Monad.hs

{-# LANGUAGE UnboxedTuples #-}
{-# OPTIONS_HADDOCK not-home #-}
-- |
-- Copyright: (c) 2021 Xy Ren
-- License: BSD3
-- Maintainer: xy.r@outlook.com
-- Stability: unstable
-- Portability: non-portable (GHC only)
--
-- This module contains the definition of the 'Eff' monad. Most of the times, you won't need to use this module
-- directly; user-facing functionalities are all exported via the "Cleff" module.
--
-- __This is an /internal/ module and its API may change even between minor versions.__ Therefore you should be
-- extra careful if you're to depend on this module.
module Cleff.Internal.Monad
  ( -- * The 'Eff' monad
    InternalHandler (InternalHandler, runHandler), Eff (Eff, unEff)
  , -- * Effect environment
    Env, HandlerPtr, emptyEnv, adjustEnv, allocaEnv, readEnv, writeEnv, replaceEnv, appendEnv, updateEnv
  , -- * Performing effect operations
    KnownList, Subset, send, sendVia
  ) where

import           Cleff.Internal.Any
import           Cleff.Internal.Effect
import           Control.Monad.Fix          (MonadFix)
import           Control.Monad.Trans.Reader (ReaderT (ReaderT))
import           Data.IntMap.Strict         (IntMap)
import qualified Data.IntMap.Strict         as Map
import           Data.Rec.SmallArray        (KnownList, Rec, Subset, pattern (:~:))
import qualified Data.Rec.SmallArray        as Rec
import           Type.Reflection            (Typeable, typeRep)

-- * The 'Eff' monad

-- | The internal representation of effect handlers. This is just a natural transformation from the effect type
-- @e ('Eff' es)@ to the effect monad @'Eff' es@ for any effect stack @es@.
--
-- In interpreting functions (see "Cleff.Internal.Interpret"), the user-facing 'Cleff.Handler' type is transformed into
-- this type.
newtype InternalHandler e = InternalHandler
  { runHandler :: ∀ es. e (Eff es) ~> Eff es }

-- | @
-- 'show' (handler :: 'InternalHandler' E) == "Handler E"
-- @
instance Typeable e => Show (InternalHandler e) where
  showsPrec p _ = ("Handler " ++) . showsPrec p (typeRep @e)

-- | The extensible effect monad. A monad @'Eff' es@ is capable of performing any effect in the /effect stack/ @es@,
-- which is a type-level list that holds all effects available. However, most of the times, for flexibility, @es@
-- should be a polymorphic type variable, and you should use the '(:>)' and '(:>>)' operators in constraints to
-- indicate what effects are in the stack. For example,
--
-- @
-- 'Cleff.Reader.Reader' 'String' ':>' es, 'Cleff.State.State' 'Bool' ':>' es => 'Eff' es 'Integer'
-- @
--
-- allows you to perform operations of the @'Cleff.Reader.Reader' 'String'@ effect and the @'Cleff.State.State' 'Bool'@
-- effect in a computation returning an 'Integer'.
type role Eff nominal representational
newtype Eff es a = Eff { unEff :: Env es -> IO a }
  -- ^ The effect monad receives an effect environment 'Env' that contains all effect handlers and produces an 'IO'
  -- action.
  deriving newtype (Semigroup, Monoid)
  deriving (Functor, Applicative, Monad, MonadFix) via (ReaderT (Env es) IO)

-- * Effect environment

-- | The /effect environment/ that corresponds effects in the stack to their respective 'InternalHandler's. This
-- structure simulates memory: handlers are retrieved via pointers ('HandlerPtr's), and for each effect in the stack
-- we can either change what pointer it uses or change the handler the pointer points to. The former is used for global
-- effect interpretation ('Cleff.reinterpretN') and the latter for local interpretation ('Cleff.toEffWith') in order to
-- retain correct HO semantics. For more details on this see https://github.com/re-xyr/cleff/issues/5.
type role Env nominal
data Env (es :: [Effect]) = Env
  {-# UNPACK #-} !(Rec HandlerPtr es) -- ^ The array.
  {-# UNPACK #-} !Int -- ^ The next memory address to allocate.
  !(IntMap Any) -- ^ The simulated memory.

-- | A pointer to 'InternalHandler' in an 'Env'.
type role HandlerPtr nominal
newtype HandlerPtr (e :: Effect) = HandlerPtr { unHandlerPtr :: Int }
  deriving newtype
    ( Eq  -- ^ Pointer equality.
    , Ord -- ^ An arbitrary total order on the pointers.
    )

-- | Create an empty 'Env' with no address allocated.
emptyEnv :: Env '[]
emptyEnv = Env Rec.empty 0 Map.empty
{-# INLINE emptyEnv #-}

-- | Adjust the effect stack via an function over 'Rec'.
adjustEnv :: ∀ es' es. (Rec HandlerPtr es -> Rec HandlerPtr es') -> Env es -> Env es'
adjustEnv f (Env re n mem) = Env (f re) n mem
{-# INLINE adjustEnv #-}

-- | Allocate a new, empty address for a handler. \( O(1) \).
allocaEnv :: ∀ e es. Env es -> (# HandlerPtr e, Env es #)
allocaEnv (Env re n mem) = (# HandlerPtr n, Env re (succ n) mem #)
{-# INLINE allocaEnv #-}

-- | Read the handler a pointer points to. \( O(1) \).
readEnv :: ∀ e es. Rec.Elem e es => Env es -> InternalHandler e
readEnv (Env re _ mem) = fromAny $ mem Map.! unHandlerPtr (Rec.index @e re)
{-# INLINE readEnv #-}

-- | Overwrite the handler a pointer points to. \( O(1) \).
writeEnv :: ∀ e es. HandlerPtr e -> InternalHandler e -> Env es -> Env es
writeEnv (HandlerPtr m) x (Env re n mem) = Env re n (Map.insert m (toAny x) mem)
{-# INLINE writeEnv #-}

-- | Replace the handler pointer of an effect in the stack. \( O(n) \).
replaceEnv :: ∀ e es. Rec.Elem e es => HandlerPtr e -> InternalHandler e -> Env es -> Env es
replaceEnv (HandlerPtr m) x (Env re n mem) = Env (Rec.update @e (HandlerPtr m) re) n (Map.insert m (toAny x) mem)
{-# INLINE replaceEnv #-}

-- | Add a new effect to the stack with its corresponding handler pointer. \( O(n) \).
appendEnv :: ∀ e es. HandlerPtr e -> InternalHandler e -> Env es -> Env (e ': es)
appendEnv (HandlerPtr m) x (Env re n mem) = Env (HandlerPtr m :~: re) n (Map.insert m (toAny x) mem)
{-# INLINE appendEnv #-}

-- | Use the state of LHS as a newer version for RHS. \( O(1) \).
updateEnv :: ∀ es es'. Env es' -> Env es -> Env es
updateEnv (Env _ n mem) (Env re' _ _) = Env re' n mem
{-# INLINE updateEnv #-}

-- * Performing effect operations

-- | Perform an effect operation, /i.e./ a value of an effect type @e :: 'Effect'@. This requires @e@ to be in the
-- effect stack.
send :: e :> es => e (Eff es) ~> Eff es
send = sendVia id

-- | Perform an action in another effect stack via a transformation to that stack; in other words, this function "maps"
-- the effect operation from effect stack @es@ to @es'@. This is a generalization of 'send'; end users most likely
-- won't need to use this.
--
-- @
-- 'send' = 'sendVia' 'id'
-- @
sendVia :: e :> es' => (Eff es ~> Eff es') -> e (Eff es) ~> Eff es'
sendVia f e = Eff \es -> unEff (f (runHandler (readEnv es) e)) es