This file defines effectful operations which encode the core operations of the (session type) pi-calculus. 
> {-# LANGUAGE TypeOperators, DataKinds, GADTs, RankNTypes, FlexibleInstances, 
>               MultiParamTypeClasses, FlexibleContexts, IncoherentInstances, 
>               TypeFamilies, MagicHash, UnboxedTuples, ConstraintKinds #-}

> module Control.Effect.Sessions.Operations where

> import Control.Effect.Sessions.Process
> import Data.Type.FiniteMap

> import Unsafe.Coerce
> import Control.Concurrent ( threadDelay )
> import qualified Control.Concurrent.Chan as C
> import qualified Control.Concurrent as Conc

> import Control.Monad.STM
> import Control.Concurrent.STM.TMVar

> import Control.Effect (Subeffect(..))

> {-| A process can be run if it is /closed/ (i.e., empty channel environment) -}
> run :: Process '[] a -> IO a
> run = getProcess

> {-| Lift IO computations to a process -}
> liftIO :: IO a -> Process '[] a
> liftIO = Process 

> {-| Print to stdout in a process -}
> print :: Show a => a -> Process '[] ()
> print = liftIO . (Prelude.print)

> {-| putStrLn in a process -}
> putStrLn = liftIO . Prelude.putStrLn
The simplest operations, send and receive of primitive values, take a named channel 'Chan c' and return a 'Process' computation indexed by the session environment '[c :-> S]' where 'S' is either a send or receive action (terminated by 'End'). 
> {-| Send a primitive-typed value -}
> send :: Chan c -> t -> Process '[c :-> t :! End] ()
> send (MkChan c) t = Process $ C.writeChan (unsafeCoerce c) t

> {-| Receive a primitive-typed value -}
> recv :: Chan c -> Process '[c :-> t :? End] t
> recv (MkChan c) = Process $ C.readChan (unsafeCoerce c) -- >>= (return . unWrap)
The 'new' combinator models $\nu$, which takes a function mapping from a pair of two channels names 'Ch c' and 'Op C' to a session with behaviour 's', and creates a session where any mention to 'Ch c' or 'Op c' is removed: 
> {-| Create a new channel and pass its two endpoints to the supplied continuation
>      (the first parameter). This channel is thus only in scope for this continuation -}
> new :: (Duality env c) 
>           =>  ((Chan (Ch c), Chan (Op c)) -> Process env t) 
>           ->  Process (env :\ (Op c) :\ (Ch c)) t
> new f = Process $ C.newChan >>= (\c -> getProcess $ f (MkChan c, MkChan c))

> {-| Parallel compose two processes, if they contain balanced sessions -}
> par :: (BalancedPar env env') => 
>         Process env () -> Process env' () -> Process (DisjointUnion env env') () 
> par (Process x) (Process y) =  Process $ do res <- newEmptyTMVarIO
>                                             res' <- newEmptyTMVarIO
>                                             Conc.forkIO $ (x >>= (atomically . (putTMVar res)))
>                                             Conc.forkIO $ (y >>= (atomically . (putTMVar res')))
>                                             () <- atomically $ do { takeTMVar res }
>                                             () <- atomically $ do { takeTMVar res' }
>                                             return ()

> {-| Turn all session types into 'balancing checked' session types |-}
> type family AllBal (env :: [Map Name Session]) :: [Map Name Session] where
>             AllBal '[] = '[]
>             AllBal ((c :-> s) ': env) = (c :-> Bal s) ': (AllBal env)

> {-| Output a channel (dual to a replicated input) -}
> rsend :: Chan c -> Chan d -> Process '[c :-> (Delg s) :*! End, d :-> Bal s] () 
> rsend (MkChan c) t = Process $ C.writeChan (unsafeCoerce c) t
Channels can then be sent and received with the 'chSend' and 'chRecv' primitives: 
> {-| Send a channel 'd' over channel 'c' -}
> chSend :: Chan c -> Chan d -> Process '[c :-> (Delg s) :! End, d :-> Bal s] ()
> chSend (MkChan c) t = Process $ C.writeChan (unsafeCoerce c) t

> {-| Receive a channel over a channel 'c', bind to the name 'd' -}
chRecv :: Chan c -> (Chan d -> Process env a) -> Process (UnionSeq '[c :-> (Delg (env :@ d)) :? (env :@ c)] (env :\ d)) a chRecv (MkChan c) f = Process $ C.readChan (unsafeCoerce c) >>= (getProcess . f . unsafeCoerce) 
> chRecv :: Chan c -> Process '[c :-> (Delg (env :@ d)) :? End]
>                         ((Chan d -> Process env a) -> Process (env :\ d) a)
> chRecv (MkChan c) = Process $ return $ 
>                                \f -> let y = (C.readChan (unsafeCoerce c) >>= 
>                                                      (getProcess . f . unsafeCoerce))
>                                      in Process $ y
Given a channel 'c', and a computation which binds channel 'd' to produces behaviour 'c', then this is provided by receiving 'd' over 'c'. Thus the resulting computation is the union of 'c' mapping to the session type of 'd' in the session environment 's', composed with the 's' but with 'd' deleted (removed). ------------------------------------------------------ Subeffecting instances for the least-upper bound :+ operator and for extending an environment with a closed session channel, i.e. with c :-> End. 
> instance Subeffect Process env env' => 
>          Subeffect Process ((c :-> s) ': env) ((c :-> s :+ t) ': env') where
>     sub (Process p) = Process p

> instance Subeffect Process env env' =>
>          Subeffect Process ((c :-> t) ': env) ((c :-> s :+ t) ': env') where
>     sub (Process p) = Process p

> instance Subeffect Process env env where
>     sub = id

> instance Subeffect Process env env' => 
>          Subeffect Process ((c :-> s) ': env) ((c :-> s) ': env') where
>     sub (Process p) = Process p

> instance Subeffect Process env env' => 
>          Subeffect Process env ((c :-> End) ': env') where
>     sub (Process p) = Process p
Explicit subeffecting operations for subtyping on the left of a conditional and subtyping on the right of a conditional 
> {-| Explicit subeffecting introduction of ':+' with the current session behaviour on the left -}
> subL :: Process '[c :-> s] a -> Process '[c :-> s :+ t] a
> subL = sub

> {-| Explicit subeffecting introduction of ':+' with the current session behaviour on the right -}
> subR :: Process '[c :-> t] a -> Process '[c :-> s :+ t] a
> subR = sub

> {-| Explicit subeffecting introduction of a terminated session for channel 'c' -}
> subEnd :: Chan c -> Process '[] a -> Process '[c :-> End] a
> subEnd _ = sub
instance Subeffect Process '[] '[d :-> s] where sub (Process p) = Process p 
> caseUnion :: Chan c -> Process env a -> Process ((c :-> s) ': env) a
> caseUnion _ (Process p) = Process p

> {-| Recursion combinator for recursive functions which have an affine fixed-point
>     equation on their effects. 
>       For example, if 'h ~ (Seq h a) :+ b' then 'ToFix h = Fix a b,'
>    -}
> affineFix :: ((a -> Process '[c :-> Star] b) 
>           -> (a -> Process '[c :-> h] b))
>           -> a -> Process '[c :-> ToFix h] b
> affineFix f x = let (Process p) = f (\x' -> let (Process y) = affineFix f x' in Process y) x
>                  in Process p