is the second part of the series of posts on this topic. You can find the first part
In the previous part of this tutorial we created a List a empty for which we could tell from its
type whether it is empty or not (by empty being other Empty or NonEmpty). This is how our
final code looked like:
The question where we left off was: can we create safeTail function that would accept only
Let’s try to construct its type signature:
Everything makes sense except one thing - we don’t know in compile time what is empty going
to be for a returned list.
It depends on the input list - if it has only one element, the result will be Empty.
Otherwise, it will be NonEmpty But the problem is that with our current type system we cannot
differentiate between them and they are both marked as NonEmpty.
[Going deeper] But what if we just put List a smth as a return type?
In the previous part of the tutorial we had cases where the created list had empty type param
which just stayed general and that worked. So what would happen if we tried that here?
Ok, so here is what we are trying to compile:
This looks like we are trying to leave to the compiler to determine what will smth actually be,
we just say “this will be something/anything”. Plus we have a type param value smth that doesn’t
appear anywhere in the function arguments, on the “left” side, but just in the result. I am not
sure if that could make sense in any case?
But interesting thing is, the following compiles:
It doesn’t say “you have type param value smth which doesn’t appear anywhere on the left side.”
which surprised me a bit. I still wonder why could that be valid?
NOTE: On the other hand, we can have Nothing :: Maybe a and in that case it is ok to have a on
the right side only, so I guess that is ok actually.
But if we try to compile the original function, it fails. The error message is a bit longer as
usual with Haskell, but from what I understood it basically says the following: “I can see from
the List constructors that any list you create will have a specific type, and you are here
trying to say it will be just anything. Tell me exactly what it is.”
TODO: I am not sure if I got this completely right. Figure out what is exactly the reason this
does not compile.
The conclusion from all this is: we need a more expressive type so we can specifically say what
is the type of the returned list going to be!
Example: Length indexed lists (vectors)
NOTE: in other tutorials often is used the term “Vector” instead of “List”,
which we used so far.
What is the next piece of information about the list we could know, besides whether it is empty or not? It is
its length - and if we could knew that, we could implement safeTail without problems. We wouldn’t
worry what “type” of non-emptiness input list has - we would just reduce the length by one.
Let’s see how we can encode length into the type of our list.
Encoding list’s length in its type
Our list type is going to look like this:
Again we have two type parameters, a is for type of elements in the list while length is for
type from which we can tell the list’s length.
Before we had just two values (or “list states”) that we needed to encode with types, Empty and
NonEmpty, so we created two types (or one type with two data constructors when we used
DataKinds - then from that DataKinds created the types for us).
But this time we have infinite amount of values, since length of a list can be
any natural number. So how do we represent that with types?
We can do it in the same way we defined the list itself, recursively:
Succ stands for Successor. We can see that since Succ is a parametrized type constructor
we can actually from it create infinite amount of types and that solves our problem. This works,
but as in a previous example it would be better to use DataKinds so we have kind safety
(otherwise somebody could write nonsense such as Succ Bool and it would be a valid term):
And this is it! From this, DataKinds will create type constructors 'Zero and 'Succ nat. Let’s
see their kinds and compare them to types of the data constructors they originated from
(Zero and Succ).
The types of data constructors look exactly the same as kinds of newly created type constructors!
This is what DataKinds does - promotes data into types, and types into kinds. We ended up with
a new kind Nat and we can create infite amount of types with that kind:
Now let’s use this and create a type for our length-indexed list:
The main difference from the previous example is how we are managing types in Cons. Instead
of just putting e.g. NonEmpty, here we are building on top of the input type, length of the input
list. So if the input list had length 'Succ 'Zero, the new one will have 'Succ ('Succ 'Zero).
And that is it! We have now defined list which will have its length contained in its type. Let’s
see it in action:
Wohoo, it works! Now we can finally implement safeTail:
Let’s test it out:
Everything works as expected. This time we didn’t have any trouble defining safeTail’s types -
we restricted input list to have at least one element ('Succ n) and then output will simply be
of length n.
The basic implementation of length-index list is now done. We can create a list and we can also
operate with safeTail and safeHead on it. Is there anything else we might need?
List concatenation - making it work on type level
For example, what if we wanted to concatenate two lists? Logically, we know that the resulting list
will have length which is the sum of lengths of the input lists. But how do we represent that on type
Let’s try to see what will the function signature look like. We will call this function append
(so we don’t confuse it with Prelude’s concat) - it will take two lists and produce a new list
which is a concatenation of those two input lists:
Let’s also see a few examples of how it would work:
So we take two lists of lengths n and m respectively (we don’t care if
they are empty or not in this case, since there isn’t any “unsafe” scenario) and we
produce a new list of length n + m. But how do we represent its
length, what do we put in place of ??
Obviously, we want to sum m and n - but how do we do that on a type level?
Wouldn’t it be handy if there was a way to define a function that operates on types? Then we could
define things like this:
Where Add n m is a “type” function that would take two types n and m and produce a new type
which would represent their sum.
Type families - functions that operate on types
Turns out there is a special mechanism for this in Haskell and it is provided in form of another
language extension named TypeFamilies. This is how we would define our type family Add n m:
Since we are dealing with recursive types ('Succ), this type function has to work in the same way.
In the base case when the left type is 'Zero, we simply return the second type. In the general
case we keep “deconstructing” the left argument and “piling” it on the right type until we
reach the base case.
This looks like a logical way to do it. But if, we try to compile it we will get the following
The problem is that GHC is here scared that our general recursion case might never terminate.
I checked out docs of UndecidableInstances and here is what it says:
These restrictions ensure that
instance resolution terminates: each reduction step makes the problem smaller by at
least one constructor.
And this is exactly what is the problem: we made a reduction step, but we still have
the same number of constructors ('Succ) - we just moved it from one argument to another and that
made GHC suspicious we are designing a system that actually terminates.
If we e.g. did this (although it is conceptually wrong, does not produce the result we want):
we wouldn’t get any errors - GHC sees that we got rid of one 'Succ and is happy and convinced
that we will eventually come to the end.
TODO: Why GHC doesn’t complain if we do Add ('Succ n) m = 'Succ (Add n m), since we still have the same number
of constructors? Is it because Add is not at the beginning anymore?
This was pretty impressive for me, I didn’t know GHC watches over this kind of stuff, “counting” how
our recursion is doing.
Anyhow, we can solve the problem from above by introducing UndecidableInstances extension. With it, our code
from above successfully compiles.
Now that we know how to sort out things on the type-level, let’s actually write the function which appends two
We again do it recursively, always taking the first element “out” and calling append again for the reduced first
list and the second list (general case). When first list reaches End, append will just return the
second list (base case).
But, if we try compile this we get an error! This is what it says:
What this error says is it basically complains that return type is not correct, it is different from what we
declared in the function signature. In the signature we said that return type is List (Add n m) a. When
append’s function body is evaluated, Cons elem (append rest xs), it will be of
type List ('Succ (Add n m) a).
Why? Let’s deconstruct Cons elem (append rest xs) from the inside out. append rest xs is of
type List (Add n m) a. And Cons’s type signature is Cons :: a -> List n a -> List ('Succ n) a - whatever n
is, Cons will put 'Succ on it. So in our case, where n is Add n m (from append rest xs), applying Cons
on it will produce type List ('Succ (Add n m)) a. And what we promised to GHC in append’s return type was
List (Add n m) a.
Even if GHC tries to evaluate Add n m to see what is under the hood, it will again see from the general step
that Add x y is produced.
So when comparing returned and expected type (List ('Succ (Add n m)) a and List (Add n m) a), GHC
sees that extra 'Succ and
concludes “wait, this is not what I expected, I was looking for
Add but I got 'Succ” and throws an error.
The root of the problem is in what we experienced when defining Add n m type family,
that GHC doesn’t understand that Add n m will eventually produce a concrete type ('Succ in this case),
because of the way we designed our recursion which always puts Add in the front.
We managed previously to patch it up with enabling UndecidableInstances, but now it is coming back
to haunt us again.
We can solve it by slightly changing Add’s definition, the general case of the recursion:
So what we did is rearrange things a bit so now 'Succ comes in front. With this change we don’t get any errors
and we can also disable UndecidableInstances. When GHC sees this it decides our
recursion will eventually terminate and doesn’t complatin. I am not sure exactly why, my guess is because here we
applied Add to the “reduced” argument (n, while input was 'Succ n) so that tells GHC that our recursion
is moving in the right direction, that we are reducing the problem.
Previously we just moved 'Succ from one argument to another so I guess that was
the problem, we haven’t “reduced” anything. This is my current assumption and I would still like to understand this
And this is it, with this last change everything works as expected! Now we can see append in action, but let’s
first just do one more thing:
I implemented List as an instance of Show typeclass so we can nicely visualize our lists.
Let’s now see append on a few examples:
We can see how everything works and also that types accurrately reflect number of elements in the list.
For the end, here some of my thoughts on type-level programming after trying it out on these
Type-level programming let’s us put put more features/properties into types and achieve compile
time safety for them, but not without a cost - we have to program things both on type and
data level (e.g. as we did with append function).
It is important to consider how we will implement and structure types to match well in all instances, since
it is possible run into non-obvious errors such as we hadd with Add n m.
All together it was really cool for me to learn about this! I hope you found it useful - let me know if you
have any questions or if I could have done anything better.
I heard a lot lately about using types in Haskell to describe function arguments in more details
(e.g. function takes a list that is non-empty) and thus achieve higher compile-time safety.
It sounded cool so I decided to research more about it and I created this blog post as a memo of
what I learned.
pretty extensive, but not so intuitive. Still the most complete intro (and pretty much
the only one) to the topic. Most of my examples below are taken from it.
Why type-level programming?
As I wrote above, my current understanding is that with it we can add more info into the type
signature of a function, making it “safer” in the compile time.
E.g. instead of just saying “this function takes a list”
we can say “this function takes a non-empty list”, or
“this function takes Int which is > 10 and < 127” (although this last one might be solved just by
creating an appropriate type, e.g. using TH?).
TODO: I would love to learn about more examples where this is used.
Example: A function that accepts only a non-empty list
We want to be able to tell from its type whether a list is empty or not. To do that we will
create a new type which will have that information stored in it.
First, let’s see how we would create a “normal” list type on our own:
This is a usual recursive definition of list (Cons stands for Constructor). Once there is
an instance of this type we can tell which type of elements the list contains (e.g. List Int
or List (Maybe String)), but nothing more than that. We cannot deduce from its type (which means
in compile time) whether it is empty or not.
We could of course check it in runtime and throw an exception if the list is empty, but we want to
be stricter than that. We want to ensure that program cannot even be compiled if an empty list is
provided where it shouldn’t be.
What are we missing?
The problem with the “normal” list we defined above is that we are missing information in its type.
We have only one piece of
information and that is type of the elements within the list - we use type parameter a to declare
that. We can also use it to define functions that work only for a specific a. E.g. here is a
function that works only on a list of integers:
This is guaranteed in compile-time. If we call this function with a list of e.g. Bools, the
compiler will throw an error at us.
Using type params to encode extra information
So here’s an idea - why don’t we just use the same mechanism again (having a type parameter) to
know whether a list is empty or not. If we added another type parameter to keep track of that,
our type (disregarding data constructors for now) would look like this:
Just as type param a means any type (e.g. Int or MyType), the same applies for empty.
E.g. we could have List Int Double or List String Bool or List Int SomeCustomType.
Just as we restricted function sumListElements above to work only when a is Int, we can use
empty in the same way.
Let’s say we want to implement a safe version of head function - that means it accepts only a
non-empty list as an argument, otherwise it won’t compile. We will call it safeHead.
Ok, we introduced empty as another type parameter, but the question we are facing now is what
do we do with it? Which concrete types will take its place and how?
Lets introduce two new types:
The interesting thing here is that we have only type constructors for these types and no data
constructors. That means we cannot create instances (values) of these types, but that is ok!
We need these types only at the type level, in function signatures. Such types are also called
uninhabited or empty.
Now let’s imagine we have a way to correctly assign Empty and NonEmpty to empty and non-empty
lists’ types. Then we could define safeHead as follows:
We wouldn’t even have to define a case for End since the type guarantees it can’t ever happen.
Assigning correct type to empty
The main question that is left is how do we produce such lists with an extra type parameter, and
how do we make sure which type empty takes when? This is what we will look at now.
This is how our type List looks once we have added empty as a second type parameter:
Except adding that extra type parameter, nothing else changed. When I first saw this,
I was confused by
the fact there is a type parameter on the left side that doesn’t appear anywhere on the right side
as a data.
How is that possible, why would that make sense? (Ok, there isempty on the right side here, but
only as a part of a type designation and not as a part of data constructor. Which means there will
never be anything of type empty in some value of this type).
But turns out it does make sense, since we use it as a designation at the type level only, to show
underlying value has a certain property (empty or non-empty in this case). Such types, which have a
type parameter(s) on the left side that don’t appear on the right are
also called phantom types.
Let’s see now what happens if we create an instance of our new List and test its type in GHCi:
As we can see, GHCi concluded that a is a string in nonEmptyList, but could not deduce anything
for empty in either case, since it is not used anywhere. So how can we solve that
and make sure that empty becomes Empty for emptyList and NonEmpty for nonEmptyList?
Before we continue, let’s check types of our data constructors, End and Cons (since they are
functions as well, we can do that):
We can see they have no power to change or specify empty type param in any way. End will leave
it unspecified, while Cons will preserve it from the input list. Also, we have no way to change
these type signatures as they are automatically derived from List type definition.
This is exactly where GADTs come in. GADTs (Generalized Algebraic Data Types) is a Haskell extension that lets us explicitly
define the type signatures of data constructors.
Before seeing GADTs in action, let’s first remind ourselves of the standard,
non-GADT definition of List we used above:
Now let’s rearrange it a bit and add types of data constructors in comments so we can more easily
reason about them:
As we mentioned, the types in the comments are automatically derived and we cannot control them. But
that is exactly what we want to do, and GADTs let us achieve that using the following syntax:
We can see it is very similar to our “rearranged” List definition above! What GADTs let us do
is write by ourselves types of data constructors (which were in the previous definition in the
comments), giving us control to specify them as we wish!
The difference in the syntax is that we have to add where after the type name and then
for each data constructor we specify its type signature.
Now we finally have the power to control empty type parameter (in List a empty)! We specified
that End will mark list as Empty, while Cons will mark it as NonEmpty. And this is exactly
what we wanted to do, because if we used End we know the list is empty, while if we used Cons
we know there is at least one element in it, which makes it non-empty.
Let’s see it in action! Using it stays the same as without GADTs, just that this time there will
be empty type param which assumes an appropriate type:
Wohoo, this works now! We see we can construct values of this type and we will always know whether
it is empty or not. safeHead function we defined above will work on these without any problems.
Can we just use smart constructors instead of GADTs?
One possible “downside” of GADTs is that it is a language extension we have to enable, thus making
our codebase a bit heavier (longer compilation time?) and less “standard”.
Sometimes we can avoid using GADTs with smart constructors. Let’s see what that is and how it would
work in this case.
Smart constructor is simply a function that is used
to create a certain value instead of using its
data constructor directly. We typically do that (hide data constructors and expose smart
constructor functions) when we want to have extra control over the value creation. E.g. we want to
make some extra checks, or make sure an invalid value isn’t provided etc.
For example, we could provide a following smart constructor to create an empty list:
And this works! By defining the type signature of createEmptyList we made sure that empty will
always assume the type of Empty when this function is called. Since End has a type signature
End :: List a empty, we just “casted” type param empty here into a specific type.
Let’s try to do the same for the other data constructor, adding an element to the list:
What we are trying to achieve here is make sure that whenever an element is added to the list,
empty becomes NonEmpty, and we again use type signature for that, to provide that extra
But if we try to compile this, we get the following error: Couldn't match type ‘empty’
To understand the problem, let’s remind ourselves of Cons’s type:
Cons :: a -> List a empty -> List a empty.
The problem is in that Cons requires empty to stay the same, so whatever type it is in the
input list, it must stay the same in the newly constructed list. Although we specified we want
to change it to NonEmpty in the addElemToList’s type signature, Cons is not flexible enough
to do that and this is why we got an error during compilation.
Although smart constructors might be a solution in some simpler cases (e.g. when we have “flat” data
and we are merely “casting” general type params into the specific ones, such as we did with End),
in this case where we have a recursive data structure it wasn’t enough because the initial
data constructor was too rigid.
What is List Int Double?
Well, List Int Double means nothing, it doesn’t make sense. We can only construct and know how
to work with lists whose empty type parameter is either Empty or NonEmpty.
But the problem is although it doesn’t make sense, we can still write things like this and it will
There is no way to execute this function since there is no way to construct such a list where
empty type param is Bool, but strange stuff can appear in our codebase and we cannot detect
it in compile time.
Here is a more “real world” example when this could be a problem: let’s say you are
using Empty and NonEmpty types for list as we explained above,
but you are also using Yes and No types for something else in your codebase. And then your
colleague starts implementing some new functionality for your lists, and by mistake he starts using
Yes and No in the place of empty. And there is nothing to stop him until he actually tries to
connect everything together and run the code!
The problem we see is there is no “safety” at the type level, we cannot say “empty can be only
this kind of type”. But, there is a mechanism that can help us.
Not all types are used in the same way
Just a short observation before we continue. I wanted to put attention to the fact that we are now
differentiating between two possible uses of a type:
type is used to produce values (store data) - e.g. Int, Maybe Bool, …
type is used only at the type level as a designation of something, never producing an
actual value - e.g. Empty and NonEmpty
Despite these very different uses, we currently don’t have a way to differentiate between such
types - we declare them both in the same way and Haskell can’t tell how are we going to use them
In standard Haskell each type has a kind, which can be thought of as a “type of a type”. E.g.:
And that is it, all kinds are expressed with *s and automatically derived for us. * means
a type that has values.
But as we saw earlier, this is not enough for us. We also want to cover that other use case so we
can say “here goes only type(s) that tell us whether a list is empty or not.”
And this is exactly what DataKinds extension allows us to do, it lets us define other kinds
Now let’s see what happened here. We made a new type ListStatus and then we use its data
constructors (prefixed with ') in the place of types in GADT for List. Wut?
The thing with DataKinds is the following: for every type we create it additionaly creates for us
new types, named after data constructors we used and prefixed with '. It also creates a new kind,
which is named after the type’s name. Specifically for this case:
DataKinds created for us two extra types, 'Empty and 'NonEmpty
Kinds of these new types are ListStatus
These types cannot have values, they can be used only at the type level
I was really confused the first time I realized this. This extension just like that creates extra
types for us, without even asking us about it, for every type we create!
Since we are using only types of ListStatus kind in List’s data constructors’ signatures,
Haskell inferred from that that empty type param must be of kind ListStatus and won’t let us
use anythng else. If we try to create a function which takes List a Bool, we will receive the
Expected kind ‘ListStatus’, but ‘Bool’ has kind ‘*’
Which is exactly what we wanted! With this we achieved kind safety, besides the usual
type safety in the compile time.
To make things even more explicit, we can turn on KindSignatures extension which lets us
explicitly define kinds of type parameters in a type:
Now everybody can see that a is a “standard” type that has values, while empty can be only
'Empty or 'NonEmpty. We didn’t have to write this explicit version as Haskell can infer it on
its own, but it is a matter of style and documentation. We can also omit ' in front of types and
Haskell in a lot of cases can infer by itself if it is a type or data constructor. I found it easier
to have everything explicit for now, a lot is going on behind the scenes so this made it clearer
And that is it for this first part! We learned about type-level programming, how to use GADTs and
data kinds and saw everything together in action. Hope you found it useful, please let me know in
the comments if you have any questions, I said something wrong or I can explain something better.
In Part 2 we will go
even deeper and take a look at some more cool examples that build on top
of this one! Here’s a teaser question: with our List a empty that we developed above, how would
you implement safeTail function which works only on non-empty lists,
analogous to what we have done with safeHead? Can you do it, what is its return type?