58 lines
1.7 KiB
Idris
58 lines
1.7 KiB
Idris
module Quox.Thin.Split
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import public Quox.Thin.Base
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import public Quox.Thin.View
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import public Quox.Thin.Eqv
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import public Quox.Thin.Append
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import public Quox.Thin.Cover
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import Data.DPair
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import Control.Relation
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%default total
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public export
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record Chunks m n where
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constructor MkChunks
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{leftMask : Nat}
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{rightMask : Nat}
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0 left : OPE m (m + n) leftMask
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0 right : OPE n (m + n) rightMask
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{auto 0 isCover : Cover [left, right]}
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%name Chunks chunks
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export
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chunks : (m, n : Nat) -> Chunks m n
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chunks 0 0 = MkChunks Stop Stop
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chunks 0 (S n) =
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let MkChunks l r = chunks 0 n in
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MkChunks (Drop l Refl) (Keep r Refl)
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chunks (S m) n =
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let MkChunks l r = chunks m n in
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MkChunks (Keep l Refl) (Drop r Refl)
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-- [todo] the masks here are just ((2 << m) - 1) << n and (2 << n) - 1
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public export
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record SplitAt m n1 n2 (ope : OPE m (n1 + n2) mask) where
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constructor MkSplitAt
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{leftMask, rightMask : Nat}
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{0 leftScope, rightScope : Nat}
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0 left : OPE leftScope n1 leftMask
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0 right : OPE rightScope n2 rightMask
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0 scopePrf : m = leftScope + rightScope
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0 opePrf : ope `Eqv` (left `app'` right).snd
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%name SplitAt split
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export
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splitAt : (n1 : Nat) -> {n2, mask : Nat} -> (0 ope : OPE m (n1 + n2) mask) ->
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SplitAt m n1 n2 ope
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splitAt 0 ope = MkSplitAt zero ope Refl reflexive
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splitAt (S n1) ope with %syntactic (view ope)
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splitAt (S n1) (Drop ope Refl) | DropV _ ope with %syntactic (splitAt n1 ope)
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_ | MkSplitAt left right scopePrf opePrf =
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MkSplitAt (Drop left Refl) right scopePrf (EqvDrop opePrf)
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splitAt (S n1) (Keep ope Refl) | KeepV _ ope with %syntactic (splitAt n1 ope)
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_ | MkSplitAt left right scopePrf opePrf =
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MkSplitAt (Keep left Refl) right (cong S scopePrf) (EqvKeep opePrf)
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