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-rw-r--r--src/Data/Array/Nested/Internal/Lemmas.hs59
1 files changed, 0 insertions, 59 deletions
diff --git a/src/Data/Array/Nested/Internal/Lemmas.hs b/src/Data/Array/Nested/Internal/Lemmas.hs
deleted file mode 100644
index b1589e0..0000000
--- a/src/Data/Array/Nested/Internal/Lemmas.hs
+++ /dev/null
@@ -1,59 +0,0 @@
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE TypeApplications #-}
-{-# LANGUAGE TypeOperators #-}
-module Data.Array.Nested.Internal.Lemmas where
-
-import Data.Proxy
-import Data.Type.Equality
-import GHC.TypeLits
-
-import Data.Array.Mixed.Lemmas
-import Data.Array.Nested.Permutation
-import Data.Array.Nested.Types
-import Data.Array.Nested.Mixed.Shape
-import Data.Array.Nested.Shaped.Shape
-
-
-lemRankMapJust :: ShS sh -> Rank (MapJust sh) :~: Rank sh
-lemRankMapJust ZSS = Refl
-lemRankMapJust (_ :$$ sh') | Refl <- lemRankMapJust sh' = Refl
-
-lemMapJustApp :: ShS sh1 -> Proxy sh2
- -> MapJust (sh1 ++ sh2) :~: MapJust sh1 ++ MapJust sh2
-lemMapJustApp ZSS _ = Refl
-lemMapJustApp (_ :$$ sh) p | Refl <- lemMapJustApp sh p = Refl
-
-lemTakeLenMapJust :: Perm is -> ShS sh -> TakeLen is (MapJust sh) :~: MapJust (TakeLen is sh)
-lemTakeLenMapJust PNil _ = Refl
-lemTakeLenMapJust (_ `PCons` is) (_ :$$ sh) | Refl <- lemTakeLenMapJust is sh = Refl
-lemTakeLenMapJust (_ `PCons` _) ZSS = error "TakeLen of empty"
-
-lemDropLenMapJust :: Perm is -> ShS sh -> DropLen is (MapJust sh) :~: MapJust (DropLen is sh)
-lemDropLenMapJust PNil _ = Refl
-lemDropLenMapJust (_ `PCons` is) (_ :$$ sh) | Refl <- lemDropLenMapJust is sh = Refl
-lemDropLenMapJust (_ `PCons` _) ZSS = error "DropLen of empty"
-
-lemIndexMapJust :: SNat i -> ShS sh -> Index i (MapJust sh) :~: Just (Index i sh)
-lemIndexMapJust SZ (_ :$$ _) = Refl
-lemIndexMapJust (SS (i :: SNat i')) ((_ :: SNat n) :$$ (sh :: ShS sh'))
- | Refl <- lemIndexMapJust i sh
- , Refl <- lemIndexSucc (Proxy @i') (Proxy @(Just n)) (Proxy @(MapJust sh'))
- , Refl <- lemIndexSucc (Proxy @i') (Proxy @n) (Proxy @sh')
- = Refl
-lemIndexMapJust _ ZSS = error "Index of empty"
-
-lemPermuteMapJust :: Perm is -> ShS sh -> Permute is (MapJust sh) :~: MapJust (Permute is sh)
-lemPermuteMapJust PNil _ = Refl
-lemPermuteMapJust (i `PCons` is) sh
- | Refl <- lemPermuteMapJust is sh
- , Refl <- lemIndexMapJust i sh
- = Refl
-
-lemKnownMapJust :: forall sh. KnownShS sh => Proxy sh -> Dict KnownShX (MapJust sh)
-lemKnownMapJust _ = lemKnownShX (go (knownShS @sh))
- where
- go :: ShS sh' -> StaticShX (MapJust sh')
- go ZSS = ZKX
- go (n :$$ sh) = SKnown n :!% go sh