28 lines
799 B
Idris
28 lines
799 B
Idris
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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split : (zs : Scope a) -> (p : xs `Sub` ys ++ zs) -> Split xs ys zs p
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split [<] p = MkSplit p zero Refl Refl
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split (zs :< z) (Keep p) with (split zs p)
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split (zs :< z) (Keep (l ++ r)) | MkSplit l r Refl Refl =
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MkSplit l (Keep r) Refl Refl
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split (zs :< z) (Drop p) {xs} with (split zs p)
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split (zs :< z) (Drop (l ++ r)) {xs = _} | MkSplit l r Refl Refl =
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MkSplit l (Drop r) Refl Refl
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