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{-# LANGUAGE UnicodeSyntax #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
module Main where
import Data.Typeable
import Control.Exception
data Attempt α = Success α
| ∀ e . Exception e ⇒ Failure e
data Inject f α = ∀ β . Inject (f β) (α → β)
class Completable f where
complete ∷ f α → α → IO Bool
instance Completable f ⇒ Completable (Inject f) where
complete (Inject f inj) = complete f . inj
class WaitOp op where
type WaitOpResult op
registerWaitOp ∷ Completable f
⇒ op → f (Attempt (WaitOpResult op)) → IO Bool
data WaitOps rs where
WaitOp ∷ WaitOp op ⇒ op → WaitOps (HSingle (WaitOpResult op))
(:?) ∷ (WaitOp op, HNonEmpty rs)
⇒ op → WaitOps rs → WaitOps (WaitOpResult op :* rs)
waitOpsNonEmpty ∷ ∀ rs . WaitOps rs → HNonEmptyInst rs
waitOpsNonEmpty (WaitOp _) = HNonEmptyInst
waitOpsNonEmpty (_ :? _) = HNonEmptyInst
infixr 7 .?
infix 8 .?.
(.?) ∷ WaitOp op ⇒ op → WaitOps rs → WaitOps (WaitOpResult op :* rs)
op .? ops = case waitOpsNonEmpty ops of
HNonEmptyInst → op :? ops
(.?.) ∷ (WaitOp op1, WaitOp op2) ⇒ op1 → op2
→ WaitOps (WaitOpResult op1 :*: WaitOpResult op2)
op1 .?. op2 = op1 .? WaitOp op2
data NthException n e = NthException (Peano n) e deriving (Typeable, Show)
instance (Typeable n, Exception e) ⇒ Exception (NthException n e)
instance WaitOp (WaitOps rs) where
type WaitOpResult (WaitOps rs) = HElemOf rs
registerWaitOp ops ev =
let register ∷ ∀ n . HDropClass n rs
⇒ Bool → Peano n → WaitOps (HDrop n rs) → IO Bool
register first n (WaitOp op) = do
let inj n (Success r) = Success (HNth n r)
inj n (Failure e) = Failure (NthException n e)
t ← try $ registerWaitOp op (Inject ev $ inj n)
r ← case t of
Right r → return r
Left e → complete ev $ inj n $ Failure (e ∷ SomeException)
return $ r || not first
register first n (op :? ops') = do
let inj n (Success r) = Success (HNth n r)
inj n (Failure e) = Failure (NthException n e)
t ← try $ registerWaitOp op (Inject ev $ inj n)
case t of
Right True → case waitOpsNonEmpty ops' of
HNonEmptyInst → case hTailDropComm ∷ HTailDropComm n rs of
HTailDropComm → register False (PSucc n) ops'
Right False → return $ not first
Left e → do
c ← complete ev $ inj $ Failure (e ∷ SomeException)
return $ c || not first
in case waitOpsNonEmpty ops of
HNonEmptyInst → register True PZero ops
main = return ()
data PZero deriving Typeable
data PSucc p deriving Typeable
data Peano n where
PZero ∷ Peano PZero
PSucc ∷ IsPeano p ⇒ Peano p → Peano (PSucc p)
instance Show (Peano n) where
show n = show (peanoNum n ∷ Int)
peanoNum ∷ Num n ⇒ Peano p → n
peanoNum PZero = 0
peanoNum (PSucc p) = 1 + peanoNum p
class Typeable n ⇒ IsPeano n where
peano ∷ Peano n
instance IsPeano PZero where
peano = PZero
instance IsPeano p ⇒ IsPeano (PSucc p) where
peano = PSucc peano
class (n ~ PSucc (PPred n)) ⇒ PHasPred n where
type PPred n
instance PHasPred (PSucc p) where
type PPred (PSucc p) = p
pPred ∷ Peano (PSucc p) → Peano p
pPred (PSucc p) = p
infixr 7 :*, .*
infix 8 :*:, .*.
data HNil
data h :* t
type HSingle α = α :* HNil
type α :*: β = α :* β :* HNil
data HList l where
HNil ∷ HList HNil
(:*) ∷ HListClass t ⇒ h → HList t → HList (h :* t)
instance Show (HList HNil) where
show _ = "HNil"
instance (Show h, Show (HList t)) ⇒ Show (HList (h :* t)) where
showsPrec d (h :* t) = showParen (d > 7) $
showsPrec 8 h . showString " .* " . showsPrec 7 t
(.*) ∷ HListClass t ⇒ h → HList t → HList (h :* t)
(.*) = (:*)
(.*.) ∷ α → β → HList (α :*: β)
a .*. b = a .* b .* HNil
data HListWitness l where
HNilList ∷ HListWitness HNil
HConsList ∷ HListClass t ⇒ HListWitness (h :* t)
class HListClass l where
hListWitness ∷ HListWitness l
instance HListClass HNil where
hListWitness = HNilList
instance HListClass t ⇒ HListClass (h :* t) where
hListWitness = HConsList
data HListInst l where
HListInst ∷ HListClass l ⇒ HListInst l
hListInst ∷ HList l → HListInst l
hListInst HNil = HListInst
hListInst (_ :* _) = HListInst
class (l ~ (HHead l :* HTail l), HListClass (HTail l)) ⇒ HNonEmpty l where
type HHead l
type HTail l
instance HListClass t ⇒ HNonEmpty (h :* t) where
type HHead (h :* t) = h
type HTail (h :* t) = t
hHead ∷ HList (h :* t) → h
hHead (h :* _) = h
hTail ∷ HList (h :* t) → HList t
hTail (_ :* t) = t
data HNonEmptyInst l where
HNonEmptyInst ∷ HListClass t ⇒ HNonEmptyInst (h :* t)
data HDropWitness n l where
HDropZero ∷ HListClass l ⇒ HDropWitness PZero l
HDropSucc ∷ HDropClass p t ⇒ HDropWitness (PSucc p) (h :* t)
class (IsPeano n, HListClass l, HListClass (HDrop n l)) ⇒ HDropClass n l where
type HDrop n l
hDropWitness ∷ HDropWitness n l
instance HListClass l ⇒ HDropClass PZero l where
type HDrop PZero l = l
hDropWitness = HDropZero
instance HDropClass p t ⇒ HDropClass (PSucc p) (h :* t) where
type HDrop (PSucc p) (h :* t) = HDrop p t
hDropWitness = case hDropWitness ∷ HDropWitness p t of
HDropZero → HDropSucc
HDropSucc → HDropSucc
data HDropInst n l where
HDropInst ∷ HDropClass n l ⇒ HDropInst n l
hDrop ∷ ∀ n l . HDropClass n l ⇒ Peano n → HList l → HList (HDrop n l)
hDrop n l = case hDropWitness ∷ HDropWitness n l of
HDropZero → l
HDropSucc → hDrop (pPred n) (hTail l)
data HNonEmptyDropInst n l where
HNonEmptyDropInst ∷ (HDropClass n l, HNonEmpty l,
HDropClass (PSucc n) l, HNonEmpty (HDrop n l))
⇒ HNonEmptyDropInst n l
pPrevDropInst ∷ ∀ n l . HDropClass (PSucc n) l ⇒ HNonEmptyDropInst n l
pPrevDropInst = case hDropWitness ∷ HDropWitness (PSucc n) l of
HDropSucc → case hDropWitness ∷ HDropWitness n (HTail l) of
HDropZero → HNonEmptyDropInst
HDropSucc → case pPrevDropInst ∷ HNonEmptyDropInst (PPred n) (HTail l) of
HNonEmptyDropInst → HNonEmptyDropInst
hNextDropInst ∷ ∀ n l . (HDropClass n l, HNonEmpty (HDrop n l))
⇒ HNonEmptyDropInst n l
hNextDropInst = case hDropWitness ∷ HDropWitness n l of
HDropZero → HNonEmptyDropInst
HDropSucc → case hNextDropInst ∷ HNonEmptyDropInst (PPred n) (HTail l) of
HNonEmptyDropInst → HNonEmptyDropInst
data HTailDropComm n l where
HTailDropComm ∷ (HNonEmpty l, HDropClass n l,
HNonEmpty (HDrop n l), HDropClass n (HTail l),
HDropClass (PSucc n) l,
HTail (HDrop n l) ~ HDrop n (HTail l),
HDrop (PSucc n) l ~ HTail (HDrop n l),
HDrop (PSucc n) l ~ HDrop n (HTail l))
⇒ HTailDropComm n l
hTailDropComm' ∷ ∀ n l . (HDropClass (PSucc n) l)
⇒ HTailDropComm n l
hTailDropComm' = case pPrevDropInst ∷ HNonEmptyDropInst n l of
HNonEmptyDropInst → hTailDropComm
hTailDropComm ∷ ∀ n l . (HDropClass n l, HNonEmpty (HDrop n l))
⇒ HTailDropComm n l
hTailDropComm = case hDropWitness ∷ HDropWitness n l of
HDropZero → HTailDropComm
HDropSucc → case hTailDropComm ∷ HTailDropComm (PPred n) (HTail l) of
HTailDropComm → HTailDropComm
type HNth n l = HHead (HDrop n l)
data HElemOf l where
HNth ∷ (HDropClass n l, HNonEmpty (HDrop n l))
⇒ Peano n → HNth n l → HElemOf l
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