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{-# LANGUAGE UnicodeSyntax #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeApplications #-}
module Bug (await, bug) where
import Data.Typeable
import Data.Functor
import Control.Exception
data Attempt α = Success α
| ∀ e . Exception e ⇒ Failure e
fromAttempt ∷ Attempt α → IO α
fromAttempt (Success a) = return a
fromAttempt (Failure e) = throwIO e
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 Awaitable f where
awaitResult ∷ f α → IO α
data FakeFuture α = FakeFuture
instance Completable FakeFuture where
complete _ _ = undefined
instance Awaitable FakeFuture where
awaitResult _ = undefined
class WaitOp op where
type WaitOpResult op
registerWaitOp ∷ Completable f
⇒ op → f (Attempt (WaitOpResult op)) → IO Bool
await ∷ WaitOp op ⇒ op → IO (WaitOpResult op)
await op = do
let fut = FakeFuture
registerWaitOp op fut
fromAttempt =<< awaitResult fut
data FakeOp α = FakeOp
instance WaitOp (FakeOp α) where
type WaitOpResult (FakeOp α) = α
registerWaitOp _ _ = return True
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
inj :: Peano n -> Attempt (HNth n l) -> Attempt (HElemOf l)
inj = error "urk"
rwo :: forall rs f. f (Attempt (WaitOpResult (WaitOps rs))) → IO Bool
rwo ev = do
let register ∷ ∀ n . Peano n → WaitOps (HDrop n rs) → IO Bool
register n (WaitOp (op :: op_ty)) =
((($) -- (px -> qx) -> px -> qx px=a_a2iT qx=b_a2iU
(Inject @f ev) -- Instantiate at ax=a2iW bx=a2iX;
-- (ax -> bx) -> Inject f ax
-- ql with arg or Inject: f bx ~ f (Attempt (WaitOpReslt (WaitOps rs)))
-- bx := Attempt (WaitOpResult (WaitOps rs) = Attempt (HElemOf rs)
-- px := (ax -> bx)
-- qx := Inject f ax
(inj @n n) -- instantiate lx=l_a2iZ;
-- Attempt (HNth n lx) -> Attempt (HElemOf lx)
-- res_ty px = (ax->bx) ~ Attempt (HNth n lx) -> Attempt (HElemOf lx)
-- ax := Attempt (HNth n lx)
-- bx := Attempt (HElemOf lx)
) :: Inject f (Attempt (WaitOpResult op_ty)))
-- Result ql: Attempt (WaitOpResult op_ty) ~ ax = Attempt (HNth n lx)
`seq` return True
return True
data Inject f a where
Inject :: ∀f a b . (f b) -> (a → b) -> Inject f a
bug ∷ IO Int
bug = do
temp ← await ((FakeOp ∷ FakeOp Int) .?. (FakeOp ∷ FakeOp String))
case temp of
(elem0 → Just _) → return 0
_ → return 1
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
hGetIfNth ∷ ∀ n l . (HDropClass n l, HNonEmpty (HDrop n l))
⇒ Peano n → HElemOf l → Maybe (HNth n l)
hGetIfNth PZero (HNth PZero x) = Just x
hGetIfNth (PSucc p) (HNth (PSucc p') x) =
case hDropWitness ∷ HDropWitness n l of
HDropSucc →
let inst ∷ ∀ m . HDropClass (PSucc m) l
⇒ Peano m → HTailDropComm m l
inst _ = hTailDropComm' in
case inst p' of
HTailDropComm → hGetIfNth p (HNth p' x ∷ HElemOf (HTail l))
_ → undefined
hGetIfNth _ _ = Nothing
elem0 ∷ HNonEmpty l ⇒ HElemOf l → Maybe (HHead l)
elem0 = hGetIfNth PZero
|