module Numeric.AD.Internal.Identity
( Id(..)
, probe
, unprobe
, probed
, unprobed
) where
import Data.Data (Data)
import Data.Monoid
import Data.Number.Erf
import Data.Typeable (Typeable)
import Numeric.AD.Mode
newtype Id a s = Id { runId :: a } deriving
(Eq, Ord, Show, Enum, Bounded, Num, Real, Fractional, Floating, RealFrac, RealFloat, Monoid, Data, Typeable, Erf, InvErf)
type instance Scalar (Id a s) = a
probe :: a -> Id a s
probe = Id
unprobe :: Id a s -> a
unprobe = runId
pid :: Functor f => f a -> f (Id a s)
pid = fmap probe
unpid :: Functor f => f (Id a s) -> f a
unpid = fmap unprobe
probed :: Functor f => f a -> f (Id a s)
probed = pid
unprobed :: Functor f => f (Id a s) -> f a
unprobed = unpid
instance Num a => Mode (Id a s) where
auto = Id
Id a ^* b = Id (a * b)
a *^ Id b = Id (a * b)