hel*_*elq 8 haskell ghc dependent-type
我正在尝试(不成功)在运行时在haskell中创建一个"对象"*,其类型在运行时使用依赖类型定义.
我正在关注依赖类型的本教程,它们用于在运行时传递值的函数是一个函数,它接受Sing一个参数并使用模式匹配值Sing来获取运行时的数字.但是我无法访问任何Sing模式匹配.
我认为下面的代码可以工作,但我得到的实际上是非常令人失望的,编译器告诉我,n从类型定义来看randomNetwork,与n我在类型定义中捕获的不一样SNat.
{-# LANGUAGE
ScopedTypeVariables, TemplateHaskell, TypeFamilies, GADTs, KindSignatures,
TypeOperators, FlexibleContexts, RankNTypes, UndecidableInstances,
FlexibleInstances, InstanceSigs, DefaultSignatures, DataKinds,
RecordWildCards, StandaloneDeriving, MultiParamTypeClasses #-}
module Main where
-- some imports to make the code below main work
import Control.Monad.Random
import GHC.TypeLits
import Data.List
--import Grenade
import Data.Singletons
import Data.Singletons.TypeLits
main = do
let sizeHidden = toSing (20 :: Integer) :: SomeSing Nat
net0 <- case sizeHidden of
SomeSing (SNat :: Sing n) ->
randomNetwork :: IO (Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ])
--net0 <- randomNetwork :: IO (Network '[ FullyConnected 75 3, FullyConnected 3 1 ] '[ 'D1 75, 'D1 3, 'D1 1 ])
print net0
-- from Grenade.Core.Network
data Network :: [*] -> [Shape] -> * where
NNil :: SingI i
=> Network '[] '[i]
(:~>) :: (SingI i, SingI h, Layer x i h)
=> !x
-> !(Network xs (h ': hs))
-> Network (x ': xs) (i ': h ': hs)
infixr 5 :~>
instance Show (Network '[] '[i]) where
show NNil = "NNil"
instance (Show x, Show (Network xs rs)) => Show (Network (x ': xs) (i ': rs)) where
show (x :~> xs) = show x ++ "\n~>\n" ++ show xs
class CreatableNetwork (xs :: [*]) (ss :: [Shape]) where
randomNetwork :: MonadRandom m => m (Network xs ss)
instance SingI i => CreatableNetwork '[] '[i] where
randomNetwork = return NNil
instance (SingI i, SingI o, Layer x i o, CreatableNetwork xs (o ': rs)) => CreatableNetwork (x ': xs) (i ': o ': rs) where
randomNetwork = (:~>) <$> createRandom <*> randomNetwork
-- from Grenade.Layers.FullyConnected
data FullyConnected i o = FullyConnected
!(FullyConnected' i o) -- Neuron weights
!(FullyConnected' i o) -- Neuron momentum
data FullyConnected' i o = FullyConnected'
!(R o) -- Bias
!(L o i) -- Activations
instance Show (FullyConnected i o) where
show FullyConnected {} = "FullyConnected"
instance (KnownNat i, KnownNat o) => UpdateLayer (FullyConnected i o) where
type Gradient (FullyConnected i o) = (FullyConnected' i o)
runUpdate = undefined
createRandom = undefined
instance (KnownNat i, KnownNat o) => Layer (FullyConnected i o) ('D1 i) ('D1 o) where
type Tape (FullyConnected i o) ('D1 i) ('D1 o) = S ('D1 i)
runForwards = undefined
runBackwards = undefined
-- from Grenade.Core.Layer
class UpdateLayer x where
type Gradient x :: *
runUpdate :: LearningParameters -> x -> Gradient x -> x
createRandom :: MonadRandom m => m x
runUpdates :: LearningParameters -> x -> [Gradient x] -> x
runUpdates rate = foldl' (runUpdate rate)
class UpdateLayer x => Layer x (i :: Shape) (o :: Shape) where
type Tape x i o :: *
runForwards :: x -> S i -> (Tape x i o, S o)
runBackwards :: x -> Tape x i o -> S o -> (Gradient x, S i)
-- from Grenade.Core.Shape
data Shape = D1 Nat
data S (n :: Shape) where
S1D :: ( KnownNat len )
=> R len
-> S ('D1 len)
deriving instance Show (S n)
instance KnownNat a => SingI ('D1 a) where
sing = D1Sing sing
data instance Sing (n :: Shape) where
D1Sing :: Sing a -> Sing ('D1 a)
-- from Grenade.Core.LearningParameters
data LearningParameters = LearningParameters {
learningRate :: Double
, learningMomentum :: Double
, learningRegulariser :: Double
} deriving (Eq, Show)
-- from Numeric.LinearAlgebra.Static
newtype Dim (n :: Nat) t = Dim t
deriving (Show)
newtype R n = R (Dim n [Double])
deriving (Show)
newtype L m n = L (Dim m (Dim n [[Double]]))
如何在运行时定义"隐藏层"的大小(不用手工构建)？我怎么能在类型级别使用我在运行时捕获的值？
顺便说一下,这是我用上面的代码得到的编译错误:
Prelude> :r
net0 <- case sizeHidden of
SomeSing (SNat :: KnownNat n => Sing n) -> randomNetwork :: IO (Network '[ FullyConnected 75 3, FullyConnected 3 1 ] '[ 'D1 75, 'D1 3, 'D1 1 ])
[1 of 1] Compiling Main ( /home/helq/Downloads/NetworkOnRuntime.hs, interpreted )
/home/helq/Downloads/NetworkOnRuntime.hs:23:15: error:
• Couldn't match type ‘a0’
with ‘Network
'[FullyConnected 75 a, FullyConnected a 1] '['D1 75, 'D1 a, 'D1 1]’
because type variable ‘a’ would escape its scope
This (rigid, skolem) type variable is bound by
a pattern with constructor:
SomeSing :: forall k k1 (k2 :: k1) (a :: k). Sing a -> SomeSing k,
in a case alternative
at /home/helq/Downloads/NetworkOnRuntime.hs:22:13-37
Expected type: IO a0
Actual type: IO
(Network
'[FullyConnected 75 a, FullyConnected a 1] '['D1 75, 'D1 a, 'D1 1])
• In the expression:
randomNetwork ::
IO (Network '[FullyConnected 75 n, FullyConnected n 1] '[D1 75,
D1 n,
D1 1])
In a case alternative:
SomeSing (SNat :: Sing n)
-> randomNetwork ::
IO (Network '[FullyConnected 75 n, FullyConnected n 1] '[D1 75,
D1 n,
D1 1])
In a stmt of a 'do' block:
net0 <- case sizeHidden of {
SomeSing (SNat :: Sing n)
-> randomNetwork ::
IO (Network '[FullyConnected 75 n, FullyConnected n 1] '[D1 75,
D1 n,
D1 1]) }
/home/helq/Downloads/NetworkOnRuntime.hs:25:3: error:
• Ambiguous type variable ‘a0’ arising from a use of ‘print’
prevents the constraint ‘(Show a0)’ from being solved.
Relevant bindings include
net0 :: a0 (bound at /home/helq/Downloads/NetworkOnRuntime.hs:21:3)
Probable fix: use a type annotation to specify what ‘a0’ should be.
These potential instances exist:
instance (Show b, Show a) => Show (Either a b)
-- Defined in ‘Data.Either’
instance Show SomeNat -- Defined in ‘GHC.TypeLits’
instance Show SomeSymbol -- Defined in ‘GHC.TypeLits’
...plus 31 others
...plus 170 instances involving out-of-scope types
(use -fprint-potential-instances to see them all)
• In a stmt of a 'do' block: print net0
In the expression:
do { let sizeHidden = ...;
net0 <- case sizeHidden of {
SomeSing (SNat :: Sing n)
-> randomNetwork ::
IO (Network '[FullyConnected 75 n, FullyConnected n 1] '[D1 75,
D1 n,
D1 1]) };
print net0 }
In an equation for ‘main’:
main
= do { let sizeHidden = ...;
net0 <- case sizeHidden of { SomeSing (SNat :: Sing n) -> ... };
print net0 }
Failed, modules loaded: none.
*:我知道,我们称之为价值观(我认为)
让我们考虑一下这一行:
net0 <- case sizeHidden of
SomeSing (SNat :: Sing n) ->
randomNetwork :: IO (Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ])
是什么类型的net0？它似乎是
Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ]
但是,是什么n？它不在环境中,因为类型环境main是空的.它也没有普遍量化.那是问题,n不能指任何东西.您需要net0在n绑定1的环境中完成所有工作,如
case sizeHidden of
SomeSing (SNat :: Sing n) -> do
net0 <- randomNetwork :: IO (Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ])
print net0
或包裹net0在自己的存在主义中:
data DogeNet =
forall n. KnownNat n => DogeNet (Network '[ FullyConnected 75 n, FullyConnected n 1 ]
'[ 'D1 75, 'D1 n, 'D1 1 ])
instance Show DogeNet where -- deriving can't handle existentials
show (DogeNet n) = show n
main = do
...
net0 <- case sizeHidden of
SomeSing (SNat :: Sing n) ->
DogeNet <$> (randomNetwork
:: IO (Network '[ FullyConnected 75 n, FullyConnected n 1 ]
'[ 'D1 75, 'D1 n, 'D1 1 ]))
print net0
randomNetwork还需要一个类型签名,因为我们需要表明我们真的打算使用n绑定上一行,迫使我们写的网络规格的两倍.但它可以使用新的TypeApplications扩展程序进行清理:
DogeNet @n <$> randomNetwork
1这并不会让事情变得不可能.您仍然可以传递net0给普遍量化的函数n.它只是意味着如果您返回涉及新类型级别编号的类型,则需要通过CPS或使用存在性类型来完成DogeNet.