split and extend Quox.Thin
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13 changed files with 893 additions and 388 deletions
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@ -1,388 +1,13 @@
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||| thinnings, covers, partitions, etc,
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||| for co-de Bruijn representation [@egtbs]
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module Quox.Thin
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module Quox.Thin
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import Quox.NatExtra
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import public Quox.Thin.Base
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import Data.Nat.Views
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import public Quox.Thin.View
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import Data.Singleton
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import public Quox.Thin.Eqv
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import Data.DPair
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import public Quox.Thin.Cons
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import Syntax.PreorderReasoning
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import public Quox.Thin.List
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import public Quox.Thin.Append
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%default total
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import public Quox.Thin.Comp
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import public Quox.Thin.Cover
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import public Quox.Thin.Coprod
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||| "order preserving embeddings", for recording a correspondence between a
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import public Quox.Thin.Split
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||| smaller scope and part of a larger one. the third argument is a bitmask
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import public Quox.Thin.Term
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||| representing this OPE, unique for a given `n`.
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public export
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data OPE : (m, n, mask : Nat) -> Type where
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[search m n]
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Stop : OPE 0 0 0
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Drop : OPE m n mask -> mask' = mask + mask -> OPE m (S n) mask'
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Keep : OPE m n mask -> mask' = (S (mask + mask)) -> OPE (S m) (S n) mask'
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%name OPE ope
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||| everything selected
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public export
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id : {m : Nat} -> Subset Nat (OPE m m)
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id {m = 0} = Element _ Stop
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id {m = S m} = Element _ $ Keep id.snd Refl
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||| nothing selected
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public export
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zero : {m : Nat} -> OPE 0 m 0
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zero {m = 0} = Stop
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zero {m = S m} = Drop zero Refl
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infix 6 `Eqv`
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public export
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data Eqv : OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Type where
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EqvStop : Eqv Stop Stop
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EqvDrop : {0 p : OPE m1 n1 mask1} ->
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{0 q : OPE m2 n2 mask2} ->
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Eqv p q -> Eqv (Drop p eq1) (Drop q eq2)
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EqvKeep : {0 p : OPE m1 n1 mask1} ->
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{0 q : OPE m2 n2 mask2} ->
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Eqv p q -> Eqv (Keep p eq1) (Keep q eq2)
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%name Eqv eqv
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export
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Reflexive (OPE m n mask) Eqv where
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reflexive {x = Stop} = EqvStop
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reflexive {x = Drop {}} = EqvDrop reflexive
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reflexive {x = Keep {}} = EqvKeep reflexive
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export
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symmetric : p `Eqv` q -> q `Eqv` p
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symmetric EqvStop = EqvStop
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symmetric (EqvDrop eqv) = EqvDrop $ symmetric eqv
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symmetric (EqvKeep eqv) = EqvKeep $ symmetric eqv
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export
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transitive : p `Eqv` q -> q `Eqv` r -> p `Eqv` r
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transitive EqvStop EqvStop = EqvStop
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transitive (EqvDrop x) (EqvDrop y) = EqvDrop (transitive x y)
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transitive (EqvKeep x) (EqvKeep y) = EqvKeep (transitive x y)
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export
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eqvIndices : {0 p : OPE m1 n1 mask1} -> {0 q : OPE m2 n2 mask2} ->
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p `Eqv` q -> (m1 = m2, n1 = n2, mask1 = mask2)
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eqvIndices EqvStop = (Refl, Refl, Refl)
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eqvIndices (EqvDrop eqv {eq1 = Refl, eq2 = Refl}) =
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let (Refl, Refl, Refl) = eqvIndices eqv in (Refl, Refl, Refl)
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eqvIndices (EqvKeep eqv {eq1 = Refl, eq2 = Refl}) =
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let (Refl, Refl, Refl) = eqvIndices eqv in (Refl, Refl, Refl)
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export
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0 eqvMask : (p : OPE m1 n mask1) -> (q : OPE m2 n mask2) ->
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mask1 = mask2 -> p `Eqv` q
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eqvMask Stop Stop _ = EqvStop
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eqvMask (Drop ope1 Refl) (Drop {mask = mm2} ope2 eq2) Refl =
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EqvDrop $ eqvMask ope1 ope2 (doubleInj _ _ eq2)
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eqvMask (Drop ope1 Refl) (Keep ope2 eq2) Refl =
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void $ notEvenOdd _ _ eq2
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eqvMask (Keep ope1 eq1) (Keep ope2 eq2) Refl =
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EqvKeep $ eqvMask ope1 ope2 (doubleInj _ _ $ inj S $ trans (sym eq1) eq2)
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eqvMask (Keep ope1 eq1) (Drop ope2 eq2) Refl =
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void $ notEvenOdd _ _ $ trans (sym eq2) eq1
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uip : (p, q : a = b) -> p = q
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uip Refl Refl = Refl
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export
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0 eqvEq' : (p, q : OPE m n mask) -> p `Eqv` q -> p === q
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eqvEq' Stop Stop EqvStop = Refl
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eqvEq' (Drop p eq1) (Drop q eq2) (EqvDrop eqv)
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with (doubleInj _ _ $ trans (sym eq1) eq2)
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_ | Refl = cong2 Drop (eqvEq' p q eqv) (uip eq1 eq2)
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eqvEq' (Keep p eq1) (Keep q eq2) (EqvKeep eqv)
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with (doubleInj _ _ $ inj S $ trans (sym eq1) eq2)
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_ | Refl = cong2 Keep (eqvEq' p q eqv) (uip eq1 eq2)
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export
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0 eqvEq : (p : OPE m1 n1 mask1) -> (q : OPE m2 n2 mask2) ->
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p `Eqv` q -> p ~=~ q
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eqvEq p q eqv = let (Refl, Refl, Refl) = eqvIndices eqv in eqvEq' p q eqv
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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 Thin.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 (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 (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 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 (half mask)
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_ | HalfOdd mask' with 0 (keepIsSucc ope)
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_ | ItIsSucc with 0 (fromKeep ope)
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_ | (ope' ** eq) = rewrite eq in KeepV mask' ope'
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_ | HalfEven mask' with 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 (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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||| inductive definition of OPE composition
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public export
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data Comp : (l : OPE n p mask1) -> (r : OPE m n mask2) ->
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(res : OPE m p mask3) -> Type where
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[search l r]
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StopZ : Comp Stop Stop Stop
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DropZ : Comp a b c -> Comp (Drop a Refl) b (Drop c Refl)
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KeepZ : Comp a b c -> Comp (Keep a Refl) (Keep b Refl) (Keep c Refl)
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KDZ : Comp a b c -> Comp (Keep a Refl) (Drop b Refl) (Drop c Refl)
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public export
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record CompResult (ope1 : OPE n p mask1) (ope2 : OPE m n mask2) where
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constructor MkComp
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{resultMask : Nat}
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{0 result : OPE m p resultMask}
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0 comp : Comp ope1 ope2 result
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%name CompResult comp
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||| compose two OPEs, if the middle scope size is already known at runtime
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export
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comp' : {n, p, mask1, mask2 : Nat} ->
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(0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
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CompResult ope1 ope2
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comp' ope1 ope2 with (view ope1) | (view ope2)
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comp' Stop Stop | StopV | StopV =
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MkComp StopZ
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comp' (Drop ope1 Refl) ope2 | DropV _ ope1 | _ =
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MkComp $ DropZ (comp' ope1 ope2).comp
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comp' (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
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MkComp $ KDZ (comp' ope1 ope2).comp
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comp' (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
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MkComp $ KeepZ (comp' ope1 ope2).comp
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||| compose two OPEs, after recomputing the middle scope size using `appOpe`
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export
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comp : {p, mask1, mask2 : Nat} ->
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(0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
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CompResult ope1 ope2
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comp ope1 ope2 = let Val n = appOpe p ope1 in comp' ope1 ope2
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-- [todo] is there a quick way to compute the mask of comp?
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export
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app' : OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Exists (OPE (m1 + m2) (n1 + n2))
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app' Stop ope2 = Evidence _ ope2
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app' (Drop ope1 Refl) ope2 = Evidence _ $ Drop (app' ope1 ope2).snd Refl
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app' (Keep ope1 Refl) ope2 = Evidence _ $ Keep (app' ope1 ope2).snd Refl
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export
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(++) : {n1, n2, mask1, mask2 : Nat} ->
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(0 ope1 : OPE m1 n1 mask1) -> (0 ope2 : OPE m2 n2 mask2) ->
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Subset Nat (OPE (m1 + m2) (n1 + n2))
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ope1 ++ ope2 with (view ope1)
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Stop ++ ope2 | StopV = Element _ ope2
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Drop ope1 Refl ++ ope2 | DropV mask ope1 =
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Element _ $ Drop (ope1 ++ ope2).snd Refl
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Keep ope1 Refl ++ ope2 | KeepV mask ope1 =
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Element _ $ Keep (ope1 ++ ope2).snd Refl
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-- [todo] this mask is just (mask1 << n2) | mask2
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-- prove it and add %transform
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||| the tail of a non-empty OPE is its behaviour on all but the innermost slot
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public export
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data Tail : (full : OPE m1 (S n) mask1) -> (tail : OPE m2 n mask2) -> Type where
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[search full]
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DropT : Tail (Drop ope eq) ope
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KeepT : Tail (Keep ope eq) ope
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%name Tail tail
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public export
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record TailRes (0 ope : OPE m (S n) mask) where
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constructor MkTail
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{0 scope : Nat}
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{tailMask : Nat}
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0 tail : OPE scope n tailMask
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0 isTail : Tail ope tail
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export
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tail : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> TailRes ope
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tail ope with (view ope)
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tail (Drop ope _) | DropV _ ope = MkTail ope DropT
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tail (Keep ope _) | KeepV _ ope = MkTail ope KeepT
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namespace OPEList
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||| a list of OPEs of a given outer scope size
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public export
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data OPEList : Nat -> Type where
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Nil : OPEList n
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(::) : OPE m n mask -> OPEList n -> OPEList n
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%name OPEList opes
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namespace Tails -- 🦊
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||| `Tails opes tails` if each i'th element of `tails` is the tail of
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||| the i'th element of `opes`
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public export
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data Tails : (full : OPEList (S n)) -> (tails : OPEList n) -> Type where
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[search full]
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Nil : Tails [] []
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(::) : Tail ope tail -> Tails opes tails ->
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Tails (ope :: opes) (tail :: tails)
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namespace Cover
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||| an OPE list is a cover if at least one of the OPEs has `Keep` as the head,
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||| and the tails are also a cover
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||| in @egtbs it is a binary relation which is fine for ×ᵣ but i don't want to
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||| write my AST in universe-of-syntaxes style. sorry
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public export data Cover : OPEList n -> Type
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||| the "`Keep` in the head" condition of a cover
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public export data Cover1 : OPEList n -> Type
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data Cover where
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Nil : Cover opes {n = 0}
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(::) : Cover1 opes -> Tails opes tails => Cover tails -> Cover opes
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%name Cover cov
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data Cover1 where
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Here : Cover1 (Keep p eq :: opes)
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There : Cover1 opes -> Cover1 (ope :: opes)
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%name Cover1 cov1
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public export
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record Coprod (ope1 : OPE m1 n mask1) (ope2 : OPE m2 n mask2) where
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constructor MkCoprod
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{0 size : Nat}
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{sizeMask : Nat}
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{leftMask : Nat}
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{rightMask : Nat}
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{0 sub : OPE size n sizeMask}
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{0 left : OPE m1 size leftMask}
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{0 right : OPE m2 size rightMask}
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0 leftComp : Comp sub left ope1
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0 rightComp : Comp sub right ope2
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{auto 0 isCover : Cover [left, right]}
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%name Coprod cop
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export
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coprod : {n, mask1, mask2 : Nat} ->
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(0 ope1 : OPE m1 n mask1) -> (0 ope2 : OPE m2 n mask2) ->
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Coprod ope1 ope2
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coprod ope1 ope2 with (view ope1) | (view ope2)
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coprod Stop Stop | StopV | StopV = MkCoprod StopZ StopZ
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coprod (Drop ope1 Refl) (Drop ope2 Refl) | DropV _ ope1 | DropV _ ope2 =
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let MkCoprod l r = coprod ope1 ope2 in MkCoprod (DropZ l) (DropZ r)
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coprod (Drop ope1 Refl) (Keep ope2 Refl) | DropV _ ope1 | KeepV _ ope2 =
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let MkCoprod l r = coprod ope1 ope2 in MkCoprod (KDZ l) (KeepZ r)
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coprod (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
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let MkCoprod l r = coprod ope1 ope2 in MkCoprod (KeepZ l) (KDZ r)
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|
||||||
coprod (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
|
|
||||||
let MkCoprod l r = coprod ope1 ope2 in MkCoprod (KeepZ l) (KeepZ r)
|
|
||||||
|
|
||||||
-- [todo] n-ary coprod
|
|
||||||
|
|
||||||
|
|
||||||
public export
|
|
||||||
record Chunks m n where
|
|
||||||
constructor MkChunks
|
|
||||||
{leftMask : Nat}
|
|
||||||
{rightMask : Nat}
|
|
||||||
0 left : OPE m (m + n) leftMask
|
|
||||||
0 right : OPE n (m + n) rightMask
|
|
||||||
{auto 0 isCover : Cover [left, right]}
|
|
||||||
%name Chunks chunks
|
|
||||||
|
|
||||||
export
|
|
||||||
chunks : (m, n : Nat) -> Chunks m n
|
|
||||||
chunks 0 0 = MkChunks Stop Stop
|
|
||||||
chunks 0 (S n) =
|
|
||||||
let MkChunks l r = chunks 0 n in
|
|
||||||
MkChunks (Drop l Refl) (Keep r Refl)
|
|
||||||
chunks (S m) n =
|
|
||||||
let MkChunks l r = chunks m n in
|
|
||||||
MkChunks (Keep l Refl) (Drop r Refl)
|
|
||||||
|
|
||||||
-- [todo] the masks here are just ((2 << m) - 1) << n and (2 << n) - 1
|
|
||||||
|
|
||||||
|
|
||||||
public export
|
|
||||||
record SplitAt m n1 n2 (ope : OPE m (n1 + n2) mask) where
|
|
||||||
constructor MkSplitAt
|
|
||||||
{leftMask, rightMask : Nat}
|
|
||||||
{0 leftScope, rightScope : Nat}
|
|
||||||
0 left : OPE leftScope n1 leftMask
|
|
||||||
0 right : OPE rightScope n2 rightMask
|
|
||||||
0 scopePrf : m = leftScope + rightScope
|
|
||||||
0 opePrf : ope `Eqv` (left `app'` right).snd
|
|
||||||
%name SplitAt split
|
|
||||||
|
|
||||||
export
|
|
||||||
splitAt : (n1 : Nat) -> {n2, mask : Nat} -> (0 ope : OPE m (n1 + n2) mask) ->
|
|
||||||
SplitAt m n1 n2 ope
|
|
||||||
splitAt 0 ope = MkSplitAt zero ope Refl reflexive
|
|
||||||
splitAt (S n1) ope with (view ope)
|
|
||||||
splitAt (S n1) (Drop ope Refl) | DropV _ ope with (splitAt n1 ope)
|
|
||||||
_ | MkSplitAt left right scopePrf opePrf =
|
|
||||||
MkSplitAt (Drop left Refl) right scopePrf (EqvDrop opePrf)
|
|
||||||
splitAt (S n1) (Keep ope Refl) | KeepV _ ope with (splitAt n1 ope)
|
|
||||||
_ | MkSplitAt left right scopePrf opePrf =
|
|
||||||
MkSplitAt (Keep left Refl) right (cong S scopePrf) (EqvKeep opePrf)
|
|
||||||
|
|
||||||
|
|
||||||
public export
|
|
||||||
record Thinned f n where
|
|
||||||
constructor Th
|
|
||||||
{0 scope : Nat}
|
|
||||||
{scopeMask : Nat}
|
|
||||||
0 ope : OPE scope n scopeMask
|
|
||||||
term : f scope
|
|
||||||
%name Thinned s, t, u
|
|
||||||
|
|
||||||
export
|
|
||||||
pure : {n : Nat} -> f n -> Thinned f n
|
|
||||||
pure term = Th id.snd term
|
|
||||||
|
|
||||||
export
|
|
||||||
join : {n : Nat} -> Thinned (Thinned f) n -> Thinned f n
|
|
||||||
join (Th ope1 (Th ope2 term)) = Th (comp ope1 ope2).result term
|
|
||||||
|
|
|
||||||
27
lib/Quox/Thin/Append.idr
Normal file
27
lib/Quox/Thin/Append.idr
Normal file
|
|
@ -0,0 +1,27 @@
|
||||||
|
module Quox.Thin.Append
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.View
|
||||||
|
import Data.DPair
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
public export
|
||||||
|
app' : OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Exists (OPE (m1 + m2) (n1 + n2))
|
||||||
|
app' Stop ope2 = Evidence _ ope2
|
||||||
|
app' (Drop ope1 Refl) ope2 = Evidence _ $ Drop (app' ope1 ope2).snd Refl
|
||||||
|
app' (Keep ope1 Refl) ope2 = Evidence _ $ Keep (app' ope1 ope2).snd Refl
|
||||||
|
|
||||||
|
public export
|
||||||
|
(++) : {n1, n2, mask1, mask2 : Nat} ->
|
||||||
|
(0 ope1 : OPE m1 n1 mask1) -> (0 ope2 : OPE m2 n2 mask2) ->
|
||||||
|
Subset Nat (OPE (m1 + m2) (n1 + n2))
|
||||||
|
ope1 ++ ope2 with %syntactic (view ope1)
|
||||||
|
Stop ++ ope2 | StopV = Element _ ope2
|
||||||
|
Drop ope1 Refl ++ ope2 | DropV mask ope1 =
|
||||||
|
Element _ $ Drop (ope1 ++ ope2).snd Refl
|
||||||
|
Keep ope1 Refl ++ ope2 | KeepV mask ope1 =
|
||||||
|
Element _ $ Keep (ope1 ++ ope2).snd Refl
|
||||||
|
|
||||||
|
-- [todo] this mask is just (mask1 << n2) | mask2
|
||||||
|
-- prove it and add %transform
|
||||||
80
lib/Quox/Thin/Base.idr
Normal file
80
lib/Quox/Thin/Base.idr
Normal file
|
|
@ -0,0 +1,80 @@
|
||||||
|
module Quox.Thin.Base
|
||||||
|
|
||||||
|
import Data.Fin
|
||||||
|
import Data.DPair
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
||| "order preserving embeddings", for recording a correspondence between a
|
||||||
|
||| smaller scope and part of a larger one. the third argument is a bitmask
|
||||||
|
||| representing this OPE, unique for a given `n`.
|
||||||
|
public export
|
||||||
|
data OPE : (m, n, mask : Nat) -> Type where
|
||||||
|
[search m n]
|
||||||
|
Stop : OPE 0 0 0
|
||||||
|
Drop : OPE m n mask -> mask' = mask + mask -> OPE m (S n) mask'
|
||||||
|
Keep : OPE m n mask -> mask' = (S (mask + mask)) -> OPE (S m) (S n) mask'
|
||||||
|
%name OPE ope
|
||||||
|
|
||||||
|
export
|
||||||
|
Show (OPE m n mask) where
|
||||||
|
showPrec d Stop = "Stop"
|
||||||
|
showPrec d (Drop ope Refl) = showCon d "Drop" $ showArg ope ++ " Refl"
|
||||||
|
showPrec d (Keep ope Refl) = showCon d "Keep" $ showArg ope ++ " Refl"
|
||||||
|
|
||||||
|
public export %inline
|
||||||
|
drop : OPE m n mask -> OPE m (S n) (mask + mask)
|
||||||
|
drop ope = Drop ope Refl
|
||||||
|
|
||||||
|
public export %inline
|
||||||
|
keep : OPE m n mask -> OPE (S m) (S n) (S (mask + mask))
|
||||||
|
keep ope = Keep ope Refl
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
data IsStop : OPE m n mask -> Type where ItIsStop : IsStop Stop
|
||||||
|
|
||||||
|
public export
|
||||||
|
data IsDrop : OPE m n mask -> Type where ItIsDrop : IsDrop (Drop ope eq)
|
||||||
|
|
||||||
|
public export
|
||||||
|
data IsKeep : OPE m n mask -> Type where ItIsKeep : IsKeep (Keep ope eq)
|
||||||
|
|
||||||
|
|
||||||
|
export
|
||||||
|
0 zeroIsStop : (ope : OPE m 0 mask) -> IsStop ope
|
||||||
|
zeroIsStop Stop = ItIsStop
|
||||||
|
|
||||||
|
|
||||||
|
||| everything selected
|
||||||
|
public export
|
||||||
|
id : {m : Nat} -> Subset Nat (OPE m m)
|
||||||
|
id {m = 0} = Element _ Stop
|
||||||
|
id {m = S m} = Element _ $ Keep id.snd Refl
|
||||||
|
|
||||||
|
public export %inline
|
||||||
|
0 id' : OPE m m Base.id.fst
|
||||||
|
id' = id.snd
|
||||||
|
|
||||||
|
||| nothing selected
|
||||||
|
public export
|
||||||
|
zero : {m : Nat} -> OPE 0 m 0
|
||||||
|
zero {m = 0} = Stop
|
||||||
|
zero {m = S m} = Drop zero Refl
|
||||||
|
|
||||||
|
||| a single slot selected
|
||||||
|
public export
|
||||||
|
one : Fin n -> Subset Nat (OPE 1 n)
|
||||||
|
one FZ = Element _ $ keep zero
|
||||||
|
one (FS i) = Element _ $ drop (one i).snd
|
||||||
|
|
||||||
|
public export %inline
|
||||||
|
0 one' : (i : Fin n) -> OPE 1 n (one i).fst
|
||||||
|
one' i = (one i).snd
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
record SomeOPE n where
|
||||||
|
constructor MkOPE
|
||||||
|
{mask : Nat}
|
||||||
|
0 ope : OPE m n mask
|
||||||
59
lib/Quox/Thin/Comp.idr
Normal file
59
lib/Quox/Thin/Comp.idr
Normal file
|
|
@ -0,0 +1,59 @@
|
||||||
|
module Quox.Thin.Comp
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.View
|
||||||
|
import Data.Singleton
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
||| inductive definition of OPE composition
|
||||||
|
public export
|
||||||
|
data Comp : (l : OPE n p mask1) -> (r : OPE m n mask2) ->
|
||||||
|
(res : OPE m p mask3) -> Type where
|
||||||
|
[search l r]
|
||||||
|
StopZ : Comp Stop Stop Stop
|
||||||
|
DropZ : Comp a b c -> Comp (Drop a Refl) b (Drop c Refl)
|
||||||
|
KeepZ : Comp a b c -> Comp (Keep a Refl) (Keep b Refl) (Keep c Refl)
|
||||||
|
KDZ : Comp a b c -> Comp (Keep a Refl) (Drop b Refl) (Drop c Refl)
|
||||||
|
|
||||||
|
public export
|
||||||
|
record CompResult (ope1 : OPE n p mask1) (ope2 : OPE m n mask2) where
|
||||||
|
constructor MkComp
|
||||||
|
{mask : Nat}
|
||||||
|
{0 ope : OPE m p mask}
|
||||||
|
0 comp : Comp ope1 ope2 ope
|
||||||
|
%name CompResult comp
|
||||||
|
|
||||||
|
||| compose two OPEs, if the middle scope size is already known at runtime
|
||||||
|
export
|
||||||
|
comp' : {n, p, mask1, mask2 : Nat} ->
|
||||||
|
(0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
|
||||||
|
CompResult ope1 ope2
|
||||||
|
comp' ope1 ope2 with %syntactic (view ope1) | (view ope2)
|
||||||
|
comp' Stop Stop | StopV | StopV =
|
||||||
|
MkComp StopZ
|
||||||
|
comp' (Drop ope1 Refl) ope2 | DropV _ ope1 | _ =
|
||||||
|
MkComp $ DropZ (comp' ope1 ope2).comp
|
||||||
|
comp' (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
|
||||||
|
MkComp $ KDZ (comp' ope1 ope2).comp
|
||||||
|
comp' (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
|
||||||
|
MkComp $ KeepZ (comp' ope1 ope2).comp
|
||||||
|
|
||||||
|
||| compose two OPEs, after recomputing the middle scope size using `appOpe`
|
||||||
|
export
|
||||||
|
comp : {p, mask1, mask2 : Nat} ->
|
||||||
|
(0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
|
||||||
|
CompResult ope1 ope2
|
||||||
|
comp ope1 ope2 = let Val n = appOpe p ope1 in comp' ope1 ope2
|
||||||
|
|
||||||
|
-- [todo] is there a quick way to compute the mask of comp?
|
||||||
|
|
||||||
|
export
|
||||||
|
0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
|
||||||
|
OPE m p (comp ope1 ope2).mask
|
||||||
|
ope1 . ope2 = (comp ope1 ope2).ope
|
||||||
|
|
||||||
|
-- export
|
||||||
|
-- 0 compMask : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
|
||||||
|
-- (ope3 : OPE m p mask3) -> Comp ope1 ope2 ope3 ->
|
||||||
|
-- mask3 = ?aaa
|
||||||
74
lib/Quox/Thin/Cons.idr
Normal file
74
lib/Quox/Thin/Cons.idr
Normal file
|
|
@ -0,0 +1,74 @@
|
||||||
|
module Quox.Thin.Cons
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import Quox.Thin.Eqv
|
||||||
|
import Quox.Thin.View
|
||||||
|
import Data.DPair
|
||||||
|
import Control.Relation
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
data IsHead : (ope : OPE m (S n) mask) -> Bool -> Type where
|
||||||
|
[search ope]
|
||||||
|
DropH : IsHead (Drop ope eq) False
|
||||||
|
KeepH : IsHead (Keep ope eq) True
|
||||||
|
|
||||||
|
public export
|
||||||
|
data IsTail : (full : OPE m (S n) mask) -> OPE m' n mask' -> Type where
|
||||||
|
[search full]
|
||||||
|
DropT : IsTail (Drop ope eq) ope
|
||||||
|
KeepT : IsTail (Keep ope eq) ope
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Uncons (ope : OPE m (S n) mask) where
|
||||||
|
constructor MkUncons
|
||||||
|
0 head : Bool
|
||||||
|
{tailMask : Nat}
|
||||||
|
0 tail : OPE scope n tailMask
|
||||||
|
{auto isHead : IsHead ope head}
|
||||||
|
{auto 0 isTail : IsTail ope tail}
|
||||||
|
|
||||||
|
public export
|
||||||
|
uncons : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Uncons ope
|
||||||
|
uncons ope with %syntactic (view ope)
|
||||||
|
uncons (Drop ope Refl) | DropV _ ope = MkUncons False ope
|
||||||
|
uncons (Keep ope Refl) | KeepV _ ope = MkUncons True ope
|
||||||
|
|
||||||
|
public export
|
||||||
|
head : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Exists $ IsHead ope
|
||||||
|
head ope = Evidence _ (uncons ope).isHead
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Tail (ope : OPE m (S n) mask) where
|
||||||
|
constructor MkTail
|
||||||
|
{tailMask : Nat}
|
||||||
|
0 tail : OPE scope n tailMask
|
||||||
|
{auto 0 isTail : IsTail ope tail}
|
||||||
|
|
||||||
|
public export
|
||||||
|
tail : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Tail ope
|
||||||
|
tail ope = let u = uncons ope in MkTail u.tail @{u.isTail}
|
||||||
|
|
||||||
|
|
||||||
|
export
|
||||||
|
cons : {mask : Nat} -> (head : Bool) -> (0 tail : OPE m n mask) ->
|
||||||
|
Subset Nat (OPE (if head then S m else m) (S n))
|
||||||
|
cons False tail = Element _ $ drop tail
|
||||||
|
cons True tail = Element _ $ keep tail
|
||||||
|
|
||||||
|
export
|
||||||
|
0 consEquiv' : (self : OPE m' (S n) mask') ->
|
||||||
|
(head : Bool) -> (tail : OPE m n mask) ->
|
||||||
|
IsHead self head -> IsTail self tail ->
|
||||||
|
(cons head tail).snd `Eqv` self
|
||||||
|
consEquiv' (Drop tail _) False tail DropH DropT = EqvDrop reflexive
|
||||||
|
consEquiv' (Keep tail _) True tail KeepH KeepT = EqvKeep reflexive
|
||||||
|
|
||||||
|
export
|
||||||
|
0 consEquiv : (full : OPE m' (S n) mask') ->
|
||||||
|
(cons (uncons full).head (uncons full).tail).snd `Eqv` full
|
||||||
|
consEquiv full with %syntactic (uncons full)
|
||||||
|
_ | MkUncons head tail {isHead, isTail} =
|
||||||
|
consEquiv' full head tail isHead isTail
|
||||||
41
lib/Quox/Thin/Coprod.idr
Normal file
41
lib/Quox/Thin/Coprod.idr
Normal file
|
|
@ -0,0 +1,41 @@
|
||||||
|
module Quox.Thin.Coprod
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.Comp
|
||||||
|
import public Quox.Thin.View
|
||||||
|
import public Quox.Thin.List
|
||||||
|
import public Quox.Thin.Cover
|
||||||
|
import Data.DPair
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Coprod2 (ope1 : OPE m1 n mask1) (ope2 : OPE m2 n mask2) where
|
||||||
|
constructor MkCoprod2
|
||||||
|
{sizeMask : Nat}
|
||||||
|
{leftMask : Nat}
|
||||||
|
{rightMask : Nat}
|
||||||
|
{0 sub : OPE size n sizeMask}
|
||||||
|
{0 left : OPE m1 size leftMask}
|
||||||
|
{0 right : OPE m2 size rightMask}
|
||||||
|
0 leftComp : Comp sub left ope1
|
||||||
|
0 rightComp : Comp sub right ope2
|
||||||
|
{auto 0 isCover : Cover [left, right]}
|
||||||
|
%name Coprod2 cop
|
||||||
|
|
||||||
|
export
|
||||||
|
coprod2 : {n, mask1, mask2 : Nat} ->
|
||||||
|
(0 ope1 : OPE m1 n mask1) -> (0 ope2 : OPE m2 n mask2) ->
|
||||||
|
Coprod2 ope1 ope2
|
||||||
|
coprod2 ope1 ope2 with (view ope1) | (view ope2)
|
||||||
|
coprod2 Stop Stop | StopV | StopV = MkCoprod2 StopZ StopZ
|
||||||
|
coprod2 (Drop ope1 Refl) (Drop ope2 Refl) | DropV _ ope1 | DropV _ ope2 =
|
||||||
|
let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (DropZ l) (DropZ r)
|
||||||
|
coprod2 (Drop ope1 Refl) (Keep ope2 Refl) | DropV _ ope1 | KeepV _ ope2 =
|
||||||
|
let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KDZ l) (KeepZ r)
|
||||||
|
coprod2 (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
|
||||||
|
let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KeepZ l) (KDZ r)
|
||||||
|
coprod2 (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
|
||||||
|
let MkCoprod2 l r = coprod2 ope1 ope2 in MkCoprod2 (KeepZ l) (KeepZ r)
|
||||||
|
|
||||||
|
-- [todo] n-ary coprod
|
||||||
26
lib/Quox/Thin/Cover.idr
Normal file
26
lib/Quox/Thin/Cover.idr
Normal file
|
|
@ -0,0 +1,26 @@
|
||||||
|
module Quox.Thin.Cover
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.List
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
||| an OPE list is a cover if at least one of the OPEs has `Keep` as the head,
|
||||||
|
||| and the tails are also a cover
|
||||||
|
|||
|
||||||
|
||| in @egtbs it is a binary relation which is fine for ×ᵣ but i don't want to
|
||||||
|
||| write my AST in universe-of-syntaxes style. sorry
|
||||||
|
public export data Cover : OPEList n -> Type
|
||||||
|
|
||||||
|
||| the "`Keep` in the head" condition of a cover
|
||||||
|
public export data Cover1 : OPEList n -> Type
|
||||||
|
|
||||||
|
data Cover where
|
||||||
|
Nil : Cover opes {n = 0}
|
||||||
|
(::) : Cover1 opes -> All2 IsTail opes tails => Cover tails -> Cover opes
|
||||||
|
%name Cover cov
|
||||||
|
|
||||||
|
data Cover1 where
|
||||||
|
Here : Cover1 (Keep ope eq :: opes)
|
||||||
|
There : Cover1 opes -> Cover1 (ope :: opes)
|
||||||
|
%name Cover1 cov1
|
||||||
128
lib/Quox/Thin/Eqv.idr
Normal file
128
lib/Quox/Thin/Eqv.idr
Normal file
|
|
@ -0,0 +1,128 @@
|
||||||
|
module Quox.Thin.Eqv
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.View
|
||||||
|
import Quox.NatExtra
|
||||||
|
import Syntax.PreorderReasoning
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
infix 6 `Eqv`
|
||||||
|
|
||||||
|
private
|
||||||
|
uip : (p, q : a = b) -> p = q
|
||||||
|
uip Refl Refl = Refl
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
data Eqv : OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Type where
|
||||||
|
EqvStop : Eqv Stop Stop
|
||||||
|
EqvDrop : {0 p : OPE m1 n1 mask1} ->
|
||||||
|
{0 q : OPE m2 n2 mask2} ->
|
||||||
|
Eqv p q -> Eqv (Drop p eq1) (Drop q eq2)
|
||||||
|
EqvKeep : {0 p : OPE m1 n1 mask1} ->
|
||||||
|
{0 q : OPE m2 n2 mask2} ->
|
||||||
|
Eqv p q -> Eqv (Keep p eq1) (Keep q eq2)
|
||||||
|
%name Eqv eqv
|
||||||
|
|
||||||
|
export Uninhabited (Stop `Eqv` Drop p e) where uninhabited _ impossible
|
||||||
|
export Uninhabited (Stop `Eqv` Keep p e) where uninhabited _ impossible
|
||||||
|
export Uninhabited (Drop p e `Eqv` Stop) where uninhabited _ impossible
|
||||||
|
export Uninhabited (Drop p e `Eqv` Keep q f) where uninhabited _ impossible
|
||||||
|
export Uninhabited (Keep p e `Eqv` Stop) where uninhabited _ impossible
|
||||||
|
export Uninhabited (Keep p e `Eqv` Drop q f) where uninhabited _ impossible
|
||||||
|
|
||||||
|
export
|
||||||
|
Reflexive (OPE m n mask) Eqv where
|
||||||
|
reflexive {x = Stop} = EqvStop
|
||||||
|
reflexive {x = Drop {}} = EqvDrop reflexive
|
||||||
|
reflexive {x = Keep {}} = EqvKeep reflexive
|
||||||
|
|
||||||
|
export
|
||||||
|
symmetric : p `Eqv` q -> q `Eqv` p
|
||||||
|
symmetric EqvStop = EqvStop
|
||||||
|
symmetric (EqvDrop eqv) = EqvDrop $ symmetric eqv
|
||||||
|
symmetric (EqvKeep eqv) = EqvKeep $ symmetric eqv
|
||||||
|
|
||||||
|
export
|
||||||
|
transitive : p `Eqv` q -> q `Eqv` r -> p `Eqv` r
|
||||||
|
transitive EqvStop EqvStop = EqvStop
|
||||||
|
transitive (EqvDrop eqv1) (EqvDrop eqv2) = EqvDrop (transitive eqv1 eqv2)
|
||||||
|
transitive (EqvKeep eqv1) (EqvKeep eqv2) = EqvKeep (transitive eqv1 eqv2)
|
||||||
|
|
||||||
|
|
||||||
|
private
|
||||||
|
recompute' : {mask1, mask2, n1, n2 : Nat} ->
|
||||||
|
(0 p : OPE m1 n1 mask1) -> (0 q : OPE m2 n2 mask2) ->
|
||||||
|
(0 eqv : p `Eqv` q) -> p `Eqv` q
|
||||||
|
recompute' p q eqv with %syntactic (view p) | (view q)
|
||||||
|
recompute' Stop Stop _ | StopV | StopV = EqvStop
|
||||||
|
recompute' (Drop p _) (Drop q _) eqv | DropV _ p | DropV _ q =
|
||||||
|
EqvDrop $ recompute' {eqv = let EqvDrop e = eqv in e, _}
|
||||||
|
recompute' (Keep p _) (Keep q _) eqv | KeepV _ p | KeepV _ q =
|
||||||
|
EqvKeep $ recompute' {eqv = let EqvKeep e = eqv in e, _}
|
||||||
|
recompute' (Drop p _) (Keep q _) eqv | DropV _ p | KeepV _ q =
|
||||||
|
void $ absurd eqv
|
||||||
|
recompute' (Keep p _) (Drop q _) eqv | KeepV _ p | DropV _ q =
|
||||||
|
void $ absurd eqv
|
||||||
|
|
||||||
|
private
|
||||||
|
recompute : {mask1, mask2, n1, n2 : Nat} ->
|
||||||
|
{0 p : OPE m1 n1 mask1} -> {0 q : OPE m2 n2 mask2} ->
|
||||||
|
(0 _ : p `Eqv` q) -> p `Eqv` q
|
||||||
|
recompute eqv = recompute' {eqv, _}
|
||||||
|
|
||||||
|
|
||||||
|
export
|
||||||
|
eqvIndices : {0 p : OPE m1 n1 mask1} -> {0 q : OPE m2 n2 mask2} ->
|
||||||
|
p `Eqv` q -> (m1 = m2, n1 = n2, mask1 = mask2)
|
||||||
|
eqvIndices EqvStop = (Refl, Refl, Refl)
|
||||||
|
eqvIndices (EqvDrop eqv {eq1 = Refl, eq2 = Refl}) =
|
||||||
|
let (Refl, Refl, Refl) = eqvIndices eqv in (Refl, Refl, Refl)
|
||||||
|
eqvIndices (EqvKeep eqv {eq1 = Refl, eq2 = Refl}) =
|
||||||
|
let (Refl, Refl, Refl) = eqvIndices eqv in (Refl, Refl, Refl)
|
||||||
|
|
||||||
|
export
|
||||||
|
0 eqvMask : (p : OPE m1 n mask1) -> (q : OPE m2 n mask2) ->
|
||||||
|
mask1 = mask2 -> p `Eqv` q
|
||||||
|
eqvMask Stop Stop _ = EqvStop
|
||||||
|
eqvMask (Drop ope1 Refl) (Drop {mask = mm2} ope2 eq2) Refl =
|
||||||
|
EqvDrop $ eqvMask ope1 ope2 (doubleInj _ _ eq2)
|
||||||
|
eqvMask (Drop ope1 Refl) (Keep ope2 eq2) Refl =
|
||||||
|
void $ notEvenOdd _ _ eq2
|
||||||
|
eqvMask (Keep ope1 eq1) (Keep ope2 eq2) Refl =
|
||||||
|
EqvKeep $ eqvMask ope1 ope2 (doubleInj _ _ $ inj S $ trans (sym eq1) eq2)
|
||||||
|
eqvMask (Keep ope1 eq1) (Drop ope2 eq2) Refl =
|
||||||
|
void $ notEvenOdd _ _ $ trans (sym eq2) eq1
|
||||||
|
|
||||||
|
export
|
||||||
|
0 eqvEq : (p, q : OPE m n mask) -> p `Eqv` q -> p === q
|
||||||
|
eqvEq Stop Stop EqvStop = Refl
|
||||||
|
eqvEq (Drop p eq1) (Drop q eq2) (EqvDrop eqv)
|
||||||
|
with %syntactic (doubleInj _ _ $ trans (sym eq1) eq2)
|
||||||
|
_ | Refl = cong2 Drop (eqvEq p q eqv) (uip eq1 eq2)
|
||||||
|
eqvEq (Keep p eq1) (Keep q eq2) (EqvKeep eqv)
|
||||||
|
with %syntactic (doubleInj _ _ $ inj S $ trans (sym eq1) eq2)
|
||||||
|
_ | Refl = cong2 Keep (eqvEq p q eqv) (uip eq1 eq2)
|
||||||
|
|
||||||
|
export
|
||||||
|
0 eqvEq' : (p : OPE m1 n1 mask1) -> (q : OPE m2 n2 mask2) ->
|
||||||
|
p `Eqv` q -> p ~=~ q
|
||||||
|
eqvEq' p q eqv = let (Refl, Refl, Refl) = eqvIndices eqv in eqvEq p q eqv
|
||||||
|
|
||||||
|
export
|
||||||
|
0 maskEqInner : (0 ope1 : OPE m1 n mask1) -> (0 ope2 : OPE m2 n mask2) ->
|
||||||
|
mask1 = mask2 -> m1 = m2
|
||||||
|
maskEqInner Stop Stop _ = Refl
|
||||||
|
maskEqInner (Drop ope1 Refl) (Drop ope2 Refl) eq =
|
||||||
|
maskEqInner ope1 ope2 (doubleInj _ _ eq)
|
||||||
|
maskEqInner (Keep ope1 Refl) (Keep ope2 Refl) eq =
|
||||||
|
cong S $ maskEqInner ope1 ope2 $ doubleInj _ _ $ inj S eq
|
||||||
|
maskEqInner (Drop ope1 Refl) (Keep ope2 Refl) eq = void $ notEvenOdd _ _ eq
|
||||||
|
maskEqInner (Keep {mask = mask1'} ope1 eq1) (Drop {mask = mask2'} ope2 eq2) eq =
|
||||||
|
-- matching on eq1, eq2, or eq here triggers that weird coverage bug ☹
|
||||||
|
void $ notEvenOdd _ _ $ Calc $
|
||||||
|
|~ mask2' + mask2'
|
||||||
|
~~ mask2 ..<(eq2)
|
||||||
|
~~ mask1 ..<(eq)
|
||||||
|
~~ S (mask1' + mask1') ...(eq1)
|
||||||
123
lib/Quox/Thin/List.idr
Normal file
123
lib/Quox/Thin/List.idr
Normal file
|
|
@ -0,0 +1,123 @@
|
||||||
|
module Quox.Thin.List
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.Cons
|
||||||
|
import Data.DPair
|
||||||
|
import Data.Nat
|
||||||
|
import Control.Function
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
||| a list of OPEs of a given outer scope size
|
||||||
|
||| (at runtime just the masks)
|
||||||
|
public export
|
||||||
|
data OPEList : Nat -> Type where
|
||||||
|
Nil : OPEList n
|
||||||
|
(::) : {mask : Nat} -> (0 ope : OPE m n mask) -> OPEList n -> OPEList n
|
||||||
|
%name OPEList opes
|
||||||
|
|
||||||
|
export
|
||||||
|
length : OPEList n -> Nat
|
||||||
|
length [] = 0
|
||||||
|
length (_ :: opes) = S $ length opes
|
||||||
|
|
||||||
|
export
|
||||||
|
toList : OPEList n -> List (SomeOPE n)
|
||||||
|
toList [] = []
|
||||||
|
toList (ope :: opes) = MkOPE ope :: toList opes
|
||||||
|
|
||||||
|
export
|
||||||
|
fromList : List (SomeOPE n) -> OPEList n
|
||||||
|
fromList [] = []
|
||||||
|
fromList (MkOPE ope :: xs) = ope :: fromList xs
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
0 Pred : Nat -> Type
|
||||||
|
Pred n = forall m, mask. OPE m n mask -> Type
|
||||||
|
|
||||||
|
public export
|
||||||
|
0 Rel : Nat -> Nat -> Type
|
||||||
|
Rel n1 n2 = forall m1, m2, mask1, mask2.
|
||||||
|
OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Type
|
||||||
|
|
||||||
|
namespace All
|
||||||
|
public export
|
||||||
|
data All : Pred n -> OPEList n -> Type where
|
||||||
|
Nil : {0 p : Pred n} -> All p []
|
||||||
|
(::) : {0 p : Pred n} -> p ope -> All p opes -> All p (ope :: opes)
|
||||||
|
%name All.All ps, qs
|
||||||
|
|
||||||
|
namespace All2
|
||||||
|
public export
|
||||||
|
data All2 : Rel n1 n2 -> OPEList n1 -> OPEList n2 -> Type where
|
||||||
|
Nil : {0 p : Rel n1 n2} -> All2 p [] []
|
||||||
|
(::) : {0 p : Rel n1 n2} -> p a b -> All2 p as bs ->
|
||||||
|
All2 p (a :: as) (b :: bs)
|
||||||
|
%name All2.All2 ps, qs
|
||||||
|
|
||||||
|
namespace Any
|
||||||
|
public export
|
||||||
|
data Any : Pred n -> OPEList n -> Type where
|
||||||
|
Here : {0 p : Pred n} -> p ope -> Any p (ope :: opes)
|
||||||
|
There : {0 p : Pred n} -> Any p opes -> Any p (ope :: opes)
|
||||||
|
%name Any.Any p, q
|
||||||
|
|
||||||
|
export
|
||||||
|
{0 p : Pred n} -> Uninhabited (Any p []) where uninhabited _ impossible
|
||||||
|
|
||||||
|
export
|
||||||
|
all : {0 p : Pred n} ->
|
||||||
|
(forall m. {mask : Nat} -> (0 ope : OPE m n mask) -> p ope) ->
|
||||||
|
(opes : OPEList n) -> All p opes
|
||||||
|
all f [] = []
|
||||||
|
all f (ope :: opes) = f ope :: all f opes
|
||||||
|
|
||||||
|
export
|
||||||
|
allDec : {0 p : Pred n} ->
|
||||||
|
(forall m. {mask : Nat} -> (0 ope : OPE m n mask) -> Dec (p ope)) ->
|
||||||
|
(opes : OPEList n) -> Dec (All p opes)
|
||||||
|
allDec f [] = Yes []
|
||||||
|
allDec f (ope :: opes) = case f ope of
|
||||||
|
Yes y => case allDec f opes of
|
||||||
|
Yes ys => Yes $ y :: ys
|
||||||
|
No k => No $ \(_ :: ps) => k ps
|
||||||
|
No k => No $ \(p :: _) => k p
|
||||||
|
|
||||||
|
export
|
||||||
|
anyDec : {0 p : Pred n} ->
|
||||||
|
(forall m. {mask : Nat} -> (0 ope : OPE m n mask) -> Dec (p ope)) ->
|
||||||
|
(opes : OPEList n) -> Dec (Any p opes)
|
||||||
|
anyDec f [] = No absurd
|
||||||
|
anyDec f (ope :: opes) = case f ope of
|
||||||
|
Yes y => Yes $ Here y
|
||||||
|
No nh => case anyDec f opes of
|
||||||
|
Yes y => Yes $ There y
|
||||||
|
No nt => No $ \case Here h => nh h; There t => nt t
|
||||||
|
|
||||||
|
|
||||||
|
export
|
||||||
|
unconses : {n : Nat} -> (opes : OPEList (S n)) -> All Uncons opes
|
||||||
|
unconses = all uncons
|
||||||
|
|
||||||
|
export
|
||||||
|
heads : {n : Nat} -> (opes : OPEList (S n)) -> All (Exists . IsHead) opes
|
||||||
|
heads = all head
|
||||||
|
|
||||||
|
export
|
||||||
|
tails : {n : Nat} -> (opes : OPEList (S n)) -> All Tail opes
|
||||||
|
tails = all tail
|
||||||
|
|
||||||
|
-- [fixme] factor this out probably
|
||||||
|
export
|
||||||
|
tails_ : {n : Nat} -> (opes : OPEList (S n)) ->
|
||||||
|
Subset (OPEList n) (All2 IsTail opes)
|
||||||
|
tails_ [] = Element [] []
|
||||||
|
tails_ (ope :: opes) = Element _ $ (tail ope).isTail :: (tails_ opes).snd
|
||||||
|
|
||||||
|
export
|
||||||
|
conses : (heads : List Bool) -> (tails : OPEList n) ->
|
||||||
|
(0 len : length heads = length tails) =>
|
||||||
|
OPEList (S n)
|
||||||
|
conses [] [] = []
|
||||||
|
conses (h :: hs) (t :: ts) = snd (cons h t) :: conses hs ts @{inj S len}
|
||||||
57
lib/Quox/Thin/Split.idr
Normal file
57
lib/Quox/Thin/Split.idr
Normal file
|
|
@ -0,0 +1,57 @@
|
||||||
|
module Quox.Thin.Split
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.View
|
||||||
|
import public Quox.Thin.Eqv
|
||||||
|
import public Quox.Thin.Append
|
||||||
|
import public Quox.Thin.Cover
|
||||||
|
import Data.DPair
|
||||||
|
import Control.Relation
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Chunks m n where
|
||||||
|
constructor MkChunks
|
||||||
|
{leftMask : Nat}
|
||||||
|
{rightMask : Nat}
|
||||||
|
0 left : OPE m (m + n) leftMask
|
||||||
|
0 right : OPE n (m + n) rightMask
|
||||||
|
{auto 0 isCover : Cover [left, right]}
|
||||||
|
%name Chunks chunks
|
||||||
|
|
||||||
|
export
|
||||||
|
chunks : (m, n : Nat) -> Chunks m n
|
||||||
|
chunks 0 0 = MkChunks Stop Stop
|
||||||
|
chunks 0 (S n) =
|
||||||
|
let MkChunks l r = chunks 0 n in
|
||||||
|
MkChunks (Drop l Refl) (Keep r Refl)
|
||||||
|
chunks (S m) n =
|
||||||
|
let MkChunks l r = chunks m n in
|
||||||
|
MkChunks (Keep l Refl) (Drop r Refl)
|
||||||
|
|
||||||
|
-- [todo] the masks here are just ((2 << m) - 1) << n and (2 << n) - 1
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
record SplitAt m n1 n2 (ope : OPE m (n1 + n2) mask) where
|
||||||
|
constructor MkSplitAt
|
||||||
|
{leftMask, rightMask : Nat}
|
||||||
|
{0 leftScope, rightScope : Nat}
|
||||||
|
0 left : OPE leftScope n1 leftMask
|
||||||
|
0 right : OPE rightScope n2 rightMask
|
||||||
|
0 scopePrf : m = leftScope + rightScope
|
||||||
|
0 opePrf : ope `Eqv` (left `app'` right).snd
|
||||||
|
%name SplitAt split
|
||||||
|
|
||||||
|
export
|
||||||
|
splitAt : (n1 : Nat) -> {n2, mask : Nat} -> (0 ope : OPE m (n1 + n2) mask) ->
|
||||||
|
SplitAt m n1 n2 ope
|
||||||
|
splitAt 0 ope = MkSplitAt zero ope Refl reflexive
|
||||||
|
splitAt (S n1) ope with %syntactic (view ope)
|
||||||
|
splitAt (S n1) (Drop ope Refl) | DropV _ ope with %syntactic (splitAt n1 ope)
|
||||||
|
_ | MkSplitAt left right scopePrf opePrf =
|
||||||
|
MkSplitAt (Drop left Refl) right scopePrf (EqvDrop opePrf)
|
||||||
|
splitAt (S n1) (Keep ope Refl) | KeepV _ ope with %syntactic (splitAt n1 ope)
|
||||||
|
_ | MkSplitAt left right scopePrf opePrf =
|
||||||
|
MkSplitAt (Keep left Refl) right (cong S scopePrf) (EqvKeep opePrf)
|
||||||
179
lib/Quox/Thin/Term.idr
Normal file
179
lib/Quox/Thin/Term.idr
Normal file
|
|
@ -0,0 +1,179 @@
|
||||||
|
module Quox.Thin.Term
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import public Quox.Thin.Comp
|
||||||
|
import public Quox.Thin.List
|
||||||
|
import Quox.Thin.Eqv
|
||||||
|
import public Quox.Thin.Cover
|
||||||
|
import Quox.Name
|
||||||
|
import Quox.Loc
|
||||||
|
import Data.DPair
|
||||||
|
import public Data.List.Quantifiers
|
||||||
|
import Data.Vect
|
||||||
|
import Data.Singleton
|
||||||
|
import Decidable.Equality
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Thinned f n where
|
||||||
|
constructor Th
|
||||||
|
{0 scope : Nat}
|
||||||
|
{scopeMask : Nat}
|
||||||
|
0 ope : OPE scope n scopeMask
|
||||||
|
term : f scope
|
||||||
|
%name Thinned s, t, u
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Eq (f n)) => Eq (Thinned f n) where
|
||||||
|
s == t = case decEq s.scopeMask t.scopeMask of
|
||||||
|
Yes eq => s.term == (rewrite maskEqInner s.ope t.ope eq in t.term)
|
||||||
|
No _ => False
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Located (f n)) => Located (Thinned f n) where
|
||||||
|
term.loc = term.term.loc
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Relocatable (f n)) => Relocatable (Thinned f n) where
|
||||||
|
setLoc loc = {term $= setLoc loc}
|
||||||
|
|
||||||
|
namespace Thinned
|
||||||
|
export
|
||||||
|
pure : {n : Nat} -> f n -> Thinned f n
|
||||||
|
pure term = Th id.snd term
|
||||||
|
|
||||||
|
export
|
||||||
|
join : {n : Nat} -> Thinned (Thinned f) n -> Thinned f n
|
||||||
|
join (Th ope1 (Th ope2 term)) = Th (ope1 . ope2) term
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
record ScopedN (s : Nat) (f : Nat -> Type) (n : Nat) where
|
||||||
|
constructor S
|
||||||
|
names : Vect s BindName
|
||||||
|
{0 scope : Nat}
|
||||||
|
{mask : Nat}
|
||||||
|
0 ope : OPE scope s mask
|
||||||
|
body : f (scope + n)
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Eq (f n)) => Eq (ScopedN s f n) where
|
||||||
|
s1 == s2 = case decEq s1.mask s2.mask of
|
||||||
|
Yes eq =>
|
||||||
|
s1.names == s2.names &&
|
||||||
|
s1.body == (rewrite maskEqInner s1.ope s2.ope eq in s2.body)
|
||||||
|
No _ => False
|
||||||
|
|
||||||
|
export
|
||||||
|
{s : Nat} -> (forall n. Show (f n)) => Show (ScopedN s f n) where
|
||||||
|
showPrec d (S ns ope body) = showCon d "S" $
|
||||||
|
showArg ns ++ showArg (unVal $ maskToOpe ope) ++ showArg body
|
||||||
|
|
||||||
|
public export
|
||||||
|
Scoped : (Nat -> Type) -> Nat -> Type
|
||||||
|
Scoped d n = ScopedN 1 d n
|
||||||
|
|
||||||
|
(.name) : Scoped f n -> BindName
|
||||||
|
(S {names = [x], _}).name = x
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Located (f n)) => Located (ScopedN s f n) where
|
||||||
|
s.loc = s.body.loc
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall n. Relocatable (f n)) => Relocatable (ScopedN s f n) where
|
||||||
|
setLoc loc = {body $= setLoc loc}
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Thinned2 f d n where
|
||||||
|
constructor Th2
|
||||||
|
{0 dscope, tscope : Nat}
|
||||||
|
{dmask, tmask : Nat}
|
||||||
|
0 dope : OPE dscope d dmask
|
||||||
|
0 tope : OPE tscope n tmask
|
||||||
|
term : f dscope tscope
|
||||||
|
%name Thinned2 term
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall d, n. Eq (f d n)) => Eq (Thinned2 f d n) where
|
||||||
|
s == t = case (decEq s.dmask t.dmask, decEq s.tmask t.tmask) of
|
||||||
|
(Yes deq, Yes teq) =>
|
||||||
|
s.term == (rewrite maskEqInner s.dope t.dope deq in
|
||||||
|
rewrite maskEqInner s.tope t.tope teq in t.term)
|
||||||
|
_ => False
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall d, n. Located (f d n)) => Located (Thinned2 f d n) where
|
||||||
|
term.loc = term.term.loc
|
||||||
|
|
||||||
|
export
|
||||||
|
(forall d, n. Relocatable (f d n)) => Relocatable (Thinned2 f d n) where
|
||||||
|
setLoc loc = {term $= setLoc loc}
|
||||||
|
|
||||||
|
namespace Thinned2
|
||||||
|
export
|
||||||
|
pure : {d, n : Nat} -> f d n -> Thinned2 f d n
|
||||||
|
pure term = Th2 id.snd id.snd term
|
||||||
|
|
||||||
|
export
|
||||||
|
join : {d, n : Nat} -> Thinned2 (Thinned2 f) d n -> Thinned2 f d n
|
||||||
|
join (Th2 dope1 tope1 (Th2 dope2 tope2 term)) =
|
||||||
|
Th2 (dope1 . dope2) (tope1 . tope2) term
|
||||||
|
|
||||||
|
|
||||||
|
namespace TermList
|
||||||
|
public export
|
||||||
|
data Element : (Nat -> Nat -> Type) ->
|
||||||
|
OPE dscope d dmask -> OPE tscope n tmask -> Type where
|
||||||
|
T : f dscope tscope ->
|
||||||
|
{dmask : Nat} -> (0 dope : OPE dscope d dmask) ->
|
||||||
|
{tmask : Nat} -> (0 tope : OPE tscope n tmask) ->
|
||||||
|
Element f dope tope
|
||||||
|
%name TermList.Element s, t, u
|
||||||
|
|
||||||
|
export
|
||||||
|
elementEq : (forall d, n. Eq (f d n)) =>
|
||||||
|
Element {d, n} f dope1 tope1 -> Element {d, n} f dope2 tope2 ->
|
||||||
|
Bool
|
||||||
|
elementEq (T s dope1 tope1 {dmask = dm1, tmask = tm1})
|
||||||
|
(T t dope2 tope2 {dmask = dm2, tmask = tm2}) =
|
||||||
|
case (decEq dm1 dm2, decEq tm1 tm2) of
|
||||||
|
(Yes deq, Yes teq) =>
|
||||||
|
s == (rewrite maskEqInner dope1 dope2 deq in
|
||||||
|
rewrite maskEqInner tope1 tope2 teq in t)
|
||||||
|
_ => False
|
||||||
|
|
||||||
|
public export
|
||||||
|
data TermList : List (Nat -> Nat -> Type) ->
|
||||||
|
OPEList d -> OPEList n -> Type where
|
||||||
|
Nil : TermList [] [] []
|
||||||
|
(::) : Element f dope tope ->
|
||||||
|
TermList fs dopes topes ->
|
||||||
|
TermList (f :: fs) (dope :: dopes) (tope :: topes)
|
||||||
|
%name TermList ss, ts, us
|
||||||
|
|
||||||
|
export
|
||||||
|
termListEq : All (\f => forall d, n. Eq (f d n)) fs =>
|
||||||
|
TermList {d, n} fs dopes1 topes1 ->
|
||||||
|
TermList {d, n} fs dopes2 topes2 ->
|
||||||
|
Bool
|
||||||
|
termListEq [] [] = True
|
||||||
|
termListEq (s :: ss) (t :: ts) @{eq :: eqs} =
|
||||||
|
elementEq s t && termListEq ss ts
|
||||||
|
|
||||||
|
|
||||||
|
public export
|
||||||
|
record Subterms (fs : List (Nat -> Nat -> Type)) d n where
|
||||||
|
constructor Sub
|
||||||
|
{0 dopes : OPEList d}
|
||||||
|
{0 topes : OPEList n}
|
||||||
|
terms : TermList fs dopes topes
|
||||||
|
0 dcov : Cover dopes
|
||||||
|
0 tcov : Cover topes
|
||||||
|
%name Subterms ss, ts, us
|
||||||
|
|
||||||
|
export
|
||||||
|
All (\f => forall d, n. Eq (f d n)) fs => Eq (Subterms fs d n) where
|
||||||
|
ss == ts = ss.terms `termListEq` ts.terms
|
||||||
76
lib/Quox/Thin/View.idr
Normal file
76
lib/Quox/Thin/View.idr
Normal file
|
|
@ -0,0 +1,76 @@
|
||||||
|
module Quox.Thin.View
|
||||||
|
|
||||||
|
import public Quox.Thin.Base
|
||||||
|
import Quox.NatExtra
|
||||||
|
import Data.Singleton
|
||||||
|
|
||||||
|
%default total
|
||||||
|
|
||||||
|
public export
|
||||||
|
data View : OPE m n mask -> Type where
|
||||||
|
StopV : View Stop
|
||||||
|
DropV : (mask : Nat) -> (0 ope : OPE m n mask) -> View (Drop ope Refl)
|
||||||
|
KeepV : (mask : Nat) -> (0 ope : OPE m n mask) -> View (Keep ope Refl)
|
||||||
|
%name View.View v
|
||||||
|
|
||||||
|
private
|
||||||
|
0 stopEqs : OPE m 0 mask -> (m = 0, mask = 0)
|
||||||
|
stopEqs Stop = (Refl, Refl)
|
||||||
|
|
||||||
|
private
|
||||||
|
0 fromStop : (ope : OPE 0 0 0) -> ope = Stop
|
||||||
|
fromStop Stop = Refl
|
||||||
|
|
||||||
|
private
|
||||||
|
0 fromDrop : (ope : OPE m (S n) (k + k)) ->
|
||||||
|
(inner : OPE m n k ** ope === Drop inner Refl)
|
||||||
|
fromDrop (Drop ope eq) with %syntactic (doubleInj _ _ eq)
|
||||||
|
fromDrop (Drop ope Refl) | Refl = (ope ** Refl)
|
||||||
|
fromDrop (Keep ope eq) = void $ notEvenOdd _ _ eq
|
||||||
|
|
||||||
|
private
|
||||||
|
0 fromKeep : (ope : OPE (S m) (S n) (S (k + k))) ->
|
||||||
|
(inner : OPE m n k ** ope === Keep inner Refl)
|
||||||
|
fromKeep (Drop ope eq) = void $ notEvenOdd _ _ $ sym eq
|
||||||
|
fromKeep (Keep ope eq) with %syntactic (doubleInj _ _ $ inj S eq)
|
||||||
|
fromKeep (Keep ope Refl) | Refl = (ope ** Refl)
|
||||||
|
|
||||||
|
private
|
||||||
|
0 keepIsSucc : (ope : OPE m n (S (k + k))) -> IsSucc m
|
||||||
|
keepIsSucc (Drop ope eq) = void $ notEvenOdd _ _ $ sym eq
|
||||||
|
keepIsSucc (Keep ope _) = ItIsSucc
|
||||||
|
|
||||||
|
export
|
||||||
|
view : {0 m : Nat} -> {n, mask : Nat} -> (0 ope : OPE m n mask) -> View ope
|
||||||
|
view {n = 0} ope with %syntactic 0 (fst $ stopEqs ope) | 0 (snd $ stopEqs ope)
|
||||||
|
_ | Refl | Refl = rewrite fromStop ope in StopV
|
||||||
|
view {n = S n} ope with %syntactic (half mask)
|
||||||
|
_ | HalfOdd mask' with %syntactic 0 (keepIsSucc ope)
|
||||||
|
_ | ItIsSucc with %syntactic 0 (fromKeep ope)
|
||||||
|
_ | (ope' ** eq) = rewrite eq in KeepV mask' ope'
|
||||||
|
_ | HalfEven mask' with %syntactic 0 (fromDrop ope)
|
||||||
|
_ | (ope' ** eq) = rewrite eq in DropV mask' ope'
|
||||||
|
|
||||||
|
|
||||||
|
export
|
||||||
|
appOpe : {0 m : Nat} -> (n : Nat) -> {mask : Nat} ->
|
||||||
|
(0 ope : OPE m n mask) -> Singleton m
|
||||||
|
appOpe n ope with %syntactic (view ope)
|
||||||
|
appOpe 0 Stop | StopV = Val 0
|
||||||
|
appOpe (S n) (Drop ope' _) | DropV _ ope' = appOpe n ope'
|
||||||
|
appOpe (S n) (Keep ope' _) | KeepV _ ope' = [|S $ appOpe n ope'|]
|
||||||
|
|
||||||
|
export
|
||||||
|
maskToOpe : {n, mask : Nat} -> (0 ope : OPE m n mask) -> Singleton ope
|
||||||
|
maskToOpe ope with %syntactic (view ope)
|
||||||
|
maskToOpe Stop | StopV = [|Stop|]
|
||||||
|
maskToOpe (Drop ope Refl) | DropV k ope = [|drop $ maskToOpe ope|]
|
||||||
|
maskToOpe (Keep ope Refl) | KeepV k ope = [|keep $ maskToOpe ope|]
|
||||||
|
|
||||||
|
export
|
||||||
|
0 outerInnerZero : OPE m 0 mask -> m = 0
|
||||||
|
outerInnerZero Stop = Refl
|
||||||
|
|
||||||
|
export
|
||||||
|
0 outerMaskZero : OPE m 0 mask -> mask = 0
|
||||||
|
outerMaskZero Stop = Refl
|
||||||
|
|
@ -16,9 +16,19 @@ modules =
|
||||||
Quox.Decidable,
|
Quox.Decidable,
|
||||||
Quox.No,
|
Quox.No,
|
||||||
Quox.Loc,
|
Quox.Loc,
|
||||||
Quox.OPE,
|
|
||||||
Quox.Thin,
|
|
||||||
Quox.Pretty,
|
Quox.Pretty,
|
||||||
|
Quox.Thin.Base,
|
||||||
|
Quox.Thin.View,
|
||||||
|
Quox.Thin.Eqv,
|
||||||
|
Quox.Thin.Cons,
|
||||||
|
Quox.Thin.List,
|
||||||
|
Quox.Thin.Append,
|
||||||
|
Quox.Thin.Comp,
|
||||||
|
Quox.Thin.Cover,
|
||||||
|
Quox.Thin.Coprod,
|
||||||
|
Quox.Thin.Split,
|
||||||
|
Quox.Thin.Term,
|
||||||
|
Quox.Thin,
|
||||||
Quox.Syntax,
|
Quox.Syntax,
|
||||||
Quox.Syntax.Dim,
|
Quox.Syntax.Dim,
|
||||||
Quox.Syntax.DimEq,
|
Quox.Syntax.DimEq,
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue