The Cache effect algebra allows interacting with a global key-value data store. It declares several abstract operations to read and write data into the store.

In order to enable this algebra, you can depend on freestyle-cache:

libraryDependencies += "io.frees" %% "frees-cache" % "0.8.2"

This algebra is parametrized on the types Key, and Val, for keys and values in the store, respectively.

class KeyValueProvider[Key, Val] {
  @free sealed trait CacheM {
    def get(key: Key):              FS[Option[Val]]
    def put(key: Key, newVal: Val): FS[Unit]
    def del(key: Key):              FS[Unit]
    def has(key: Key):              FS[Boolean]
    def keys:                       FS[List[Key]]
    def clear:                      FS[Unit]

To create the algebra parametric on the types of Key and Value, we wrap the declaration of the algebra inside a KeyValueProvider; but note that this class has no instance data. The algebra assumes no specific implementation or representation of the data store, since that is a matter for each handler of the algebra. For the same reason, it poses no type constraint on Key or Val with regards to ordering, hashing, or encoding, but it is assumed that equality is defined for both types.

Using the Cache Effect

The following code snippet shows how to import and use the operations from the Cache algebra inside a program:

// import

// import

// import

import cats.implicits._
// import cats.implicits._

val prov = new KeyValueProvider[Char, Int]
// prov:[Char,Int] =

import prov.CacheM
// import prov.CacheM

import prov.implicits._
// import prov.implicits._

def loadFrom[F[_]: prov.CacheM] = {
  for {
    a <- FreeS.pure(1)
    b <- CacheM[F].get('a')
    c <- FreeS.pure(1)
  } yield a + b.getOrElse(0) + c
// loadFrom: [F[_]](implicit evidence$1: prov.CacheM[F])[[β$0$][F,β$0$],Int]


The set of abstract operations of the Cache algebra are specified as follows:

  • get(key: Key): M[Option[Val]] issues a query to the data store on a given key. The result can be None, if the store has no mapping for that key, or Some(v) if the key is mapped to the value v.
  • put(key: Key, v: Value) issues a command to associate a given key to a given value
  • del(key: Key) issues a command to disassociate a given key from the store, if it was present.
  • clear is an abstract operation to disassociate all keys and values in the store.
  • keys is a query to retrieve a list of keys for which an association is present in the store. No restriction is posed on the order in which the keys will appear on the list, in relation to any ordering for the Key type.


In this section we describe some laws that specify the intended semantics of the CacheM effect algebra, which any handler or interpreter for it should hold. These laws are applicable to any group of independent operations within the FreeS.Par[F, ?] type, which is the Applicable fragment. However, the laws may not hold in the general Free[FreeS.Par[F, ?], ?] case, of a sequential group of independent operations. Intuitively, a group FreeS.Par of operations is run atomically on the data store, without interleaving any other operations, and every command’s effect should be immediately visible on succeeding operations.

Each law is an equality between two programs of type FreeS.Par[F, A], where equality means that:

  • The results of type A from interpreting both programs should be equal; and
  • their side-effects on the data store are not distinguishable: there is no sequence FreeS.Par of CacheM foperations that, if attached to both programs to the left or to the right, would yield a different result.

In these laws, we use the binary operators <*, *>, and |@|, to indicate the composition and projection of operations on the left, on the right, or on a pair. These operators come from the cats.syntax.CartesianOps trait. We use variables x and y to denote keys of type Key, with x != y, and we use v, or w to denote values of type Value.


A get abstract operation is a query that should not modify the store. This can be expressed with these conditions:

  1. Any get operation whose result is ignored can be discarded from the program.
  2. Consecutive get operations on a same key x should give the same result.
  3. Consecutive get operations on different keys should give the same result for each key.
get(x) *> ff   === ff <* get(x) === ff   // for any other operation ff
get(x) |@| get(x)  === get(x).map( dup )
get(x) |@| get(y)  === ( get(y) |@| get(x) ).map( swap )

Where swap is the function of type (A,B) => (B,A), and dup is the function of type A => (A,A).


A put operation on a key in the store is like an assignment to a mutable variable. The following laws restrict put operations and get operations:

  1. Two put operations on the same key are equivalent to the rightmost (last) one.
  2. Two put operations on different keys can be swapped.
  3. On a same key x, a put followed by the get is the same as giving the put value, right after the put operation.
  4. Operations get and put on different keys can be swapped.
put( x, v) *> put( x, w) === put( x, w)
put( x, v) *> put( y, w) === put( y, w) *> put( x, v)
put( x, v) *> get( x)    === put( x, v) *> pure( Some(v) )
put( x, v) *> get( y)    === get( y) <* put( x, v)

The laws concerning del with get are the following ones:

  • On a same key x, the result of a del right after a get should be None:
  • On different keys x and n, a del and a get can be swapped:
del( x) *> get( x) === del( x) *> pure( None)
del( x) *> get( y) === get( y) <* del( x)

The following laws concern several delete interactions, as well as put and delete operations.

  1. Two del operations on a same key x are equivalent to just one of them.
  2. Two del operations on different keys x, y, can be swapped.
  3. On a same key x, a put followed by a delete should be equivalent to just the delete.
  4. On a same key x, a del followed by a put should be equivalent to just the put operation.
  5. Operations put and del on different keys can be reordered swapped.
del( x) *> del( x) === del( x)                     // 1
del( x) *> del( y) === del( y) *> del( x)          // 2
put( x, v) *> del( x) === del( x)                  // 3
del( x, v) *> put( x, v) === put( x, v)            // 4
del( x, v) *> put( y, v) === put( y, v) *> del( x) // 5
Keys, Clear

The clear abstract operation is equivalent to issuing a del on all existing keys.

  1. After a clear, a get should always return None:
  2. After a clear, any del is redundant:
  3. Any put operation right before a clear can be ignored:
clear *> get( x) === clear *> pure( None)
clear *> del( x) === clear
put( x, v) *> clear === clear

The keys abstract operation, that returns a list of keys of type Key, must hold the following conditions:

  1. The list should contain a key if and only if the get on that key would be Some.
  2. The keys should not modify the data-store, so any get following it should give the same result.
get(x).map(_.isDefined) === ) //1
keys *> get(x) === get(x)


Concurrent Hash Map

The package freestyle.cache.hashmap in the project freestyle-cache, contains an in-program (no I/O needed) effect-handler / interpreter for the CacheM effect algebra. This interpreter implements the data store with a Concurrent Hash Map. Note that the ConcurrentHashMap provides no global locking, nor any facilities for issuing and executing transactionally a set of operations. Thus, the laws described above may not hold for this interpreter.

Hashable Type Class

A hash table divides keys according to each key’s hash code. In particular, a ConcurrentHashMap uses the hashCode() method from the Object class (Any in Scala). Most classes from the Java or Scala libraries define this method, and in Scala each case class has a definition based on its fields. However, using this methods directly has two problems:

  • Because hashCode is an object method, fixed by the class, we can not use different hash algorithms in different hash tables.
  • Since Object provides a default implementation of hashCode, most programmer-defined classes may not override it.

To avoid these problems, we define a Scala typeclass Hasher[A], i.e. a trait with a single hashCode function, and for building the CacheM interpreter we require an instance of Hasher for the Key type. We provide default implementations of this trait for several simple types.


The package freestyle.cache.redis in the project freestyle-cache-redis provides a handler-interpreter for the CacheM effect algebra. This interpreter implements the data store using a Redis database. Access to a Redis server is done through rediscala, an Akka-based client library for Scala.


In the rediscala client for Redis, the keys used for indexing values are always of type String; whereas a special binary codification is needed for values (of type Value). in the Redis integration we use a couple of typeclasses to transform either keys or values, to and from String:

  • The Format[A] trait defines the function from the Key type (the parameter for the CacheM algebra) to String. The companion object provides a few helper methods and default instances.
  • The Parse[A] trait is a function to try to parse a Key from a String. The return type is an Option[Key], to indicate the possibility of failure.

These typeclasses are used for transforming

The use of these typeclasses is also intended to avoid coupling the programs based on freestyle to a particular client library.

Batching and Transactions

As explained in the guide, any Freestyle program has two levels: the applicative level (in type FreeS.Par) contains sequences of locally independent operations, where the result of one can not be used as argument to another. Such dependencies are only handled in the monadic level, in which the results from a group of operations are retrieved to be used in another group.

In Redis, since each command is issued through the network, retrieving any value incurs in a round-trip latency. This reduces performance, and exposes the results of fqueries to concurrent modifications of the data store. To avoid these problems, we want the Redis handler to run any sequence of operations inside a FreeS.Par so that:

  • Commands issued to the Redis server are pipelined, so as to reduce the total roundtrip to one; and
  • the whole command sequence is run atomically, that is, without interleaving any other operation.

Regarding pipelining, the rediscala client already uses Redis pipelining to issue operations as soon as they are enqueued. For atomicity, the implementation runs each FreeS.Par sequence of independent operations in a Redis transaction. This allows the implementation to hold the laws for the CacheM effect algebra given above.


To combine several CacheM operations in a single FreeS.Par, we use the Kleisli class from the cats library. Intuitively, for each single CacheM operation the interpreter does not issue an operation to the client, but instead creates a Function that, when applied to a client, will issue the command through it.

def del[Key](keys: List[Key])(implicit format: Format[Key]): Ops[Future, Long] =
  Kleisli((client: KeyCommands) => client.del( _*))

Given two such Kleisli objects that correspond to two independent operations, composing them can be done through the default instance of Applicative for Kleisli in cats. The result would be a function that takes a client and issues the commands for the operations in the order in which they appear.