This is a catalogue of the major functions, type classes, and data types in Cats. It serves as a bird’s-eye view of each class capabilities. It is also intended as a go-to reference for Cats users, who may not recall the answer to questions like these:

  • What is the difference between unit and void?
  • To discard the first value and keep only the first effect, is it <* or *>?
  • How do I make a computation F[A] fail by checking a condition on the value?

The signatures and type-classes have been simplified, are described below. If you want a printable version, you can also check out this cats-cheatsheet.

WARNING: this page is written manually, and not automatically generated, so many things may be missing. If you find a mistake, or addition, please submit a PR following the guidelines below.

Type-Classes over an F[_]


Type Method Name
F[A] => F[Unit] void
F[A] => B => F[B] as
F[A] => (A => B) => F[B] map
F[A] => (A => B) => F[(A,B)] fproduct
F[A] => (A => B) => F[(B,A)] fproductLeft
F[A] => B => F[(B, A)] tupleLeft
F[A] => B => F[(A, B)] tupleRight
(A => B) => (F[A] => F[B]) lift


Type Method Name Symbol
F[A] => F[B] => F[A] productL <*
F[A] => F[B] => F[B] productR *>
F[A] => F[B] => F[(A,B)] product  
F[A => B] => F[A] => F[B] ap <*>
F[A => B => C] => F[A] => F[B] => F[C] ap2  
F[A] => F[B] => (A => B => C) => F[C] map2  


Type Method Name Notes
A => F[A] pure  
=> F[Unit] unit  
Boolean => F[Unit] => F[Unit] when Performs effect iff condition is true
  unless Adds effect iff condition is false


Type Method Name
F[F[A]] => F[A] flatten
F[A] => (A => F[B]) => F[B] flatMap
F[A] => (A => F[B]) => F[(A,B)] mproduct
F[Boolean] => F[A] => F[A] => F[A] ifM
F[A] => (A => F[B]) => F[A] flatTap


Type Method Name Notes
F[A] => (A => Boolean) => F[A] filter  
F[A] => (A => Option[B]) => F[B] mapFilter  
F[A] => (A => B) => F[B] collect The A => B is a PartialFunction
F[Option[A]] => F[A] flattenOption  


The source code of Cats uses the E type variable for the error type.

Type Method Name Notes
E => F[A] raiseError  
F[A] => F[Either[E,A]] attempt  
F[A] => (E => A) => F[A] handleError  
F[A] => (E => F[A]) => F[A] handleErrorWith  
F[A] => (E => A) => F[A] recover The E => A is a PartialFunction.
F[A] => (E => F[A]) => F[A] recoverWith The E => F[A] is a PartialFunction.
F[A] => (E => F[Unit]) => F[A] onError The E => F[Unit] is a PartialFunction.
Either[E,A] => F[A] fromEither  
Option[A] => E => F[A] liftFromOption  


Like the previous section, we use the E for the error parameter type.

Type Method Name Notes
F[A] => E => (A => Boolean) => F[A] ensure  
F[A] => (A => E) => (A => Boolean) => F[A] ensureOr  
F[A] => (E => E) => F[A] adaptError The E => E is a PartialFunction.
F[Either[E,A]] => F[A] rethrow  


Type Method Name Constraints
F[A] => Boolean isEmpty  
F[A] => Boolean nonEmpty  
F[A] => Long size  
F[A] => (A => Boolean) => Boolean forall  
F[A] => (A => Boolean) => Boolean exists  
F[A] => A unorderedFold A: CommutativeMonoid
F[A] => (A => B) => B unorderedFoldMap B: CommutativeMonoid


Type Method Name Constraints
F[A] => A fold A: Monoid
F[A] => B => ((B,A) => B) => F[B] foldLeft  
F[A] => (A => B) => B foldMap B: Monoid
F[A] => (A => G[B]) => G[B] foldMapM G: Monad and B: Monoid
F[A] => (A => B) => Option[B] collectFirst The A => B is a PartialFunction
F[A] => (A => Option[B]) => Option[B] collectFirstSome  
F[A] => (A => G[B]) => G[Unit] traverse_ G: Applicative
F[G[A]] => G[Unit] sequence_ G: Applicative
F[A] => (A => Either[B, C] => (F[B], F[C]) partitionEither G: Applicative


Type Method Name Constraints
F[A] => ((A,A) => A) => A reduceLeft  
F[A] => A reduce A: Semigroup


Type Method Name Constraints
F[G[A]] => G[F[A]] sequence G: Applicative
F[A] => (A => G[B]) => G[F[B]] traverse G: Applicative
F[A] => (A => G[F[B]]) => G[F[B]] flatTraverse F: FlatMap and G: Applicative
F[G[F[A]]] => G[F[A]] flatSequence G: Applicative and F: FlatMap
F[A] => F[(A,Int)] zipWithIndex  
F[A] => ((A,Int) => B) => F[B] mapWithIndex  
F[A] => ((A,Int) => G[B]) => G[F[B]] traverseWithIndex F: Monad


Constructors and wrappers

Data Type is an alias or wrapper of
OptionT[F[_], A] F[Option[A]]
EitherT[F[_], A, B] F[Either[A,B]
Kleisli[F[_], A, B] A => F[B]
Reader[A, B] A => B
ReaderT[F[_], A, B] Kleisli[F, A, B]
Writer[A, B] (A,B)
WriterT[F[_], A, B] F[(A,B)]
Tuple2K[F[_], G[_], A] (F[A], G[A])
EitherK[F[_], G[_], A] Either[F[A], G[A]]
FunctionK[F[_], G[_]] F[X] => G[X] for every X
F ~> G Alias of FunctionK[F, G]


For convenience, in these types we use the symbol OT to abbreviate OptionT.

Type Method Name Constraints
=> OT[F, A] none F: Applicative
A => OT[F, A] some or pure F: Applicative
F[A] => OT[F, A] liftF F: Functor
OT[F, A] => F[Option[A]] value  
OT[F, A] => (A => B) => OT[F, B] map F: Functor
OT[F, A] => (F ~> G) => OT[G, B] mapK  
OT[F, A] => (A => Option[B]) => OT[F, B] mapFilter F: Functor
OT[F, A] => B => (A => B) => F[B] fold or cata  
OT[F, A] => (A => OT[F, B]) => OT[F,B] flatMap  
OT[F, A] => (A => F[Option[B]]) => F[B] flatMapF F: Monad
OT[F, A] => A => F[A] getOrElse F: Functor
OT[F, A] => F[A] => F[A] getOrElseF F: Monad
OT[F, A] => OT[F, A] => OT[F, A]    


Here, we use ET to abbreviate EitherT; and we use A and B as type variables for the left and right sides of the Either.

Type Method Name Constraints
A => ET[F, A, B] leftT F: Applicative
B => ET[F, A, B] rightT F: Applicative
  pure F: Applicative
F[A] => ET[F, A, B] left F: Applicative
F[B] => ET[F, A, B] right F: Applicative
  liftF F: Applicative
Either[A, B] => ET[F, A, B] fromEither F: Applicative
Option[B] => A => ET[F, A, B] fromOption F: Applicative
F[Option[B]] => A => ET[F, A, B] fromOptionF F: Functor
F[Option[B]] => F[A] => ET[F, A, B] fromOptionM F: Monad
Boolean => B => A => ET[F, A, B] cond F: Applicative
ET[F, A, B] => (A => C) => (B => C) => F[C] fold F: Functor
ET[F, A, B] => ET[F, B, A] swap F: Functor
ET[F, A, A] => F[A] merge  

Kleisli (or ReaderT)

Here, we use Ki as a short-hand for Kleisli.

Type Method Name Constraints
Ki[F, A, B] => (A => F[B]) run  
Ki[F, A, B] => A => F[B] apply  
A => Ki[F, A, A] ask F: Applicative
B => Ki[F, A, B] pure F: Applicative
F[B] => Ki[F, A, B] liftF  
Ki[F, A, B] => (C => A) => Ki[F, C, B] local  
Ki[F, A, B] => Ki[F, A, A] tap  
Ki[F, A, B] => (B => C) => Ki[F, A, C] map  
Ki[F, A, B] => (F ~> G) => Ki[G, A, B] mapK  
Ki[F, A, B] => (F[B] => G[C]) => Ki[F, A, C] mapF  
Ki[F, A, B] => Ki[F, A, F[B]] lower  

Type Classes for types F[_, _]


Type Method Name
F[A,B] => (A => C) => F[C,B] leftMap
F[A,B] => (B => D) => F[A,D] .rightFunctor and .map
F[A,B] => (A => C) => (B => D) => F[C,D] bimap


Type Method Name
F[A, B] => (B => C) => F[A, C] rmap
F[A, B] => (C => A) => F[C, B] lmap
F[A, B] => (C => A) => (B => D) => F[C,D] dimap

Strong Profunctor

Type Method Name
F[A, B] => F[(A,C), (B,C)] first
F[A, B] => F[(C,A), (C,B)] second

Compose, Category, Choice

Type Method Name Symbol
F[A, B] => F[C, A] => F[C, B] compose <<<
F[A, B] => F[B, C] => F[A, C] andThen >>>
=> F[A,A] id  
F[A, B] => F[C, B] => F[Either[A, C], B] choice |||
=> F[ Either[A, A], A] codiagonal  


Type Method Name Symbol
(A => B) => F[A, B] lift  
F[A,B] => F[C,D] => F[(A,C), (B,D)] split ***
F[A,B] => F[A,C] => F[A, (B,C)] merge &&&


Type Method Name Symbol
F[A,B] => F[C,D] => F[Either[A, C], Either[B, D]] choose +++
F[A,B] => F[Either[A, C], Either[B, C]] left  
F[A,B] => F[Either[C, A], Either[C, B]] right  


Because Сats is a Scala library and Scala has many knobs and switches, the actual definitions and the implementations of the functions and type-classes in Сats can be a bit obfuscated at first. To alleviate this, in this glossary we focus on the plain type signatures of the method, and ignore many of the details from Scala. In particular, in our type signatures:

  • We use A,B,C for type variables of kind *, and F, G, H for type variables of a higher kind.
  • We write type signatures in currified form: parameters are taken one at a time, and they are separated with the arrow => operation. In Scala, a method’s parameters may be split in several comma-separated lists.
  • We do not differentiate between methods from the type-class trait (e.g. trait Functor), or the companion object, or the syntax companion (implicit class).
  • For functions defined as method of the typeclass trait, we ignore the receiver object.
  • We ignore implicit parameters that represent type-class constraints; and write them on a side column instead.
  • We use A => B for both Function1[A, B] and PartialFunction[A, B] parameters, without distinction. We add a side note when one is a PartialFunction.
  • Some functions are defined through the Partially Applied Type Params pattern. We ignore this.
  • We ignore the distinction between by-name and by-value input parameters. We use the notation => A, without parameters, to indicate constant functions.
  • We ignore Scala variance annotations. We also ignore extra type parameters, which in some methods are added with a subtype-constraint, (e.g. B >: A). These are usually meant for flexibility, but we replace each one by its bound.