Update documentation

README.md

@@ -1,6 +1,11 @@
 # CRDT
 
-**TODO: Add description**
+This is a set of basic, composable and extensible CRDTs.
+
+A CRDT is defined as Conflict-free Replicated Data Type,
+see https://en.wikipedia.org/wiki/Conflict-free_replicated_data_type
+
+Please refer to the API Reference for usage documentation and examples.
 
 ## Installation
 
@@ -19,3 +24,213 @@ Documentation can be generated with [ExDoc](https://github.com/elixir-lang/ex_do
 and published on [HexDocs](https://hexdocs.pm). Once published, the docs can
 be found at <https://hexdocs.pm/crdt>.
 
+## List of implemented CRDTs
+
+```
+           +----------------++---------++-----------++------------++---------++----------------+
+Data Type  |  LWW-Register  || AWORSet || G-Counter || PN-Counter || AWORMap || Delta-AWORSet  |
+           +----------------++---------++-----------++------------++---------++----------------+
+CRDT Type  |  Commutative    |                        Convergent                               |
+           +-----------------+-----------------------------------------------------------------+
+```
+
+## Examples
+
+These are simple examples that should give an idea of how to use some of the data types,
+and what to expect in each case.
+
+### `CRDT.GCounter`
+
+A `CRDT.GCounter` is a growth-only counter. It can be initialized with positive values on
+behalf of actors. The resulting value will always be the sum of the values across actors.
+An empty counter will have the value '0'.
+
+
+#### Initializing
+
+``` elixir
+counter = CRDT.GCounter.new
+CRDT.value(counter) # => 0
+
+counter = CRDT.GCounter.new(actor1: 5, actor2: 10)
+CRDT.value(counter) # => 15
+```
+
+#### Incrementing
+
+Incrementing a `CRDT.GCounter` is done via the `CRDT.GCounter.inc/2` function.
+If the actor key does not exist yet, it is assumed that the given value is the starting
+value.
+
+``` elixir
+counter = CRDT.GCounter.new
+counter = counter |> CRDT.GCounter.inc(:a, 5) # => %CRDT.GCounter{value: %{a: 5}}
+counter = counter |> CRDT.GCounter.inc(:a, 2) # => %CRDT.GCounter{value: %{a: 7}}
+CRDT.value(counter) # => 7
+```
+
+#### Merging
+
+Merging two GCounters preserves all actors in both, taking the higher value if an actor exists in both GCounters.
+
+``` elixir
+counter1 = CRDT.GCounter.new(actor1: 5, actor2: 3)
+counter2 = CRDT.GCounter.new(actor2: 1, actor3: 8)
+CRDT.merge(counter1, counter2) # => %CRDT.GCounter{value: %{actor1: 5, actor2: 3, actor3: 8}}
+```
+
+### `CRDT.PNCounter`
+
+A `CRDT.PNCounter` is used to process events that can increment or decrement the value.
+
+#### Initializing
+
+When initialized without starting values, the `CRDT.PNCounter` initial value is '0'.
+
+``` elixir
+counter = CRDT.PNCounter.new #=> %CRDT.PNCounter{pos: %{}, neg: %{}}
+CRDT.value(counter) #=> 0
+```
+
+Initial values can be supplied as positive and negative actor => value maps.
+
+``` elixir
+counter = CRDT.PNCounter.new(pos: %{a: 1, b: 2}, neg: %{a: 8, b: 7}) 
+CRDT.value(counter) #=> -12
+```
+
+#### Incrementing
+Incrementing a `CRDT.PNCounter` is done via the `CRDT.PNCounter.increment/3` function.
+Incrementing a pncounter will update only the `pos` actor => value map.
+If no value is given, it will be updated by 1 by default.
+
+``` elixir
+pncounter = CRDT.PNCounter.new
+pncounter = pncounter |> CRDT.PNCounter.increment(:a, 5) # => %CRDT.PNCounter{pos: %{a: 2}, neg: %{}}
+pncounter = pncounter |> CRDT.PNCounter.increment(:a, 2) # => %CRDT.PNCounter{pos: %{a: 4}, neg: %{}}
+CRDT.value(pncounter) # => 7
+```
+
+#### Decrementing
+Decrementing a `CRDT.PNCounter` is done via the `CRDT.PNCounter.decrement/3` function.
+Incrementing a pncounter will update only the `neg` actor => value map.
+If no value is given, it will be updated by 1 by default.
+
+``` elixir
+pncounter = CRDT.PNCounter.new
+pncounter = pncounter |> CRDT.PNCounter.decrement(:a, 5) # => %CRDT.PNCounter{pos: %{}, neg: %{a: 5}}
+pncounter = pncounter |> CRDT.PNCounter.decrement(:a, 2) # => %CRDT.PNCounter{pos: %{}, neg: %{a: 7}}
+CRDT.value(pncounter) # => -7
+```
+
+#### Merging
+Merging two PNCounters preserves all actors in both, taking the total sum of all positive and negative values.
+
+``` elixir
+pncounter1 = CRDT.PNCounter.new |> CRDT.PNCounter.increment(actor1: 5, actor2: 3)
+pncounter2 = CRDT.PNCounter.new |> CRDT.PNCounter.decrement(actor1: 5, actor3: 3)
+merged = CRDT.merge(pncounter1, pncounter2) # => %CRDT.PNCounter{value: %{actor1: 5, actor2: 3, actor3: 8}}
+CRDT.value(merged) # => 0
+```
+
+### `CRDT.LWWRegister`
+
+A `CRDT.LWWRegister` is a crdt used when we are interested in having the most recent information available (Least Write Wins).
+It contains a value and the corresponding timestamp.
+
+#### Initializing
+
+When initialized without starting values, the `CRDT.LWWRegister` initial value is 'nil'.
+
+``` elixir
+register = CRDT.LWWRegister.new #=> %CRDT.LWWRegister{value: nil, timestamp: 1698400752943930708}
+CRDT.value(counter) #=> nil
+```
+
+#### Updating
+
+Updating a `CRDT.LWWRegister` is done via the `CRDT.LWWRegister.set/2` function.
+This will update the value with the current system time.
+
+``` elixir
+register = CRDT.LWWRegister.new
+register = register |> CRDT.LWWRegister.set("hello register") # => %CRDT.LWWRegister{value: "hello register", timestamp: 1700218890688914751}
+CRDT.value(register) # => "hello register"
+```
+
+#### Merging
+
+Merging two LWWRegisters will simply take the most recent value.
+
+``` elixir
+register1 = CRDT.LWWRegister.new |> CRDT.LWWRegister.set("hello")
+register2 = CRDT.LWWRegister.new |> CRDT.LWWRegister.set("latest_hello")
+merged = CRDT.merge(register1, register2)
+CRDT.value(merged) # => "latest_hello"
+```
+
+### `CRDT.AWORMap`
+
+A `CRDT.AWORMap` is used to store events in a key => value map. The values stored in an AWORMap are crdts themselves.
+Merging strategy follows those of the crdts contained in the map.
+
+#### Initializing
+The value of a new map is an empty map.
+
+``` elixir
+map = CRDT.AWORMap.new
+CRDT.value(map) #=> %{}
+```
+When initialized the `CRDT.AWORMap` has this structure:
+
+``` elixir
+%CRDT.AWORMap{
+  keys: %CRDT.AWORSet{
+    dot_kernel: %CRDT.DotKernel{
+      dot_context: %CRDT.DotContext{version_vector: %{}, dot_cloud: []},
+      entries: %{}
+    }
+  },
+  entries: %{}
+}
+```
+
+Inside `CRDT.DotKernel` are the operations performed on the map: which actor made the change, the number of operation and the value added.
+Inside the outer entries there is the map keylist with the current values.
+
+It's possible to put a crdt in the `CRDT.AWORMap` through the `CRDT.AWORMap.put/4` function.
+It's necessary to specify the actor who make the change, the key under which the crdt will be stored and the crdt itself.
+
+``` elixir
+map = CRDT.AWORMap.new
+map = map |> CRDT.AWORMap.put(:a, :key, CRDT.GCounter.new())
+CRDT.value(map) #=> %{key: 0}
+```
+
+#### Updating
+
+Updating a `CRDT.AWORMap` is done via the `CRDT.AWORMap.update!/4` function.
+It's possible to pass a function as an argument that will be applied as the updated value of `key`
+
+``` elixir
+map = CRDT.AWORMap.new
+map = map |> CRDT.AWORMap.put(:a, :key, CRDT.GCounter.new() |> CRDT.GCounter.inc(:a, 1))
+CRDT.value(map) #=> %{key: 1}
+map = map |> CRDT.AWORMap.update!(:a, :key, &(CRDT.GCounter.inc(&1, :a, 100)))
+CRDT.value(map) #=> %{key: 101}
+```
+
+##### Update vs Update! 
+- `CRDT.AWORMap.update!/4` if the given "key" is not present in the AWORMap, a `KeyError` exception is raised.
+- `CRDT.AWORMap.update/5` if the given "key" is not present in the AWORMap, the default value is inserted as the crdt of `key`
+
+#### Merging
+
+Merging two AWORMaps uses the same merge strategies as their crdts stored inside them.
+
+``` elixir
+map1 = CRDT.AWORMap.new |> CRDT.AWORMap.put(:a, :key, CRDT.GCounter.new() |> CRDT.GCounter.inc(:a, 1))
+map2 = CRDT.AWORMap.new |> CRDT.AWORMap.put(:a, :key2, CRDT.GCounter.new() |> CRDT.GCounter.inc(:a, 100))
+merged_map = CRDT.merge(map1, map2)
+CRDT.value(merged_map) #=> %{key: 100}
+```

lib/crdt.ex

@@ -1,6 +1,7 @@
 defprotocol CRDT do
   @moduledoc """
   Protocol defining the interface for CRDTs.
+
   """
 
   @type actor :: term()

lib/crdt/access.ex

@@ -1,8 +1,22 @@
 defprotocol CRDT.Access do
+  @moduledoc """
+  This protocol defines the access methods for CRDTs.
+  """
+  @doc """
+  Returns the value at the given path.
+  """
   @spec get_in(t(), nonempty_list(term())) :: term()
   def get_in(t, list)
+
+  @doc """
+  Adds the given value to the given path.
+  """
   @spec put_in(t(), term(), nonempty_list(term()), CRDT.crdt()) :: CRDT.crdt()
   def put_in(t, actor, list, value)
+
+  @doc """
+  Updates the value at the given path.
+  """
   @spec update_in(t(), term(), nonempty_list(term()), (term() -> term())) :: CRDT.crdt()
   def update_in(t, actor, list, fun)
 end

lib/crdt/awor_map.ex

@@ -1,5 +1,10 @@
 defmodule CRDT.AWORMap do
-  @moduledoc false
+  @moduledoc """
+  An add-wins observed-remove map (AWORMap) is a map of keys to CRDTs based on sets.
+
+  An AWORMap is a map of keys to CRDTs. It is a CRDT itself and can be used to
+  implement other CRDTs.
+  """
 
   @type t :: %__MODULE__{
           keys: CRDT.AWORSet.t(),
@@ -102,7 +107,7 @@ defmodule CRDT.AWORMap do
   def get(%__MODULE__{entries: entries}, key, default \\ nil), do: Map.get(entries, key, default)
 
   @doc """
-  Updates the `key` in the AWORMap with the the given function to the crdt on behalf of `actor`.
+  Updates the `key` in the AWORMap with the given function to the crdt on behalf of `actor`.
 
   If `key` is present in AWORMap then the existing crdt is passed to `fun` and its result is
   used as the updated crdt of `key`. If `key` is

lib/crdt/awor_set.ex

@@ -1,5 +1,10 @@
 defmodule CRDT.AWORSet do
-  @moduledoc false
+  @moduledoc """
+  An add-wins observed-remove set (AWORSet) is a set that allows adding and
+  removing elements.
+
+  It is a variant of a 2P-Set that uses a DotKernel to track the additions and removals.
+  """
 
   @type actor :: term
   @type value :: term

lib/crdt/delta_awor_set.ex

@@ -1,5 +1,12 @@
 defmodule CRDT.DeltaAWORSet do
-  @moduledoc false
+  @moduledoc """
+  A delta add-wins observed-remove set (DeltaAWORSet) is an opimized set that
+  allows adding and removing elements.
+
+  It is a variant of a 2P-Set that uses a DotKernel to track the additions and removals.
+  The delta variant optimizes the merge operation by only merging the delta of the
+  two sets.
+  """
 
   @type actor :: term
   @type value :: term

lib/crdt/dot_context.ex

@@ -1,5 +1,10 @@
 defmodule CRDT.DotContext do
-  @moduledoc false
+  @moduledoc """
+  A DotContext is a data structure that contains a version vector and a dot cloud.
+
+  The version vector is a map from actors to the maximum version of a dot that has been added to
+  the dot context on behalf of that actor.
+  """
 
   @type actor :: term
   @type version :: pos_integer

lib/crdt/dot_kernel.ex

@@ -1,5 +1,12 @@
 defmodule CRDT.DotKernel do
-  @moduledoc false
+  @moduledoc """
+  A DotKernel is a data structure that contains a DotContext and a map of dots to values.
+
+  The DotContext is a data structure that contains a version vector and a dot cloud.
+
+  The version vector is a map from actors to the maximum version of a dot that has been added to
+  the dot context on behalf of that actor.
+  """
 
   @type actor :: term
   @type version :: pos_integer
@@ -121,7 +128,7 @@ defmodule CRDT.DotKernel do
       for {dot, entry_value} <- entries, entry_value == value, reduce: entries do
         entries ->
           # The corresponding dot says in the dot context and acts as a tombstone.
-          # So we can avoid readding it when merging with an out of date replica.
+          # So we can avoid reading it when merging with an out of date replica.
           Map.delete(entries, dot)
       end