103 lines
3.3 KiB
Idris
103 lines
3.3 KiB
Idris
module Quox.Thin.View
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import public Quox.Thin.Base
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import Quox.NatExtra
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import Data.Singleton
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import Data.SnocVect
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%default total
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public export
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data View : OPE m n mask -> Type where
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StopV : View Stop
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DropV : (mask : Nat) -> (0 ope : OPE m n mask) -> View (Drop ope Refl)
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KeepV : (mask : Nat) -> (0 ope : OPE m n mask) -> View (Keep ope Refl)
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%name View.View v
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private
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0 stopEqs : OPE m 0 mask -> (m = 0, mask = 0)
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stopEqs Stop = (Refl, Refl)
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private
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0 fromStop : (ope : OPE 0 0 0) -> ope = Stop
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fromStop Stop = Refl
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private
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0 fromDrop : (ope : OPE m (S n) (k + k)) ->
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(inner : OPE m n k ** ope === Drop inner Refl)
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fromDrop (Drop ope eq) with %syntactic (doubleInj _ _ eq)
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fromDrop (Drop ope Refl) | Refl = (ope ** Refl)
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fromDrop (Keep ope eq) = void $ notEvenOdd _ _ eq
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private
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0 fromKeep : (ope : OPE (S m) (S n) (S (k + k))) ->
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(inner : OPE m n k ** ope === Keep inner Refl)
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fromKeep (Drop ope eq) = void $ notEvenOdd _ _ $ sym eq
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fromKeep (Keep ope eq) with %syntactic (doubleInj _ _ $ inj S eq)
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fromKeep (Keep ope Refl) | Refl = (ope ** Refl)
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private
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0 keepIsSucc : (ope : OPE m n (S (k + k))) -> IsSucc m
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keepIsSucc (Drop ope eq) = void $ notEvenOdd _ _ $ sym eq
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keepIsSucc (Keep ope _) = ItIsSucc
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export
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view : {0 m : Nat} -> {n, mask : Nat} -> (0 ope : OPE m n mask) -> View ope
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view {n = 0} ope with %syntactic 0 (fst $ stopEqs ope) | 0 (snd $ stopEqs ope)
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_ | Refl | Refl = rewrite fromStop ope in StopV
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view {n = S n} ope with %syntactic (half mask)
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_ | HalfOdd mask' with %syntactic 0 (keepIsSucc ope)
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_ | ItIsSucc with %syntactic 0 (fromKeep ope)
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_ | (ope' ** eq) = rewrite eq in KeepV mask' ope'
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_ | HalfEven mask' with %syntactic 0 (fromDrop ope)
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_ | (ope' ** eq) = rewrite eq in DropV mask' ope'
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export
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appOpe : {0 m : Nat} -> (n : Nat) -> {mask : Nat} ->
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(0 ope : OPE m n mask) -> Singleton m
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appOpe n ope with %syntactic (view ope)
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appOpe 0 Stop | StopV = Val 0
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appOpe (S n) (Drop ope' _) | DropV _ ope' = appOpe n ope'
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appOpe (S n) (Keep ope' _) | KeepV _ ope' = [|S $ appOpe n ope'|]
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export
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maskToOpe : {n, mask : Nat} -> (0 ope : OPE m n mask) -> Singleton ope
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maskToOpe ope with %syntactic (view ope)
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maskToOpe Stop | StopV = [|Stop|]
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maskToOpe (Drop ope Refl) | DropV k ope = [|drop $ maskToOpe ope|]
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maskToOpe (Keep ope Refl) | KeepV k ope = [|keep $ maskToOpe ope|]
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export
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0 outerInnerZero : OPE m 0 mask -> m = 0
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outerInnerZero Stop = Refl
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export
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0 outerMaskZero : OPE m 0 mask -> mask = 0
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outerMaskZero Stop = Refl
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export
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0 viewStop : view Stop = StopV
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viewStop = Refl
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export
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0 viewDrop : (ope : OPE m n mask) -> (eq : mask2 = mask + mask) ->
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view (Drop {mask} ope eq) = DropV mask ope
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viewDrop ope eq with (view (Drop ope eq))
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viewDrop ope Refl | DropV _ ope = Refl
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export
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0 viewKeep : (ope : OPE m n mask) -> (eq : mask2 = S (mask + mask)) ->
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view (Keep {mask} ope eq) = KeepV mask ope
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viewKeep ope eq with (view (Keep ope eq))
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viewKeep ope Refl | KeepV _ ope = Refl
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namespace SnocVect
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export
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select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
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SnocVect n a -> SnocVect m a
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select ope sx with (view ope)
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select _ [<] | StopV = [<]
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select _ (sx :< x) | DropV _ ope = select ope sx
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select _ (sx :< x) | KeepV _ ope = select ope sx :< x
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