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Compiler plugin for making type lambdas (type projections) easier to write
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Kind Projector


"But I don't want to go among mad people," Alice remarked.

"Oh, you can't help that," said the Cat: "we're all mad here. I'm mad. You're mad."

"How do you know I'm mad?" said Alice.

"You must be," said the Cat, "or you wouldn't have come here."

--Lewis Carroll, "Alice's Adventures in Wonderland"


One piece of Scala syntactic noise that often trips people up is the use of type projections to implement anonymous, partially-applied types. For example:

// partially-applied type named "IntOrA"
type IntOrA[A] = Either[Int, A]

// type projection implementing the same type anonymously (without a name).
({type L[A] = Either[Int, A]})#L

Many people have wished for a better way to do this.

The goal of this plugin is to add a syntax for type lambdas. We do this by rewriting syntactically valid programs into new programs, letting us seem to add new keywords to the language. This is achieved through a compiler plugin performing an (un-typed) tree transformation.

One problem with this approach is that it changes the meaning of (potentially) valid programs. In practice this means that you must avoid defining the following identifiers:

  1. Lambda and λ
  2. ?, +?, and -?
  3. Λ$
  4. α, β, ...

If you find yourself using lots of type lambdas, and you don't mind reserving those identifiers, then this compiler plugin is for you!

Using the plugin

Kind-projector supports Scala 2.10, 2.11, and 2.12.0-M3.

To use this plugin in your own projects, add the following lines to your build.sbt file:

resolvers += Resolver.sonatypeRepo("releases")

addCompilerPlugin("org.spire-math" %% "kind-projector" % "0.7.1")

// if your project uses multiple Scala versions, use this for cross building
addCompilerPlugin("org.spire-math" % "kind-projector" % "0.7.1" cross CrossVersion.binary)

That's it!

Versions of the plugin earlier than 0.6.2 require a different resolver. For these earlier releases, use this:

resolvers += "bintray/non" at ""

Inline Syntax

The simplest syntax to use is the inline syntax. This syntax resembles Scala's use of underscores to define anonymous functions like _ + _.

Since underscore is used for existential types in Scala (and it is probably too late to change this syntax), we use ? for the same purpose. We also use +? and -? to handle covariant and contravariant types parameters.

Here are a few examples:

Tuple2[?, Double]        // equivalent to: type R[A] = Tuple2[A, Double]
Either[Int, +?]          // equivalent to: type R[+A] = Either[Int, A]
Function2[-?, Long, +?]  // equivalent to: type R[-A, +B] = Function2[A, Long, B]
EitherT[?[_], Int, ?]    // equivalent to: type R[F[_], B] = EitherT[F, Int, B]

As you can see, this syntax works when each type parameter in the type lambda is only used in the body once, and in the same order. For more complex type lambda expressions, you will need to use the function syntax.

Function Syntax

The more powerful syntax to use is the function syntax. This syntax resembles anonymous functions like x => x + 1 or (x, y) => x + y. In the case of type lambdas, we wrap the entire function type in a Lambda or λ type. Both names are equivalent: the former may be easier to type or say, and the latter is less verbose.

Here are some examples:

Lambda[A => (A, A)]              // equivalent to: type R[A] = (A, A)
Lambda[(A, B) => Either[B, A]]   // equivalent to: type R[A, B] = Either[B, A]
Lambda[A => Either[A, List[A]]]  // equivalent to: type R[A] = Either[A, List[A]]

Since types like (+A, +B) => Either[A, B] are not syntactically valid, we provide two alternate methods to specify variance when using function syntax:

  • Plus/minus: (+[A], +[B]) => Either[A, B]
  • Backticks: (`+A`, `+B`) => Either[A, B]

(Note that unlike names like ?, + and - do not have to be reserved. They will only be interpreted this way when used in parameters to Lambda[...] types, which should never conflict with other usage.)

Here are some examples with variance:

λ[`-A` => Function1[A, Double]]          // equivalent to: type R[-A] = Function1[A, Double]
λ[(-[A], +[B]) => Function2[A, Int, B]]  // equivalent to: type R[-A, +B] = Function2[A, Int, B]
λ[`+A` => Either[List[A], List[A]]]      // equivalent to: type R[+A] = Either[List[A], List[A]]

The function syntax also supports higher-kinded types as type parameters. The syntax overloads the existential syntax in this case (since the type parameters to a type lambda should never contain an existential).

Here are a few examples with higher-kinded types:

Lambda[A[_] => List[A[Int]]]  // equivalent to: type R[A[_]] = List[A[Int]]
Lambda[(A, B[_]) => B[A]]     // equivalent to: type R[A, B[_]] = B[A]

Finally, variance annotations on higher-kinded sub-parameters are supported using backticks:

Lambda[`x[+_]` => Q[x, List] // equivalent to: type R[x[+_]] = Q[x, List]
Lambda[`f[-_, +_]` => B[f]   // equivalent to: type R[f[-_, +_]] = B[f]

The function syntax with backtick type parameters is the most expressive syntax kind-projector supports. The other syntaxes are easier to read at the cost of being unable to express certain (hopefully rare) type lambdas.


The inline syntax is the tersest and is often preferable when possible. However, there are some type lambdas which it cannot express.

For example, imagine that we have trait Functor[F[_]].

You might want to write Functor[Future[List[?]]], expecting to get something like:

type X[a] = Future[List[a]]

However, ? always binds at the tightest level, meaning that List[?] is interpreted as type X[a] = List[a], and that Future[List[?]] is invalid.

In these cases you should prefer the lambda syntax, which would be written as:

Functor[Lambda[a => Future[List[a]]]]

Other types which cannot be written correctly using inline syntax are:

  • Lambda[a => (a, a)] (repeated use of a).
  • Lambda[(a, b) => Either[b, a] (reverse order of type params).
  • Lambda[(a, b) => Function1[a, Option[b]] (similar to example).

(And of course, you can use λ[...] instead of Lambda[...] in any of these expressions.)

Under The Hood

This section shows the exact code produced for a few type lambda expressions.

Either[Int, ?]
({type Λ$[β] = Either[Int, β]})#Λ$

Function2[-?, String, +?]
({type Λ$[-α, +γ] = Function2[α, String, γ]})#Λ$

Lambda[A => (A, A)]
({type Λ$[A] = (A, A)})#Λ$

Lambda[(`+A`, B) => Either[A, Option[B]]]
({type Λ$[+A, B] = Either[A, Option[B]]})#Λ$

Lambda[(A, B[_]) => B[A]]
({type Λ$[A, B[_]] = B[A]})#Λ$

As you can see, names like Λ$ and α are forbidden because they might conflict with names the plugin generates.

If you dislike these unicode names, pass -Dkp:genAsciiNames=true to scalac to use munged ASCII names. This will use L_kp in place of Λ$, X_kp0 in place of α, and so on.

Building the plugin

You can build kind-projector using SBT 0.13.0 or newer.

Here are some useful targets:

  • compile: compile the code
  • package: build the plugin jar
  • test: compile the test files (no tests run; compilation is the test)
  • console: launch a REPL with the plugin loaded so you can play around

You can use the plugin with scalac by specifying it on the command-line. For instance:

scalac -Xplugin:kind-projector_2.10-0.6.0.jar test.scala

Known issues & errata

When dealing with type parameters that take covariant or contravariant type parameters, only the function syntax is supported. Huh???

Here's an example that highlights this issue:

def xyz[F[_[+_]]] = 12345
trait Q[A[+_], B[+_]]

// we can use kind-projector to adapt Q for xyz
xyz[λ[`x[+_]` => Q[x, List]] // ok

// but these don't work (although support for the second form
// could be added in a future release).
xyz[Q[?[+_], List]]          // invalid syntax
xyz[Q[?[`+_`], List]]        // unsupported

There have been suggestions for better syntax, like [A, B]Either[B, A] or [A, B] => Either[B, A] instead of Lambda[(A, B) => Either[B, A]]. Unfortunately this would actually require modifying the parser (i.e. the language itself) which is outside the scope of this project (at least, until there is an earlier compiler phase to plug into).

Others have noted that it would be nicer to be able to use _ for types the way we do for values, so that we could use Either[Int, _] to define a type lambda the way we use 3 + _ to define a function. Unfortunately, it's probably too late to modify the meaning of _, which is why we chose to use ? instead.

Update: the Typelevel compiler contains a built-in syntax for type lambdas!

Future Work

As of 0.5.3, kind-projector should be able to support any type lambda that can be expressed via type projections, at least using the function syntax. If you come across a type for which kind-projector lacks a syntax, please report it.


Kind projector is an unusual compiler plugin in that it runs before the typer phase. This means that the rewrites and renaming we are doing are relatively fragile, and the author disclaims all warranty or liability of any kind.

(That said, there are currently no known bugs.)

If you are using kind-projector in one of your projects, please feel free to get in touch to report problems (or a lack of problems)!

Copyright and License

All code is available to you under the MIT license, available at and also in the COPYING file.

Copyright Erik Osheim, 2011-2015.

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