I've being trying (unsuccessfully) to create an "object"* in haskell in runtime with its type defined at runtime using dependent types.
I was following this tutorial on dependent types and what they use to pass a value on runtime is a function that takes a Sing
as a parameter and uses pattern matching on the value of Sing
to obtain the number on runtime.
But I don't have access to any Sing
to pattern match.
I thought the code below could work, but what I get is actually pretty disappointing, the compiler tells me that n
from the type definition for randomNetwork
is not the same n
that I captured in the type definition of 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]]))
How could I define the size of the "hidden layer" on runtime (without constructing it by hand)? how could I use the value I captured in runtime at the type level?
Btw, this is the compiling error I get with the code above:
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.
*: I know, we call them values (I think)
Let's think about this line:
net0 <- case sizeHidden of
SomeSing (SNat :: Sing n) ->
randomNetwork :: IO (Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ])
What is the type of net0
? It appears to be
Network '[ FullyConnected 75 n, FullyConnected n 1 ] '[ 'D1 75, 'D1 n, 'D1 1 ]
However, what is n
? It's not in the environment, because the type environment of main
is empty. And it's not universally quantified either. That's the problem, n
can't refer to anything. You need to either do all your work with net0
inside the environment where n
is bound1, as in
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
or wrap net0
in its own existential:
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
still needs a type signature because we need to indicate that we really intend to use the n
bound on the previous line, forcing us to write the network spec twice. But it can be cleaned up with the new TypeApplications
extension:
DogeNet @n <$> randomNetwork
1 This doesn't make things as impossible as it looks. You can still pass net0
to functions that are universally quantified in n
. It just means that if you ever return a type involving a new type level number, you need to do it by CPS or use an existential like DogeNet
.
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