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44 lines
1.1 KiB
Idris
44 lines
1.1 KiB
Idris
||| The content of this file is taken from the paper
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||| Heterogeneous Binary Random-access lists
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module Data.Vect.Binary
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import Data.Binary.Digit
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import Data.Binary
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import Data.IMaybe
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import Data.Nat
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import Data.Nat.Exponentiation
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import Data.Nat.Properties
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import Data.Tree.Perfect
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%default total
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public export
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data BVect : Nat -> Bin -> Type -> Type where
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Nil : BVect n [] a
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(::) : IMaybe (isI b) (Tree n a) -> BVect (S n) bs a -> BVect n (b :: bs) a
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public export
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data Path : Nat -> Bin -> Type where
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Here : Path n -> Path n (I :: bs)
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There : Path (S n) bs -> Path n (b :: bs)
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public export
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zero : {bs : Bin} -> {n : Nat} -> Path n (suc bs)
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zero {bs} = case bs of
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[] => Here (fromNat 0 n (ltePow2 {m = n}))
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(O :: bs) => Here (fromNat 0 n (ltePow2 {m = n}))
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(I :: bs) => There zero
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public export
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lookup : BVect n bs a -> Path n bs -> a
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lookup (hd :: _) (Here p) = lookup (fromJust hd) p
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lookup (_ :: tl) (There p) = lookup tl p
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public export
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cons : {bs : _} -> Tree n a -> BVect n bs a -> BVect n (suc bs) a
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cons t [] = [Just t]
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cons {bs = b :: _} t (u :: us) = case b of
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I => Nothing :: cons (Node t (fromJust u)) us
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O => Just t :: us
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