@spec allowed([t()],
  from: state(),
  to: state(),
  with: event(),
  as: :states | :transitions
) :: [
  {state(), state(), event()}
]

Returns the list of all the transitions, matching the options.

Used internally for the validations.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse(
...>     "idle --> |to_s1| s1\n" <>
...>     "s1 --> |to_s2| s2\n" <>
...>     "s1 --> |to_s3| s3\n" <>
...>     "s2 --> |to_s3| s3")
...> Finitomata.Transition.allowed(transitions, to: [:idle, :*])
[{:*, :idle, :__start__}, {:s3, :*, :__end__}]
iex> Finitomata.Transition.allowed(transitions, from: :s1)
[{:s1, :s2, :to_s2}, {:s1, :s3, :to_s3}]
iex> Finitomata.Transition.allowed(transitions, from: :s1, to: :s3)
[{:s1, :s3, :to_s3}]
iex> Finitomata.Transition.allowed(transitions, from: :s1, with: :to_s3)
[{:s1, :s3, :to_s3}]
iex> Finitomata.Transition.allowed(transitions, from: :s2, with: :to_s2)
[]

@spec allowed([t()], state(), event()) :: [state()]

Returns the list of all the transitions, matching the from state and the event.

Used internally for the validations.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns2 --> [*] : ko")
...> Finitomata.Transition.allowed(transitions, :s1, :foo)
[:s2]
...> Finitomata.Transition.allowed(transitions, :s1, :*)
[]

@spec allowed?([t()], state(), state()) :: boolean()

Returns true if the transition from → to is allowed, false otherwise.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns2 --> [*] : ko")
...> Finitomata.Transition.allowed?(transitions, :s1, :s2)
true
...> Finitomata.Transition.allowed?(transitions, :s1, :*)
false

@spec ambiguous([t()]) :: [{state(), {event(), state()}}]

Returns keyword list of {Finitomata.Transition.state(), [Finitomata.Transition.event()]} for transitions which do not have a determined to state.

Used internally for the validations.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse(
...>     "idle --> |to_s1| s1\n" <>
...>     "s1 --> |to_s2| s2\n" <>
...>     "s1 --> |to_s3| s3\n" <>
...>     "s2 --> |to_s1| s3\n" <>
...>     "s2 --> |ambiguous| s3\n" <>
...>     "s2 --> |ambiguous| s4\n" <>
...>     "s3 --> |determined| s3\n" <>
...>     "s3 --> |determined| s4\n")
...> Finitomata.Transition.ambiguous(transitions)
[s3: {:determined, [:s3, :s4]}, s2: {:ambiguous, [:s3, :s4]}]

@spec continuation(:states | :transitions, state(), [t()]) ::
  nil | Finitomata.Transition.Path.t() | [t()]

Returns the continuation from the state given which inevitably lead to other state(s).

All the transitions from this state are hard (ending with !,) which makes the FSM to go through all these states in :continue callbacks.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> entry : start\nentry --> exit : go!\nexit --> done : finish\ndone --> [*] : terminate")
...> Finitomata.Transition.continuation(:entry, Finitomata.Transition.hard(:transitions, transitions))
%Finitomata.Transition.Path{from: :entry, to: :exit, path: [go!: :exit]}

@spec determined([t()]) :: [{state(), {event(), state()}}]

Returns keyword list of {Finitomata.Transition.state(), Finitomata.Transition.event()} tuples for determined transition from the current state.

The transition is determined, if it is the only transition allowed from the state.

Used internally for the validations.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse(
...>     "idle --> |to_s1| s1\n" <>
...>     "s1 --> |to_s2| s2\n" <>
...>     "s1 --> |to_s3| s3\n" <>
...>     "s2 --> |to_s1| s3\n" <>
...>     "s2 --> |ambiguous| s3\n" <>
...>     "s2 --> |ambiguous| s4\n" <>
...>     "s3 --> |determined| s3\n" <>
...>     "s3 --> |determined| s4\n")
...> Finitomata.Transition.determined(transitions)
[s4: :__end__, s3: :determined, idle: :to_s1]

@spec determined([t()], state()) :: {:ok, {event(), state()}} | :error

Returns {:ok, {event(), state()}} tuple if there is a determined transition from the current state, :error otherwise.

The transition is determined, if it is the only transition allowed from the state.

Used internally for the validations.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse(
...>     "idle --> |to_s1| s1\n" <>
...>     "s1 --> |to_s2| s2\n" <>
...>     "s1 --> |to_s3| s3\n" <>
...>     "s2 --> |to_s3| s3")
...> Finitomata.Transition.determined(transitions, :s1)
:error
iex> Finitomata.Transition.determined(transitions, :s2)
{:ok, {:to_s3, :s3}}
iex> Finitomata.Transition.determined(transitions, :s3)
{:ok, {:__end__, :*}}

@spec entry(:state | :transition, [t()]) :: state()

Returns the state after starting one, so-called entry state.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> entry : foo\nentry --> exit : go\nexit --> [*] : terminate")
...> Finitomata.Transition.entry(transitions)
:entry

@spec event_kind(event() | t()) :: event_kind()

Returns the kind of event.

If event ends up with an exclamation sign, it’s :hard, meaning the respective transition would be initiated automatically when the from state of such a transition is reached.

If event ends up with a question mark, it’s :soft, meaning no error would have been reported in a case transition fails.

Otherwise the event is :normal.

iex> {:ok, [_, hard, _]} =
...>   Finitomata.PlantUML.parse("[*] --> entry : foo\nentry --> exit : go!\nexit --> [*] : terminate")
...> Finitomata.Transition.event_kind(hard)
:hard

@spec events([t()], boolean()) :: [state()]

Returns the not ordered list of events, including or excluding the internal starting and ending transitions :__start__ and __end__ according to the second argument.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse("s1 --> |ok| s2\ns1 --> |ko| s3")
...> Finitomata.Transition.events(transitions, true)
[:ok, :ko]
...> Finitomata.Transition.events(transitions)
[:__start__, :ok, :ko, :__end__]

@spec exit(:states | :transitions, [t()]) :: [state()]

Returns the states before ending one, so-called exit states.

iex> {:ok, transitions} =
...>   Finitomata.Mermaid.parse(
...>     "entry --> |process| processing\nprocessing --> |ok| success\nprocessing --> |ko| error"
...>   )
...> Finitomata.Transition.exit(transitions)
[:error, :success]

@spec exiting(:states | :transitions, [t()]) ::
  Enumerable.t([t()]) | [Finitomata.Transition.Path.t()]

Returns all the states which inevitably lead to the ending one.

All the transitions from these states to the ending one are hard (ending with !,) which makes the FSM to go through all these states in :continue callbacks.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> entry : start\nentry --> exit : go!\nexit --> [*] : terminate")
...> Finitomata.Transition.exiting(transitions)
[%Finitomata.Transition.Path{from: :entry, to: :*, path: [go!: :exit, terminate: :*]}]

@spec hard(:states | :transitions, [t()]) ::
  Enumerable.t(t()) | [Finitomata.Transition.Path.t()]

Returns all the hard transitions which inevitably lead to the next state (events ending with an exclamation sign,) which makes the FSM to go to the next state with :continue callback.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> entry : start\nentry --> exit : go!\nexit --> [*] : terminate")
...> Finitomata.Transition.hard(transitions)
[entry: :go!]
...> Finitomata.Transition.hard(:transitions, transitions)
[%Finitomata.Transition{from: :entry, to: :exit, event: :go!}]

@spec loops(:states | :transitions, [t()]) ::
  Enumerable.t(t()) | [Finitomata.Transition.Path.t()]

Returns all the loops aka internal paths where starting and ending states are the same one.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns2 --> s1 : ok\ns2 --> [*] : ko")
...> Finitomata.Transition.loops(transitions)
[%Finitomata.Transition.Path{from: :s1, to: :s1, path: [ok: :s2, ok: :s1]},
 %Finitomata.Transition.Path{from: :s2, to: :s2, path: [ok: :s1, ok: :s2]}]

@spec paths(:states | :transitions, [t()], state(), state()) ::
  Enumerable.t(t()) | [Finitomata.Transition.Path.t()]

Returns all the paths from starting to ending state.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns1 --> s3 : ok\ns2 --> [*] : ko\ns3 --> [*] : ko")
...> Finitomata.Transition.paths(transitions)
[%Finitomata.Transition.Path{from: :*, to: :*, path: [foo: :s1, ok: :s2, ko: :*]},
 %Finitomata.Transition.Path{from: :*, to: :*, path: [foo: :s1, ok: :s3, ko: :*]}]

@spec responds?([t()], state(), event()) :: boolean()

Returns true if the state from hsa an outgoing transition with event, false otherwise.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns2 --> [*] : ko")
...> Finitomata.Transition.responds?(transitions, :s1, :ok)
true
...> Finitomata.Transition.responds?(transitions, :s1, :ko)
false

@spec states([t()], boolean()) :: [state()]

Returns the not ordered list of states, including or excluding the starting and ending states :* according to the second argument.

iex> {:ok, transitions} =
...>   Finitomata.PlantUML.parse("[*] --> s1 : foo\ns1 --> s2 : ok\ns2 --> [*] : ko")
...> Finitomata.Transition.states(transitions, true)
[:s1, :s2]
...> Finitomata.Transition.states(transitions)
[:*, :s1, :s2]