Motor: Finite-State Machines in Haskell

While writing my talk “Finite-state machines? Your compiler wants in!”, I have worked on porting the Idris ST library to Haskell. I call it Motor.

Motor is an experimental Haskell library for building finite-state machines with type-safe transitions and effects. I have just published it on Hackage, written a bunch of documentation with Haddock, and put the source code on GitHub.

This blog post is very similar to the Hackage documentation, and aims to pique your interest. The library and documentation will probably evolve and outdate this description, though.

State Machines using Row Types

The central finite-state machine abstraction in Motor is the MonadFSM type class. MonadFSM is an indexed monad type class, meaning that it has not one, but three type parameters:

1. A Row of input resource states
2. A Row of output resource states
3. A return type (just as in Monad)

The MonadFSM parameter kinds might look a bit scary, but they state the same:

class IxMonad m =>
  MonadFSM (m :: (Row *) -> (Row *) -> * -> *) where
  ...

The rows describe how the FSM computation will affect the state of its resources when evaluated. A row is essentially a type-level map, from resource names to state types, and the FSM computation's rows describe the resource states before and after the computation.

An FSM computation newConn that adds a resource named "connection" with state Idle could have the following type:

newConn :: MonadFSM m =>
  m r ("connection" ::= Idle :| r) ()

A computation spawnTwoPlayers that adds two resources could have this type:

spawnTwoPlayers :: MonadFSM m =>
  m r ("hero2" ::= Standing :| "hero1" ::= Standing :| r) ()

Motor uses the extensible records in Data.OpenRecords, provided by the CTRex library, for row kinds. Have a look at it's documentation to learn more about the type-level operators available for rows.

Building on Indexed Monads

As mentioned above, MonadFSM is an indexed monad. It uses the definition from Control.Monad.Indexed, in the indexed package. This means that you can use ibind and friends to compose FSM computations.

-- 'c1' and 'c2' are FSM computations
c1 >>>= \_ -> c2

You can combine this with the RebindableSyntax language extension to get do-syntax for FSM programs:

test :: MonadFSM m => m Empty Empty ()
test = do
  c1
  c2
  r <- c3
  c4 r
  where
    (>>) a = (>>>=) a . const
    (>>=) = (>>>=)

See 24 Days of GHC Extensions: Rebindable Syntax for some more information on how to use RebindableSyntax.

State Actions

To make it easier to read and write FSM computation types, there is some syntax sugar available.

State actions allow you to describe state changes of named resources with a single list, as opposed two writing two rows. They also take care of matching the CTRex row combinators with the expectations of Motor, which can be tricky to do by hand.

There are three state actions:

• Add adds a new resource.
• To transitions the state of a resource.
• Delete deletes an existing resource.

A mapping between a resource name is written using the :-> type operator, with a Symbol on the left, and a state action type on the right. Here are some examples:

"container" :-> Add Empty

"list" :-> To Empty NonEmpty

"game" :-> Delete GameEnded

So, the list of mappings from resource names to state actions describe what happens to each resource. Together with an initial row of resources r, and a return value a, we can declare the type of an FSM computation using the Actions type:

MonadFSM m => Actions m '[ n1 :-> a1, n2 :-> a2, ... ] r a

A computation that adds two resources could have the following type:

addingTwoThings ::
  MonadFSM m =>
  Actions m '[ "container" :-> Add Empty
              , "game" :-> Add Started
              ] r ()

Infix Operators

As an alternative to the Add, To, and Delete types, Motor offers infix operator aliases. These start with ! to indicate that they can be effectful.

The !--> operator is an infix alias for To:

useStateMachines ::
  MonadFSM m =>
  Actions m '[ "program" :-> NotCool !--> Cool ] r ()

The !+ and !- are infix aliases for mappings from resource names to Add and Delete state actions, respectively:

startNewGame ::
    MonadFSM m =>
    Actions m '[ "game" !+ Started ] r ()

endGameWhenWon ::
    MonadFSM m =>
    Actions m '[ "game" !- Won ] r ()

Row Polymorphism

Because of how CTRex works, FSM computations that have a free variable as their input row of resources, i.e. that are polymorphic in the sense of other resource states, must list all their actions in reverse order.

doFourThings ::
     Game m
  => Actions m '[ "hero2" !- Standing
                , "hero1" !- Standing
                , "hero2" !+ Standing
                , "hero1" !+ Standing
                ] r ()
doFourThings = do
  spawn hero1
  spawn hero2
  perish hero1
  perish hero

  where
    (>>) a = (>>>=) a . const
    (>>=) = (>>>=)

This is obviously quite clumsy. If anyone has ideas on how to fix or work around it, please get in touch. Had the r been replaced by Empty in the type signature above, it could have had type NoActions m Empty () instead.

Running the State Machine

The runFSM function in Motor.FSM runs an FSM computation in some base monad:

runFSM :: Monad m => FSM m Empty Empty a -> m a

FSM has instances for IxMonadTrans and a bunch of other type classes. More might be added as they are needed.

Examples

There is only one small Door example in the repository, along with some test programs. I haven’t had much time to write examples, but hopefully I will soon. The door example does feature most of the relevant concepts, though.