Rename inductive naturals to INat

1 files changed, 0 insertions, 87 deletions

diff --git a/src/Data/Nat.hs b/src/Data/Nat.hs
deleted file mode 100644
index b154f67..0000000
--- a/src/Data/Nat.hs
+++ /dev/null
@@ -1,87 +0,0 @@
-{-# 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 Data.Nat where
-
-import Data.Proxy
-import Numeric.Natural
-import qualified GHC.TypeLits as G
-
-
--- | Evidence for the constraint @c a@.
-data Dict c a where
-  Dict :: c a => Dict c a
-
--- | A peano natural number. Intended to be used at the type level.
-data Nat = Z | S Nat
-  deriving (Show)
-
--- | Singleton for a 'Nat'.
-data SNat n where
-  SZ :: SNat Z
-  SS :: SNat n -> SNat (S n)
-deriving instance Show (SNat n)
-
--- | A singleton 'SNat' corresponding to @n@.
-class KnownNat n where knownNat :: SNat n
-instance KnownNat Z where knownNat = SZ
-instance KnownNat n => KnownNat (S n) where knownNat = SS knownNat
-
--- | Convert a 'Nat' to a normal number.
-unNat :: Nat -> Natural
-unNat Z = 0
-unNat (S n) = 1 + unNat n
-
--- | Convert an 'SNat' to a normal number.
-unSNat :: SNat n -> Natural
-unSNat SZ = 0
-unSNat (SS n) = 1 + unSNat n
-
--- | Convert an 'SNat' to an integer.
-unSNat' :: SNat n -> Int
-unSNat' = fromIntegral . unSNat
-
--- | A 'KnownNat' dictionary is just a singleton natural, so we can create
--- evidence of 'KnownNat' given an 'SNat'.
-snatKnown :: SNat n -> Dict KnownNat n
-snatKnown SZ = Dict
-snatKnown (SS n) | Dict <- snatKnown n = Dict
-
--- | Add two 'Nat's
-type family n + m where
-  Z + m = m
-  S n + m = S (n + m)
-
--- | Convert a 'Nat' to a "GHC.TypeLits" 'G.Nat'.
-type family GNat n where
-  GNat Z = 0
-  GNat (S n) = 1 G.+ GNat n
-
--- | If an inductive 'Nat' is known, then the corresponding "GHC.TypeLits"
--- 'G.Nat' is also known.
-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
-
--- * Some type-level naturals
-
-type N0 = Z
-type N1 = S N0
-type N2 = S N1
-type N3 = S N2
-type N4 = S N3
-type N5 = S N4
-type N6 = S N5
-type N7 = S N6
-type N8 = S N7
-type N9 = S N8