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{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
module Nats where
import Data.Proxy
import Numeric.Natural
import qualified GHC.TypeLits as G
data Dict c a where
Dict :: c a => Dict c a
data Nat = Z | S Nat
deriving (Show)
data SNat n where
SZ :: SNat Z
SS :: SNat n -> SNat (S n)
deriving instance Show (SNat n)
class KnownNat n where knownNat :: SNat n
instance KnownNat Z where knownNat = SZ
instance KnownNat n => KnownNat (S n) where knownNat = SS knownNat
unSNat :: SNat n -> Natural
unSNat SZ = 0
unSNat (SS n) = 1 + unSNat n
unNat :: Nat -> Natural
unNat Z = 0
unNat (S n) = 1 + unNat n
snatKnown :: SNat n -> Dict KnownNat n
snatKnown SZ = Dict
snatKnown (SS n) | Dict <- snatKnown n = Dict
type family GNat n where
GNat Z = 0
GNat (S n) = 1 G.+ GNat n
gknownNat :: KnownNat n => Proxy n -> Dict G.KnownNat (GNat n)
gknownNat (Proxy @n) = go (knownNat @n)
where
go :: SNat m -> Dict G.KnownNat (GNat m)
go SZ = Dict
go (SS n) | Dict <- go n = Dict
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