2022-11-06 06:39:33 -05:00
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module Quox.OPE.Split
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import Quox.OPE.Basics
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import Quox.OPE.Length
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import Quox.OPE.Sub
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%default total
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public export
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record Split {a : Type} (xs, ys, zs : Scope a) (p : xs `Sub` ys ++ zs) where
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constructor MkSplit
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{0 leftSub, rightSub : Scope a}
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leftThin : leftSub `Sub` ys
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rightThin : rightSub `Sub` zs
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0 eqScope : xs = leftSub ++ rightSub
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0 eqThin : p ~=~ leftThin ++ rightThin
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export
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2022-11-15 09:44:49 -05:00
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split : Length ys =>
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(zs : Scope a) -> (p : xs `Sub` ys ++ zs) -> Split xs ys zs p
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split [<] p = MkSplit p zero Refl (endRight p)
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split (zs :< z) p @{ys} with (p.view @{S (lengthApp ys %search)})
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split (zs :< z) (SubM (S (2 * n)) (Keep p) v0) | (KEEP v Refl) =
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case split zs (sub v) of
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MkSplit l r Refl t =>
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MkSplit l (keep r) Refl $
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rewrite viewIrrel v0 (KEEP v Refl) in
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trans (cong keep {a = sub v} t) $
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sym $ keepAppRight l r
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split (zs :< z) (SubM (2 * n) (Drop p) v0) | (DROP v Refl) =
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case split zs (sub v) of
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MkSplit l r Refl t =>
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MkSplit l (drop r) Refl $
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rewrite viewIrrel v0 (DROP v Refl) in
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trans (cong drop {a = sub v} t) $
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sym $ dropAppRight l r
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