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14 changed files with 890 additions and 672 deletions
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@ -6,12 +6,16 @@ import Quox.Name
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import Data.DPair
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import Data.Nat
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import Data.Fin
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import Data.Singleton
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import Data.SnocList
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import Data.SnocVect
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import Data.Vect
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import Control.Monad.Identity
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import Derive.Prelude
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%default total
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%language ElabReflection
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||| a sequence of bindings under an existing context. each successive element
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@ -83,6 +87,13 @@ export %inline
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toSnocList' : Telescope' a _ _ -> SnocList a
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toSnocList' = toSnocListWith id
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export %inline
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toSnocListRelevant : {n1 : Nat} -> Telescope tm n1 n2 -> SnocList (n ** tm n)
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toSnocListRelevant tel = toSnocList' $ snd $ go tel where
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go : Telescope tm n1 n2' -> (Singleton n2', Telescope' (n ** tm n) n1 n2')
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go [<] = (Val n1, [<])
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go (tel :< x) = let (Val n, tel) = go tel in (Val (S n), tel :< (n ** x))
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export %inline
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toList : Telescope tm _ _ -> List (Exists tm)
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toList = toListWith (Evidence _)
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@ -136,34 +147,34 @@ tel ++ (sx :< x) = (tel ++ sx) :< x
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public export
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getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) ->
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Shift len out -> Context tm len -> Var len -> tm out
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getShiftWith shft by (ctx :< t) VZ = t `shft` ssDown by
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getShiftWith shft by (ctx :< t) (VS i) = getShiftWith shft (ssDown by) ctx i
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Shift len out -> Context tm len -> Fin len -> tm out
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getShiftWith shft by (ctx :< t) FZ = t `shft` ssDown by
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getShiftWith shft by (ctx :< t) (FS i) = getShiftWith shft (ssDown by) ctx i
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public export %inline
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getShift : CanShift tm => Shift len out -> Context tm len -> Var len -> tm out
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getShift : CanShift tm => Shift len out -> Context tm len -> Fin len -> tm out
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getShift = getShiftWith (//)
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public export %inline
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getWith : (forall from, to. tm from -> Shift from to -> tm to) ->
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Context tm len -> Var len -> tm len
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Context tm len -> Fin len -> tm len
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getWith shft = getShiftWith shft SZ
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infixl 8 !!
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public export %inline
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(!!) : CanShift tm => Context tm len -> Var len -> tm len
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(!!) : CanShift tm => Context tm len -> Fin len -> tm len
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(!!) = getWith (//)
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infixl 8 !!!
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public export %inline
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(!!!) : Context' tm len -> Var len -> tm
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(!!!) : Context' tm len -> Fin len -> tm
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(!!!) = getWith const
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public export
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find : Alternative f =>
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(forall n. tm n -> Bool) -> Context tm len -> f (Var len)
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(forall n. tm n -> Bool) -> Context tm len -> f (Fin len)
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find p [<] = empty
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find p (ctx :< x) = (guard (p x) $> VZ) <|> (VS <$> find p ctx)
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find p (ctx :< x) = (guard (p x) $> FZ) <|> (FS <$> find p ctx)
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export
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@ -320,6 +331,14 @@ export %inline
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where Show (Exists tm) where showPrec d t = showPrec d t.snd
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export
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implementation [ShowTelRelevant]
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{n1 : Nat} -> ({n : Nat} -> Show (f n)) => Show (Telescope f n1 n2)
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where
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showPrec d = showPrec d . toSnocListRelevant
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where Show (n : Nat ** f n) where showPrec d (_ ** t) = showPrec d t
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parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
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(nameHL : HL)
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(pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts))
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44
lib/Quox/FinExtra.idr
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44
lib/Quox/FinExtra.idr
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@ -0,0 +1,44 @@
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module Quox.FinExtra
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import public Data.Fin
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import Quox.Decidable
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public export
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data LT : Rel (Fin n) where
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LTZ : FZ `LT` FS i
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LTS : i `LT` j -> FS i `LT` FS j
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%builtin Natural FinExtra.LT
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%name FinExtra.LT lt
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public export %inline
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GT : Rel (Fin n)
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GT = flip LT
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export
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Transitive (Fin n) LT where
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transitive LTZ (LTS _) = LTZ
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transitive (LTS p) (LTS q) = LTS $ transitive p q
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export Uninhabited (i `FinExtra.LT` i) where uninhabited (LTS p) = uninhabited p
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export Uninhabited (FS i `LT` FZ) where uninhabited _ impossible
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public export
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data Compare : Rel (Fin n) where
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IsLT : (lt : i `LT` j) -> Compare i j
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IsEQ : Compare i i
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IsGT : (gt : i `GT` j) -> Compare i j
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%name Compare cmp
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export
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compareS : Compare i j -> Compare (FS i) (FS j)
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compareS (IsLT lt) = IsLT (LTS lt)
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compareS IsEQ = IsEQ
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compareS (IsGT gt) = IsGT (LTS gt)
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export
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compareP : (i, j : Fin n) -> Compare i j
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compareP FZ FZ = IsEQ
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compareP FZ (FS j) = IsLT LTZ
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compareP (FS i) FZ = IsGT LTZ
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compareP (FS i) (FS j) = compareS $ compareP i j
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@ -1,15 +1,18 @@
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module Quox.Syntax.Dim
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import Quox.Loc
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import Quox.Name
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import Quox.Thin
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import Quox.Syntax.Var
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import Quox.Syntax.Subst
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import Quox.Pretty
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import Quox.Name
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import Quox.Loc
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import Quox.Context
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import Decidable.Equality
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import Control.Function
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import Derive.Prelude
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import Data.DPair
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import Data.SnocVect
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%default total
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%language ElabReflection
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@ -39,38 +42,48 @@ DecEq DimConst where
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public export
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data Dim : Nat -> Type where
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K : DimConst -> Loc -> Dim d
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B : Var d -> Loc -> Dim d
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K : DimConst -> Loc -> Dim 0
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B : Loc -> Dim 1
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%name Dim.Dim p, q
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%runElab deriveIndexed "Dim" [Eq, Ord, Show]
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public export
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DimT : Nat -> Type
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DimT = Thinned Dim
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public export %inline
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KT : DimConst -> Loc -> DimT d
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KT e loc = Th zero $ K e loc
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||| `endsOr l r x p` returns `ends l r ε` if `p` is a constant ε, and
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||| `x` otherwise.
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public export
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endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a
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endsOr l r x (K e _) = ends l r e
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endsOr l r x (B _ _) = x
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endsOr l r x (B _) = x
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export
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Located (Dim d) where
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(K _ loc).loc = loc
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(B _ loc).loc = loc
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(B loc).loc = loc
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export
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Relocatable (Dim d) where
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setLoc loc (K e _) = K e loc
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setLoc loc (B i _) = B i loc
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setLoc loc (B _) = B loc
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export
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prettyDimConst : {opts : _} -> DimConst -> Eff Pretty (Doc opts)
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prettyDimConst = hl Dim . text . ends "0" "1"
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parameters {opts : LayoutOpts}
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export
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prettyDimConst : DimConst -> Eff Pretty (Doc opts)
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prettyDimConst = hl Dim . text . ends "0" "1"
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export
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prettyDim : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
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prettyDim names (K e _) = prettyDimConst e
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prettyDim names (B i _) = prettyDBind $ names !!! i
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export
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prettyDim : {d : Nat} -> BContext d -> DimT d -> Eff Pretty (Doc opts)
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prettyDim names (Th _ (K e _)) = prettyDimConst e
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prettyDim names (Th i (B _)) = prettyDBind $ names !!! i.fin
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public export %inline
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@ -83,57 +96,54 @@ DSubst : Nat -> Nat -> Type
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DSubst = Subst Dim
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public export FromVar Dim where fromVarLoc = B
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-- public export FromVar Dim where fromVarLoc = B
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export
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CanShift Dim where
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K e loc // _ = K e loc
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B i loc // by = B (i // by) loc
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-- export
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-- CanShift Dim where
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-- K e loc // _ = K e loc
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-- B i loc // by = B (i // by) loc
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export
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export %inline FromVar Dim where var = B
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export %inline
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CanSubstSelf Dim where
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K e loc // _ = K e loc
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B i loc // th = getLoc th i loc
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Th _ (K e loc) // _ = KT e loc
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Th i (B loc) // th = get th i.fin
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export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
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export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible
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export Uninhabited (B loc1 = K e loc2) where uninhabited _ impossible
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export Uninhabited (K e loc1 = B loc2) where uninhabited _ impossible
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public export
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data Eqv : Dim d1 -> Dim d2 -> Type where
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EK : K e _ `Eqv` K e _
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EB : i `Eqv` j -> B i _ `Eqv` B j _
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-- public export
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-- data Eqv : Dim d1 -> Dim d2 -> Type where
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-- EK : K e _ `Eqv` K e _
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-- EB : i `Eqv` j -> B i _ `Eqv` B j _
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export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
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export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
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-- export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
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-- export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
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export
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injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
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injectiveB (EB e) = e
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-- export
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-- injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
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-- injectiveB (EB e) = e
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export
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injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
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injectiveK EK = Refl
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-- export
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-- injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
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-- injectiveK EK = Refl
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public export
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decEqv : Dec2 Dim.Eqv
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decEqv (K e _) (K f _) = case decEq e f of
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Yes Refl => Yes EK
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No n => No $ n . injectiveK
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decEqv (B i _) (B j _) = case decEqv i j of
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Yes y => Yes $ EB y
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No n => No $ \(EB y) => n y
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decEqv (B _ _) (K _ _) = No absurd
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decEqv (K _ _) (B _ _) = No absurd
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-- public export
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-- decEqv : Dec2 Dim.Eqv
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-- decEqv (K e _) (K f _) = case decEq e f of
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-- Yes Refl => Yes EK
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-- No n => No $ n . injectiveK
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-- decEqv (B i _) (B j _) = case decEqv i j of
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-- Yes y => Yes $ EB y
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-- No n => No $ \(EB y) => n y
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-- decEqv (B _ _) (K _ _) = No absurd
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-- decEqv (K _ _) (B _ _) = No absurd
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||| abbreviation for a bound variable like `BV 4` instead of
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||| `B (VS (VS (VS (VS VZ))))`
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public export %inline
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BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d
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BV i loc = B (V i) loc
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export
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weakD : (by : Nat) -> Dim d -> Dim (by + d)
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weakD by p = p // shift by
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BV : (i : Fin d) -> (loc : Loc) -> DimT d
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BV i loc = Th (one' i) $ B loc
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@ -6,11 +6,14 @@ import public Quox.Syntax.Subst
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import public Quox.Context
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import Quox.Pretty
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import Quox.Name
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import Quox.Thin
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import Quox.FinExtra
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import Data.Maybe
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import Data.Nat
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import Data.DPair
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import Data.Fun.Graph
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import Data.SnocVect
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import Decidable.Decidable
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import Decidable.Equality
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import Derive.Prelude
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@ -21,7 +24,7 @@ import Derive.Prelude
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public export
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DimEq' : Nat -> Type
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DimEq' = Context (Maybe . Dim)
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DimEq' = Context (Maybe . DimT)
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public export
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@ -29,7 +32,12 @@ data DimEq : Nat -> Type where
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ZeroIsOne : DimEq d
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C : (eqs : DimEq' d) -> DimEq d
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%name DimEq eqs
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%runElab deriveIndexed "DimEq" [Eq, Ord, Show]
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%runElab deriveIndexed "DimEq" [Eq]
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export
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Show (DimEq d) where
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showPrec d ZeroIsOne = "ZeroIsOne"
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showPrec d (C eq') = showCon d "C" $ showArg eq' @{ShowTelRelevant}
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public export
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@ -72,7 +80,7 @@ toMaybe (Just x) = Just x
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export
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fromGround' : Context' DimConst d -> DimEq' d
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fromGround' [<] = [<]
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fromGround' (ctx :< e) = fromGround' ctx :< Just (K e noLoc)
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fromGround' (ctx :< e) = fromGround' ctx :< Just (KT e noLoc)
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export
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fromGround : Context' DimConst d -> DimEq d
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@ -94,39 +102,40 @@ new = C new'
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public export %inline
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get' : DimEq' d -> Var d -> Maybe (Dim d)
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get' : DimEq' d -> Fin d -> Maybe (DimT d)
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get' = getWith $ \p, by => map (// by) p
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public export %inline
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getVar : DimEq' d -> Var d -> Loc -> Dim d
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getVar eqs i loc = fromMaybe (B i loc) $ get' eqs i
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public export %inline
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getShift' : Shift len out -> DimEq' len -> Var len -> Maybe (Dim out)
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getShift' : Shift len out -> DimEq' len -> Fin len -> Maybe (DimT out)
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getShift' = getShiftWith $ \p, by => map (// by) p
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public export %inline
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get : DimEq' d -> Dim d -> Dim d
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get _ (K e loc) = K e loc
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get eqs (B i loc) = getVar eqs i loc
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get : {d : Nat} -> DimEq' d -> DimT d -> DimT d
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get eqs p@(Th _ (K {})) = p
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get eqs p@(Th i (B _)) = fromMaybe p $ get' eqs i.fin
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public export %inline
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equal : DimEq d -> (p, q : Dim d) -> Bool
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equal : {d : Nat} -> DimEq d -> (p, q : DimT d) -> Bool
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equal ZeroIsOne p q = True
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equal (C eqs) p q = get eqs p == get eqs q
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infixl 7 :<?
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export %inline
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(:<?) : DimEq d -> Maybe (Dim d) -> DimEq (S d)
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(:<?) : {d : Nat} -> DimEq d -> Maybe (DimT d) -> DimEq (S d)
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ZeroIsOne :<? d = ZeroIsOne
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C eqs :<? d = C $ eqs :< map (get eqs) d
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private %inline
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ifVar : Var d -> Dim d -> Maybe (Dim d) -> Maybe (Dim d)
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ifVar i p = map $ \q => if q == B i noLoc then p else q
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isVar : {d : Nat} -> Fin d -> DimT d -> Bool
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isVar i (Th j (B _)) = i == j.fin
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isVar i (Th _ (K {})) = False
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private %inline
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ifVar : {d : Nat} -> Fin d -> DimT d -> Maybe (DimT d) -> Maybe (DimT d)
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ifVar i p = map $ \q => if isVar i q then p else q
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-- (using decEq instead of (==) because of the proofs below)
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private %inline
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@ -135,43 +144,45 @@ checkConst e f eqs = if isYes $ e `decEq` f then C eqs else ZeroIsOne
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export
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setConst : Var d -> DimConst -> Loc -> DimEq' d -> DimEq d
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setConst VZ e loc (eqs :< Nothing) =
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C $ eqs :< Just (K e loc)
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setConst VZ e _ (eqs :< Just (K f loc)) =
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checkConst e f $ eqs :< Just (K f loc)
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setConst VZ e loc (eqs :< Just (B i _)) =
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setConst i e loc eqs :<? Just (K e loc)
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setConst (VS i) e loc (eqs :< p) =
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setConst i e loc eqs :<? ifVar i (K e loc) p
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setConst : {d : Nat} -> Fin d -> DimConst -> Loc -> DimEq' d -> DimEq d
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setConst FZ e loc (eqs :< Nothing) =
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C $ eqs :< Just (KT e loc)
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setConst FZ e _ (eqs :< Just (Th _ (K f loc))) =
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checkConst e f $ eqs :< Just (KT f loc)
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setConst FZ e loc (eqs :< Just (Th j (B _))) =
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setConst j.fin e loc eqs :<? Just (KT e loc)
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setConst (FS i) e loc (eqs :< p) =
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setConst i e loc eqs :<? ifVar i (KT e loc) p
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mutual
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private
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setVar' : (i, j : Var d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
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setVar' VZ (VS i) LTZ loc (eqs :< Nothing) =
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C eqs :<? Just (B i loc)
|
||||
setVar' VZ (VS i) LTZ loc (eqs :< Just (K e eloc)) =
|
||||
setConst i e loc eqs :<? Just (K e eloc)
|
||||
setVar' VZ (VS i) LTZ loc (eqs :< Just (B j jloc)) =
|
||||
setVar i j loc jloc eqs :<? Just (if j > i then B j jloc else B i loc)
|
||||
setVar' (VS i) (VS j) (LTS lt) loc (eqs :< p) =
|
||||
setVar' i j lt loc eqs :<? ifVar i (B j loc) p
|
||||
setVar' : {d : Nat} ->
|
||||
(i, j : Fin d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
|
||||
setVar' FZ (FS i) LTZ loc (eqs :< Nothing) =
|
||||
C eqs :<? Just (BV i loc)
|
||||
setVar' FZ (FS i) LTZ loc (eqs :< Just (Th _ (K e eloc))) =
|
||||
setConst i e loc eqs :<? Just (KT e eloc)
|
||||
setVar' FZ (FS i) LTZ loc (eqs :< Just (Th j (B jloc))) =
|
||||
let j = j.fin in
|
||||
setVar i j loc jloc eqs :<? Just (if j > i then BV j jloc else BV i loc)
|
||||
setVar' (FS i) (FS j) (LTS lt) loc (eqs :< p) =
|
||||
setVar' i j lt loc eqs :<? ifVar i (BV j loc) p
|
||||
|
||||
export %inline
|
||||
setVar : (i, j : Var d) -> Loc -> Loc -> DimEq' d -> DimEq d
|
||||
setVar i j li lj eqs with (compareP i j) | (compare i.nat j.nat)
|
||||
setVar i j li lj eqs | IsLT lt | LT = setVar' i j lt lj eqs
|
||||
setVar i i li lj eqs | IsEQ | EQ = C eqs
|
||||
setVar i j li lj eqs | IsGT gt | GT = setVar' j i gt li eqs
|
||||
setVar : {d : Nat} -> (i, j : Fin d) -> Loc -> Loc -> DimEq' d -> DimEq d
|
||||
setVar i j li lj eqs with (compareP i j)
|
||||
setVar i j li lj eqs | IsLT lt = setVar' i j lt lj eqs
|
||||
setVar i i li lj eqs | IsEQ = C eqs
|
||||
setVar i j li lj eqs | IsGT gt = setVar' j i gt li eqs
|
||||
|
||||
|
||||
export %inline
|
||||
set : (p, q : Dim d) -> DimEq d -> DimEq d
|
||||
set : {d : Nat} -> (p, q : DimT d) -> DimEq d -> DimEq d
|
||||
set _ _ ZeroIsOne = ZeroIsOne
|
||||
set (K e eloc) (K f floc) (C eqs) = checkConst e f eqs
|
||||
set (K e eloc) (B i iloc) (C eqs) = setConst i e eloc eqs
|
||||
set (B i iloc) (K e eloc) (C eqs) = setConst i e eloc eqs
|
||||
set (B i iloc) (B j jloc) (C eqs) = setVar i j iloc jloc eqs
|
||||
set (Th _ (K e _)) (Th _ (K f _)) (C eqs) = checkConst e f eqs
|
||||
set (Th _ (K e el)) (Th j (B _)) (C eqs) = setConst j.fin e el eqs
|
||||
set (Th i (B _)) (Th _ (K e el)) (C eqs) = setConst i.fin e el eqs
|
||||
set (Th i (B il)) (Th j (B jl)) (C eqs) = setVar i.fin j.fin il jl eqs
|
||||
|
||||
|
||||
public export %inline
|
||||
|
@ -179,97 +190,99 @@ Split : Nat -> Type
|
|||
Split d = (DimEq' d, DSubst (S d) d)
|
||||
|
||||
export %inline
|
||||
split1 : DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
|
||||
split1 e loc eqs = case setConst VZ e loc eqs of
|
||||
split1 : {d : Nat} -> DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
|
||||
split1 e loc eqs = case setConst 0 e loc eqs of
|
||||
ZeroIsOne => Nothing
|
||||
C (eqs :< _) => Just (eqs, K e loc ::: id)
|
||||
C (eqs :< _) => Just (eqs, id (B loc) :< KT e loc)
|
||||
|
||||
export %inline
|
||||
split : Loc -> DimEq' (S d) -> List (Split d)
|
||||
split : {d : Nat} -> Loc -> DimEq' (S d) -> List (Split d)
|
||||
split loc eqs = toList (split1 Zero loc eqs) <+> toList (split1 One loc eqs)
|
||||
|
||||
export
|
||||
splits' : Loc -> DimEq' d -> List (DSubst d 0)
|
||||
splits' _ [<] = [id]
|
||||
splits' : {d : Nat} -> Loc -> DimEq' d -> List (DSubst d 0)
|
||||
splits' _ [<] = [[<]]
|
||||
splits' loc eqs@(_ :< _) =
|
||||
[th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs']
|
||||
|
||||
||| the Loc is put into each of the DimConsts
|
||||
export %inline
|
||||
splits : Loc -> DimEq d -> List (DSubst d 0)
|
||||
splits : {d : Nat} -> Loc -> DimEq d -> List (DSubst d 0)
|
||||
splits _ ZeroIsOne = []
|
||||
splits loc (C eqs) = splits' loc eqs
|
||||
|
||||
|
||||
private
|
||||
0 newGetShift : (d : Nat) -> (i : Var d) -> (by : Shift d d') ->
|
||||
getShift' by (new' {d}) i = Nothing
|
||||
newGetShift (S d) VZ by = Refl
|
||||
newGetShift (S d) (VS i) by = newGetShift d i (ssDown by)
|
||||
-- private
|
||||
-- 0 newGetShift : (d : Nat) -> (i : Fin d) -> (by : Shift d d') ->
|
||||
-- getShift' by (new' {d}) i = Nothing
|
||||
-- newGetShift (S d) FZ by = Refl
|
||||
-- newGetShift (S d) (FS i) by = newGetShift d i (ssDown by)
|
||||
|
||||
export
|
||||
0 newGet' : (d : Nat) -> (i : Var d) -> get' (new' {d}) i = Nothing
|
||||
newGet' d i = newGetShift d i SZ
|
||||
-- export
|
||||
-- 0 newGet' : (d : Nat) -> (i : Fin d) -> get' (new' {d}) i = Nothing
|
||||
-- newGet' d i = newGetShift d i SZ
|
||||
|
||||
export
|
||||
0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
|
||||
newGet d (K e _) = Refl
|
||||
newGet d (B i _) = rewrite newGet' d i in Refl
|
||||
-- export
|
||||
-- 0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
|
||||
-- newGet d (K e _) = Refl
|
||||
-- newGet d (B i _) = rewrite newGet' d i in Refl
|
||||
|
||||
|
||||
export
|
||||
0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
|
||||
setSelf p ZeroIsOne = Refl
|
||||
setSelf (K Zero _) (C eqs) = Refl
|
||||
setSelf (K One _) (C eqs) = Refl
|
||||
setSelf (B i _) (C eqs) with (compareP i i) | (compare i.nat i.nat)
|
||||
_ | IsLT lt | LT = absurd lt
|
||||
_ | IsEQ | EQ = Refl
|
||||
_ | IsGT gt | GT = absurd gt
|
||||
-- export
|
||||
-- 0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
|
||||
-- setSelf p ZeroIsOne = Refl
|
||||
-- setSelf (K Zero _) (C eqs) = Refl
|
||||
-- setSelf (K One _) (C eqs) = Refl
|
||||
-- setSelf (B i _) (C eqs) with (compareP i i) | (compare i.nat i.nat)
|
||||
-- _ | IsLT lt | LT = absurd lt
|
||||
-- _ | IsEQ | EQ = Refl
|
||||
-- _ | IsGT gt | GT = absurd gt
|
||||
|
||||
|
||||
private
|
||||
prettyDVars : {opts : _} -> BContext d -> Eff Pretty (SnocList (Doc opts))
|
||||
prettyDVars = traverse prettyDBind . toSnocList'
|
||||
parameters {opts : LayoutOpts}
|
||||
private
|
||||
prettyDVars : {d : Nat} -> BContext d -> Eff Pretty (SnocList (Doc opts))
|
||||
prettyDVars = traverse prettyDBind . toSnocList'
|
||||
|
||||
private
|
||||
prettyCst : {opts : _} -> BContext d -> Dim d -> Dim d -> Eff Pretty (Doc opts)
|
||||
prettyCst dnames p q =
|
||||
hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
|
||||
private
|
||||
prettyCst : {d : Nat} -> BContext d -> DimT d -> DimT d -> Eff Pretty (Doc opts)
|
||||
prettyCst dnames p q =
|
||||
hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
|
||||
|
||||
private
|
||||
prettyCsts : {opts : _} -> BContext d -> DimEq' d ->
|
||||
Eff Pretty (SnocList (Doc opts))
|
||||
prettyCsts [<] [<] = pure [<]
|
||||
prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
|
||||
prettyCsts dnames (eqs :< Just q) =
|
||||
[|prettyCsts (tail dnames) eqs :< prettyCst dnames (BV 0 noLoc) (weakD 1 q)|]
|
||||
private
|
||||
prettyCsts : {d : Nat} -> BContext d -> DimEq' d ->
|
||||
Eff Pretty (SnocList (Doc opts))
|
||||
prettyCsts [<] [<] = pure [<]
|
||||
prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
|
||||
prettyCsts dnames (eqs :< Just q) =
|
||||
[|prettyCsts (tail dnames) eqs :<
|
||||
prettyCst dnames (BV 0 noLoc) (weak 1 q)|]
|
||||
|
||||
export
|
||||
prettyDimEq' : {opts : _} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
|
||||
prettyDimEq' dnames eqs = do
|
||||
vars <- prettyDVars dnames
|
||||
eqs <- prettyCsts dnames eqs
|
||||
let prec = if length vars <= 1 && null eqs then Arg else Outer
|
||||
parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
|
||||
export
|
||||
prettyDimEq' : {d : Nat} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
|
||||
prettyDimEq' dnames eqs = do
|
||||
vars <- prettyDVars dnames
|
||||
eqs <- prettyCsts dnames eqs
|
||||
let prec = if length vars <= 1 && null eqs then Arg else Outer
|
||||
parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
|
||||
|
||||
export
|
||||
prettyDimEq : {opts : _} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
|
||||
prettyDimEq dnames ZeroIsOne = do
|
||||
vars <- prettyDVars dnames
|
||||
cst <- prettyCst [<] (K Zero noLoc) (K One noLoc)
|
||||
pure $ separateTight !commaD $ vars :< cst
|
||||
prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
|
||||
export
|
||||
prettyDimEq : {d : Nat} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
|
||||
prettyDimEq dnames ZeroIsOne = do
|
||||
vars <- prettyDVars dnames
|
||||
cst <- prettyCst [<] (KT Zero noLoc) (KT One noLoc)
|
||||
pure $ separateTight !commaD $ vars :< cst
|
||||
prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
|
||||
|
||||
|
||||
public export
|
||||
wf' : DimEq' d -> Bool
|
||||
wf' [<] = True
|
||||
wf' (eqs :< Nothing) = wf' eqs
|
||||
wf' (eqs :< Just (K e _)) = wf' eqs
|
||||
wf' (eqs :< Just (B i _)) = isNothing (get' eqs i) && wf' eqs
|
||||
wf' : {d : Nat} -> DimEq' d -> Bool
|
||||
wf' [<] = True
|
||||
wf' (eqs :< Nothing) = wf' eqs
|
||||
wf' (eqs :< Just (Th _ (K {}))) = wf' eqs
|
||||
wf' (eqs :< Just (Th i (B _))) = isNothing (get' eqs i.fin) && wf' eqs
|
||||
|
||||
public export
|
||||
wf : DimEq d -> Bool
|
||||
wf : {d : Nat} -> DimEq d -> Bool
|
||||
wf ZeroIsOne = True
|
||||
wf (C eqs) = wf' eqs
|
||||
|
|
|
@ -1,9 +1,11 @@
|
|||
module Quox.Syntax.Shift
|
||||
|
||||
import public Quox.Syntax.Var
|
||||
import public Quox.Thin
|
||||
|
||||
import Data.Nat
|
||||
import Data.So
|
||||
import Data.DPair
|
||||
|
||||
%default total
|
||||
|
||||
|
@ -220,3 +222,15 @@ namespace CanShift
|
|||
|
||||
public export %inline
|
||||
[Const] CanShift (\_ => a) where x // _ = x
|
||||
|
||||
|
||||
export
|
||||
shiftOPE : {mask : Nat} -> (0 ope : OPE m n mask) ->
|
||||
Shift n n' -> Subset Nat (OPE m n')
|
||||
shiftOPE ope SZ = Element _ ope
|
||||
shiftOPE ope (SS by) =
|
||||
let Element _ ope = shiftOPE ope by in Element _ $ drop ope
|
||||
|
||||
export
|
||||
CanShift (Thinned f) where
|
||||
Th ope tm // by = Th (shiftOPE ope by).snd tm
|
||||
|
|
|
@ -1,10 +1,9 @@
|
|||
module Quox.Syntax.Subst
|
||||
|
||||
import public Quox.Syntax.Shift
|
||||
import Quox.Syntax.Var
|
||||
import Quox.Name
|
||||
import Quox.Thin
|
||||
import Quox.Loc
|
||||
|
||||
import Data.Nat
|
||||
import Data.DPair
|
||||
import Data.List
|
||||
import Data.SnocVect
|
||||
import Derive.Prelude
|
||||
|
@ -14,149 +13,159 @@ import Derive.Prelude
|
|||
|
||||
|
||||
public export
|
||||
data Subst : (Nat -> Type) -> Nat -> Nat -> Type where
|
||||
Shift : Shift from to -> Subst env from to
|
||||
(:::) : (t : Lazy (env to)) -> Subst env from to -> Subst env (S from) to
|
||||
%name Subst th, ph, ps
|
||||
Subst : (Nat -> Type) -> Nat -> Nat -> Type
|
||||
Subst env from to = SnocVect from (Lazy (Thinned env to))
|
||||
|
||||
infixr 7 !:::
|
||||
||| in case the automatic laziness insertion gets confused
|
||||
public export
|
||||
(!:::) : env to -> Subst env from to -> Subst env (S from) to
|
||||
t !::: ts = t ::: ts
|
||||
Subst2 : (Nat -> Nat -> Type) -> Nat -> Nat -> Nat -> Type
|
||||
Subst2 env d from to = SnocVect from (Lazy (Thinned2 env d to))
|
||||
|
||||
|
||||
private
|
||||
Repr : (Nat -> Type) -> Nat -> Type
|
||||
Repr f to = (List (f to), Nat)
|
||||
|
||||
private
|
||||
repr : Subst f from to -> Repr f to
|
||||
repr (Shift by) = ([], by.nat)
|
||||
repr (t ::: th) = let (ts, i) = repr th in (t::ts, i)
|
||||
public export
|
||||
get : Subst env f t -> Fin f -> Thinned env t
|
||||
get (sx :< x) FZ = x
|
||||
get (sx :< x) (FS i) = get sx i
|
||||
|
||||
|
||||
export Eq (f to) => Eq (Subst f from to) where (==) = (==) `on` repr
|
||||
export Ord (f to) => Ord (Subst f from to) where compare = compare `on` repr
|
||||
export Show (f to) => Show (Subst f from to) where show = show . repr
|
||||
public export
|
||||
interface FromVar (0 term : Nat -> Type) where
|
||||
var : Loc -> term 1
|
||||
|
||||
public export
|
||||
0 FromVar2 : (Nat -> Nat -> Type) -> Type
|
||||
FromVar2 t = FromVar (t 0)
|
||||
|
||||
public export
|
||||
varT : FromVar term => Fin n -> Loc -> Thinned term n
|
||||
varT i loc = Th (one' i) (var loc)
|
||||
|
||||
public export
|
||||
varT2 : FromVar2 term => Fin n -> Loc -> Thinned2 term d n
|
||||
varT2 i loc = Th2 zero (one' i) (var loc)
|
||||
|
||||
infixl 8 //
|
||||
namespace CanSubstSelf
|
||||
public export
|
||||
interface FromVar term => CanSubstSelf term where
|
||||
(//) : {f : Nat} -> Thinned term f -> Subst term f t -> Thinned term t
|
||||
|
||||
namespace CanSubstSelf2
|
||||
public export
|
||||
interface FromVar2 term => CanSubstSelf2 term where
|
||||
(//) : {f : Nat} -> Thinned2 term d f ->
|
||||
Subst2 term d f t -> Thinned2 term d t
|
||||
|
||||
public export
|
||||
interface FromVar term => CanSubstSelf term where
|
||||
(//) : term from -> Lazy (Subst term from to) -> term to
|
||||
(.) : {mid : Nat} -> CanSubstSelf f =>
|
||||
Subst f from mid -> Subst f mid to -> Subst f from to
|
||||
th . ph = map (\(Delay x) => x // ph) th
|
||||
|
||||
infixr 9 .%
|
||||
|
||||
public export
|
||||
(.%) : {mid : Nat} -> CanSubstSelf2 f =>
|
||||
Subst2 f d from mid -> Subst2 f d mid to -> Subst2 f d from to
|
||||
th .% ph = map (\(Delay x) => x // ph) th
|
||||
|
||||
|
||||
public export
|
||||
getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
|
||||
getLoc (Shift by) i loc = fromVarLoc (shift by i) loc
|
||||
getLoc (t ::: th) VZ _ = t
|
||||
getLoc (t ::: th) (VS i) loc = getLoc th i loc
|
||||
|
||||
tabulate : (n : Nat) -> SnocVect n (Fin n)
|
||||
tabulate n = go n id where
|
||||
go : (n : Nat) -> (Fin n -> Fin n') -> SnocVect n (Fin n')
|
||||
go 0 f = [<]
|
||||
go (S n) f = go n (f . FS) :< f FZ
|
||||
|
||||
public export
|
||||
CanSubstSelf Var where
|
||||
i // Shift by = shift by i
|
||||
VZ // (t ::: th) = t
|
||||
VS i // (t ::: th) = i // th
|
||||
|
||||
|
||||
public export %inline
|
||||
shift : (by : Nat) -> Subst env from (by + from)
|
||||
shift by = Shift $ fromNat by
|
||||
|
||||
public export %inline
|
||||
shift0 : (by : Nat) -> Subst env 0 by
|
||||
shift0 by = rewrite sym $ plusZeroRightNeutral by in Shift $ fromNat by
|
||||
|
||||
id : FromVar term => {n : Nat} -> (under : Nat) -> Loc ->
|
||||
Subst term n (n + under)
|
||||
id under loc =
|
||||
map (\i => delay $ varT (weakenN under i) loc) (tabulate n)
|
||||
|
||||
public export
|
||||
(.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to
|
||||
Shift by . Shift bz = Shift $ by . bz
|
||||
Shift SZ . ph = ph
|
||||
Shift (SS by) . (t ::: th) = Shift by . th
|
||||
(t ::: th) . ph = (t // ph) ::: (th . ph)
|
||||
id2 : FromVar2 term => {n : Nat} -> Loc -> Subst2 term d n n
|
||||
id2 loc = map (\i => delay $ varT2 i loc) $ tabulate n
|
||||
|
||||
public export %inline
|
||||
id : Subst f n n
|
||||
id = shift 0
|
||||
|
||||
public export
|
||||
traverse : Applicative m =>
|
||||
(f to -> m (g to)) -> Subst f from to -> m (Subst g from to)
|
||||
traverse f (Shift by) = pure $ Shift by
|
||||
traverse f (t ::: th) = [|f t !::: traverse f th|]
|
||||
|
||||
-- not in terms of traverse because this map can maintain laziness better
|
||||
public export
|
||||
map : (f to -> g to) -> Subst f from to -> Subst g from to
|
||||
map f (Shift by) = Shift by
|
||||
map f (t ::: th) = f t ::: map f th
|
||||
|
||||
|
||||
public export %inline
|
||||
push : CanSubstSelf f => Subst f from to -> Subst f (S from) (S to)
|
||||
push th = fromVar VZ ::: (th . shift 1)
|
||||
|
||||
-- [fixme] a better way to do this?
|
||||
public export
|
||||
pushN : CanSubstSelf f => (s : Nat) ->
|
||||
Subst f from to -> Subst f (s + from) (s + to)
|
||||
pushN 0 th = th
|
||||
pushN (S s) th =
|
||||
rewrite plusSuccRightSucc s from in
|
||||
rewrite plusSuccRightSucc s to in
|
||||
pushN s $ fromVar VZ ::: (th . shift 1)
|
||||
|
||||
public export
|
||||
drop1 : Subst f (S from) to -> Subst f from to
|
||||
drop1 (Shift by) = Shift $ ssDown by
|
||||
drop1 (t ::: th) = th
|
||||
|
||||
|
||||
public export
|
||||
fromSnocVect : SnocVect s (f n) -> Subst f (s + n) n
|
||||
fromSnocVect [<] = id
|
||||
fromSnocVect (xs :< x) = x ::: fromSnocVect xs
|
||||
|
||||
public export %inline
|
||||
one : f n -> Subst f (S n) n
|
||||
one x = fromSnocVect [< x]
|
||||
|
||||
|
||||
||| whether two substitutions with the same codomain have the same shape
|
||||
||| (the same number of terms and the same shift at the end). if so, they
|
||||
||| also have the same domain
|
||||
export
|
||||
cmpShape : Subst env from1 to -> Subst env from2 to ->
|
||||
Either Ordering (from1 = from2)
|
||||
cmpShape (Shift by) (Shift bz) = cmpLen by bz
|
||||
cmpShape (Shift _) (_ ::: _) = Left LT
|
||||
cmpShape (_ ::: _) (Shift _) = Left GT
|
||||
cmpShape (_ ::: th) (_ ::: ph) = cong S <$> cmpShape th ph
|
||||
select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
|
||||
SnocVect n a -> SnocVect m a
|
||||
select ope sx with %syntactic (view ope)
|
||||
select _ [<] | StopV = [<]
|
||||
select _ (sx :< x) | DropV _ ope = select ope sx
|
||||
select _ (sx :< x) | KeepV _ ope = select ope sx :< x
|
||||
|
||||
export
|
||||
opeToFins : {n, mask : Nat} ->
|
||||
(0 ope : OPE m n mask) -> SnocVect m (Fin n)
|
||||
opeToFins ope = select ope $ tabulate n
|
||||
|
||||
export
|
||||
shift : FromVar term => {from : Nat} ->
|
||||
(n : Nat) -> Loc -> Subst term from (n + from)
|
||||
shift n loc = map (\i => delay $ varT (shift n i) loc) $ tabulate from
|
||||
|
||||
public export
|
||||
pushN : CanSubstSelf term => {to : Nat} -> (by : Nat) ->
|
||||
Subst term from to -> Loc -> Subst term (by + from) (by + to)
|
||||
pushN by th loc =
|
||||
rewrite plusCommutative by from in
|
||||
(th . shift by loc) ++ id to loc
|
||||
|
||||
public export %inline
|
||||
push : CanSubstSelf f => {to : Nat} ->
|
||||
Subst f from to -> Loc -> Subst f (S from) (S to)
|
||||
push = pushN 1
|
||||
|
||||
|
||||
public export %inline
|
||||
one : Thinned f n -> Subst f 1 n
|
||||
one x = [< x]
|
||||
|
||||
|
||||
||| whether two substitutions with the same codomain have the same domain
|
||||
export
|
||||
cmpShape : SnocVect m a -> SnocVect n a -> Either Ordering (m = n)
|
||||
cmpShape [<] [<] = Right Refl
|
||||
cmpShape [<] (sx :< _) = Left LT
|
||||
cmpShape (sx :< _) [<] = Left GT
|
||||
cmpShape (sx :< _) (sy :< _) = cong S <$> cmpShape sx sy
|
||||
|
||||
|
||||
public export
|
||||
record WithSubst tm env n where
|
||||
constructor Sub
|
||||
term : tm from
|
||||
subst : Lazy (Subst env from n)
|
||||
subst : Subst env from n
|
||||
|
||||
{-
|
||||
export
|
||||
(Eq (env n), forall n. Eq (tm n)) => Eq (WithSubst tm env n) where
|
||||
(forall n. Eq (env n), forall n. Eq (tm n)) =>
|
||||
Eq (WithSubst tm env n) where
|
||||
Sub t1 s1 == Sub t2 s2 =
|
||||
case cmpShape s1 s2 of
|
||||
Left _ => False
|
||||
Right Refl => t1 == t2 && s1 == s2
|
||||
Right Refl =>
|
||||
t1 == t2 && concat @{All} (zipWith ((==) `on` force) s1 s2)
|
||||
|
||||
export
|
||||
(Ord (env n), forall n. Ord (tm n)) => Ord (WithSubst tm env n) where
|
||||
(forall n. Ord (env n), forall n. Ord (tm n)) =>
|
||||
Ord (WithSubst tm env n) where
|
||||
Sub t1 s1 `compare` Sub t2 s2 =
|
||||
case cmpShape s1 s2 of
|
||||
Left o => o
|
||||
Right Refl => compare (t1, s1) (t2, s2)
|
||||
Right Refl =>
|
||||
compare t1 t2 <+> concat (zipWith (compare `on` force) s1 s2)
|
||||
|
||||
export %hint
|
||||
ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
|
||||
ShowWithSubst : {n : Nat} ->
|
||||
(forall n. Show (env n), forall n. Show (tm n)) =>
|
||||
Show (WithSubst tm env n)
|
||||
ShowWithSubst = deriveShow
|
||||
ShowWithSubst = deriveShow where
|
||||
Show (Lazy (Thinned env n)) where showPrec d = showPrec d . force
|
||||
-}
|
||||
|
||||
|
||||
public export
|
||||
record WithSubst2 tm env d n where
|
||||
constructor Sub2
|
||||
term : tm d from
|
||||
subst : Subst2 env d from n
|
||||
|
|
|
@ -129,7 +129,7 @@ data Term where
|
|||
E : Elim d n -> Term d n
|
||||
|
||||
||| term closure/suspended substitution
|
||||
CloT : WithSubst (Term d) (Elim d) n -> Term d n
|
||||
CloT : WithSubst2 Term Elim d n -> Term d n
|
||||
||| dimension closure/suspended substitution
|
||||
DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
|
||||
|
||||
|
@ -194,7 +194,7 @@ data Elim where
|
|||
] d n -> Loc -> Elim d n
|
||||
|
||||
||| term closure/suspended substitution
|
||||
CloE : WithSubst (Elim d) (Elim d) n -> Elim d n
|
||||
CloE : WithSubst2 Elim Elim d n -> Elim d n
|
||||
||| dimension closure/suspended substitution
|
||||
DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
|
||||
|
||||
|
@ -325,7 +325,7 @@ Located (Elim d n) where
|
|||
(Coe _ loc).loc = loc
|
||||
(Comp _ loc).loc = loc
|
||||
(TypeCase _ loc).loc = loc
|
||||
(CloE (Sub e _)).loc = e.loc
|
||||
(CloE (Sub2 e _)).loc = e.loc
|
||||
(DCloE (Sub e _)).loc = e.loc
|
||||
|
||||
export
|
||||
|
@ -345,7 +345,7 @@ Located (Term d n) where
|
|||
(BOX _ _ loc).loc = loc
|
||||
(Box _ loc).loc = loc
|
||||
(E e).loc = e.loc
|
||||
(CloT (Sub t _)).loc = t.loc
|
||||
(CloT (Sub2 t _)).loc = t.loc
|
||||
(DCloT (Sub t _)).loc = t.loc
|
||||
|
||||
|
||||
|
@ -363,7 +363,7 @@ Relocatable (Elim d n) where
|
|||
setLoc loc (Coe ts _) = Coe ts loc
|
||||
setLoc loc (Comp ts _) = Comp ts loc
|
||||
setLoc loc (TypeCase ts _) = TypeCase ts loc
|
||||
setLoc loc (CloE (Sub term subst)) = CloE $ Sub (setLoc loc term) subst
|
||||
setLoc loc (CloE (Sub2 term subst)) = CloE $ Sub2 (setLoc loc term) subst
|
||||
setLoc loc (DCloE (Sub term subst)) = DCloE $ Sub (setLoc loc term) subst
|
||||
|
||||
export
|
||||
|
@ -383,5 +383,5 @@ Relocatable (Term d n) where
|
|||
setLoc loc (BOX qty ty _) = BOX qty ty loc
|
||||
setLoc loc (Box val _) = Box val loc
|
||||
setLoc loc (E e) = E $ setLoc loc e
|
||||
setLoc loc (CloT (Sub term subst)) = CloT $ Sub (setLoc loc term) subst
|
||||
setLoc loc (CloT (Sub2 term subst)) = CloT $ Sub2 (setLoc loc term) subst
|
||||
setLoc loc (DCloT (Sub term subst)) = DCloT $ Sub (setLoc loc term) subst
|
||||
|
|
|
@ -18,11 +18,11 @@ prettyUniverse = hl Universe . text . show
|
|||
|
||||
|
||||
export
|
||||
prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n ->
|
||||
prettyTerm : {opts : _} -> BContext d -> BContext n -> TermT d n ->
|
||||
Eff Pretty (Doc opts)
|
||||
|
||||
export
|
||||
prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n ->
|
||||
prettyElim : {opts : _} -> BContext d -> BContext n -> ElimT d n ->
|
||||
Eff Pretty (Doc opts)
|
||||
|
||||
private
|
||||
|
|
|
@ -2,374 +2,462 @@ module Quox.Syntax.Term.Subst
|
|||
|
||||
import Quox.No
|
||||
import Quox.Syntax.Term.Base
|
||||
import Quox.Syntax.Term.Tighten
|
||||
import Quox.Syntax.Subst
|
||||
|
||||
import Data.SnocVect
|
||||
import Data.Singleton
|
||||
|
||||
%default total
|
||||
|
||||
namespace CanDSubst
|
||||
public export
|
||||
interface CanDSubst (0 tm : TermLike) where
|
||||
(//) : tm d1 n -> Lazy (DSubst d1 d2) -> tm d2 n
|
||||
|
||||
||| does the minimal reasonable work:
|
||||
||| - deletes the closure around an atomic constant like `TYPE`
|
||||
||| - deletes an identity substitution
|
||||
||| - composes (lazily) with an existing top-level dim-closure
|
||||
||| - otherwise, wraps in a new closure
|
||||
export
|
||||
CanDSubst Term where
|
||||
s // Shift SZ = s
|
||||
TYPE l loc // _ = TYPE l loc
|
||||
DCloT (Sub s ph) // th = DCloT $ Sub s $ ph . th
|
||||
s // th = DCloT $ Sub s th
|
||||
infixl 8 ///
|
||||
|
||||
private
|
||||
subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
|
||||
subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
|
||||
subDArgs e th = DCloE $ Sub e th
|
||||
parameters {0 f : Nat -> Nat -> Type}
|
||||
private
|
||||
th0 : f 0 0 -> Thinned2 f d n
|
||||
th0 = Th2 zero zero
|
||||
|
||||
||| does the minimal reasonable work:
|
||||
||| - deletes the closure around a term variable
|
||||
||| - deletes an identity substitution
|
||||
||| - composes (lazily) with an existing top-level dim-closure
|
||||
||| - immediately looks up bound variables in a
|
||||
||| top-level sequence of dimension applications
|
||||
||| - otherwise, wraps in a new closure
|
||||
export
|
||||
CanDSubst Elim where
|
||||
e // Shift SZ = e
|
||||
F x u loc // _ = F x u loc
|
||||
B i loc // _ = B i loc
|
||||
e@(DApp {}) // th = subDArgs e th
|
||||
DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th
|
||||
e // th = DCloE $ Sub e th
|
||||
private
|
||||
th1 : {d, n : Nat} -> f d n -> Thinned2 f d n
|
||||
th1 = Th2 id' id'
|
||||
|
||||
namespace DSubst.ScopeTermN
|
||||
export %inline
|
||||
(//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
|
||||
ScopeTermN s d2 n
|
||||
S ns (Y body) // th = S ns $ Y $ body // th
|
||||
S ns (N body) // th = S ns $ N $ body // th
|
||||
private dsubTerm : {d1, d2, n : Nat} -> Term d1 n -> DSubst d1 d2 -> TermT d2 n
|
||||
private dsubElim : {d1, d2, n : Nat} -> Elim d1 n -> DSubst d1 d2 -> ElimT d2 n
|
||||
|
||||
namespace DSubst.DScopeTermN
|
||||
export %inline
|
||||
(//) : {s : Nat} ->
|
||||
DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
|
||||
DScopeTermN s d2 n
|
||||
S ns (Y body) // th = S ns $ Y $ body // pushN s th
|
||||
S ns (N body) // th = S ns $ N $ body // th
|
||||
dsubTerm (TYPE l loc) th = th0 $ TYPE l loc
|
||||
dsubTerm (Enum strs loc) th = th0 $ Enum strs loc
|
||||
dsubTerm (Tag str loc) th = th0 $ Tag str loc
|
||||
dsubTerm (Nat loc) th = th0 $ Nat loc
|
||||
dsubTerm (Zero loc) th = th0 $ Zero loc
|
||||
dsubTerm (E e) th =
|
||||
let Th2 dope tope e' = dsubElim e th in
|
||||
Th2 dope tope $ E e'
|
||||
dsubTerm (DCloT (Sub t ph)) th = th1 $ DCloT $ Sub t $ ph . th
|
||||
dsubTerm t th = th1 $ DCloT $ Sub t th
|
||||
|
||||
|
||||
export %inline FromVar (Elim d) where fromVarLoc = B
|
||||
export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
|
||||
|
||||
|
||||
||| does the minimal reasonable work:
|
||||
||| - deletes the closure around a *free* name
|
||||
||| - deletes an identity substitution
|
||||
||| - composes (lazily) with an existing top-level closure
|
||||
||| - immediately looks up a bound variable
|
||||
||| - otherwise, wraps in a new closure
|
||||
export
|
||||
CanSubstSelf (Elim d) where
|
||||
F x u loc // _ = F x u loc
|
||||
B i loc // th = getLoc th i loc
|
||||
CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
|
||||
e // th = case force th of
|
||||
Shift SZ => e
|
||||
th => CloE $ Sub e th
|
||||
|
||||
namespace CanTSubst
|
||||
public export
|
||||
interface CanTSubst (0 tm : TermLike) where
|
||||
(//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
|
||||
|
||||
||| does the minimal reasonable work:
|
||||
||| - deletes the closure around an atomic constant like `TYPE`
|
||||
||| - deletes an identity substitution
|
||||
||| - composes (lazily) with an existing top-level closure
|
||||
||| - goes inside `E` in case it is a simple variable or something
|
||||
||| - otherwise, wraps in a new closure
|
||||
export
|
||||
CanTSubst Term where
|
||||
TYPE l loc // _ = TYPE l loc
|
||||
E e // th = E $ e // th
|
||||
CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
|
||||
s // th = case force th of
|
||||
Shift SZ => s
|
||||
th => CloT $ Sub s th
|
||||
|
||||
namespace ScopeTermN
|
||||
export %inline
|
||||
(//) : {s : Nat} ->
|
||||
ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
|
||||
ScopeTermN s d n2
|
||||
S ns (Y body) // th = S ns $ Y $ body // pushN s th
|
||||
S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
namespace DScopeTermN
|
||||
export %inline
|
||||
(//) : {s : Nat} ->
|
||||
DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
|
||||
S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
|
||||
S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
export %inline CanShift (Term d) where s // by = s // Shift by
|
||||
export %inline CanShift (Elim d) where e // by = e // Shift by
|
||||
|
||||
export %inline
|
||||
{s : Nat} -> CanShift (ScopeTermN s d) where
|
||||
b // by = b // Shift by
|
||||
|
||||
|
||||
export %inline
|
||||
comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
|
||||
comp th ps ph = map (// th) ps . ph
|
||||
|
||||
|
||||
public export %inline
|
||||
dweakT : (by : Nat) -> Term d n -> Term (by + d) n
|
||||
dweakT by t = t // shift by
|
||||
|
||||
public export %inline
|
||||
dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
|
||||
dweakE by t = t // shift by
|
||||
|
||||
|
||||
public export %inline
|
||||
weakT : (by : Nat) -> Term d n -> Term d (by + n)
|
||||
weakT by t = t // shift by
|
||||
|
||||
public export %inline
|
||||
weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
|
||||
weakE by t = t // shift by
|
||||
|
||||
|
||||
parameters {s : Nat}
|
||||
namespace ScopeTermBody
|
||||
export %inline
|
||||
(.term) : ScopedBody s (Term d) n -> Term d (s + n)
|
||||
(Y b).term = b
|
||||
(N b).term = weakT s b
|
||||
|
||||
namespace ScopeTermN
|
||||
export %inline
|
||||
(.term) : ScopeTermN s d n -> Term d (s + n)
|
||||
t.term = t.body.term
|
||||
|
||||
namespace DScopeTermBody
|
||||
export %inline
|
||||
(.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
|
||||
(Y b).term = b
|
||||
(N b).term = dweakT s b
|
||||
|
||||
namespace DScopeTermN
|
||||
export %inline
|
||||
(.term) : DScopeTermN s d n -> Term (s + d) n
|
||||
t.term = t.body.term
|
||||
|
||||
|
||||
export %inline
|
||||
subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
|
||||
subN (S _ (Y body)) es = body // fromSnocVect es
|
||||
subN (S _ (N body)) _ = body
|
||||
|
||||
export %inline
|
||||
sub1 : ScopeTerm d n -> Elim d n -> Term d n
|
||||
sub1 t e = subN t [< e]
|
||||
|
||||
export %inline
|
||||
dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
|
||||
dsubN (S _ (Y body)) ps = body // fromSnocVect ps
|
||||
dsubN (S _ (N body)) _ = body
|
||||
|
||||
export %inline
|
||||
dsub1 : DScopeTerm d n -> Dim d -> Term d n
|
||||
dsub1 t p = dsubN t [< p]
|
||||
|
||||
|
||||
public export %inline
|
||||
(.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
|
||||
body.zero = dsub1 body $ K Zero loc
|
||||
|
||||
public export %inline
|
||||
(.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
|
||||
body.one = dsub1 body $ K One loc
|
||||
|
||||
|
||||
public export
|
||||
0 CloTest : TermLike -> Type
|
||||
CloTest tm = forall d, n. tm d n -> Bool
|
||||
|
||||
interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
|
||||
pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
|
||||
tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
|
||||
|
||||
public export
|
||||
0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
|
||||
NotClo = No . isClo
|
||||
|
||||
public export
|
||||
0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
|
||||
PushSubsts tm isClo => TermLike
|
||||
NonClo tm d n = Subset (tm d n) NotClo
|
||||
|
||||
public export %inline
|
||||
nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
|
||||
(t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n
|
||||
nclo t = Element t nc
|
||||
|
||||
parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
|
||||
||| if the input term has any top-level closures, push them under one layer of
|
||||
||| syntax
|
||||
export %inline
|
||||
pushSubsts : tm d n -> NonClo tm d n
|
||||
pushSubsts s = pushSubstsWith id id s
|
||||
|
||||
export %inline
|
||||
pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
|
||||
pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
|
||||
|
||||
export %inline
|
||||
pushSubsts' : tm d n -> tm d n
|
||||
pushSubsts' s = fst $ pushSubsts s
|
||||
dsubElim (F x l loc) th = th0 $ F x l loc
|
||||
dsubElim (B loc) th = Th2 zero id' $ B loc
|
||||
dsubElim (DCloE (Sub e ph)) th = th1 $ DCloE $ Sub e $ ph . th
|
||||
dsubElim e th = th1 $ DCloE $ Sub e th
|
||||
|
||||
mutual
|
||||
public export
|
||||
isCloT : CloTest Term
|
||||
isCloT (CloT {}) = True
|
||||
isCloT (DCloT {}) = True
|
||||
isCloT (E e) = isCloE e
|
||||
isCloT _ = False
|
||||
namespace Term
|
||||
export
|
||||
(///) : {d1, d2, n : Nat} -> TermT d1 n -> DSubst d1 d2 -> TermT d2 n
|
||||
Th2 dope tope term /// th =
|
||||
let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
|
||||
Th2 dope' tope' term' = dsubTerm term (select dope th)
|
||||
in
|
||||
Th2 dope' (tope . tope') term'
|
||||
|
||||
public export
|
||||
isCloE : CloTest Elim
|
||||
isCloE (CloE {}) = True
|
||||
isCloE (DCloE {}) = True
|
||||
isCloE _ = False
|
||||
|
||||
mutual
|
||||
export
|
||||
PushSubsts Term Subst.isCloT where
|
||||
pushSubstsWith th ph (TYPE l loc) =
|
||||
nclo $ TYPE l loc
|
||||
pushSubstsWith th ph (Pi qty a body loc) =
|
||||
nclo $ Pi qty (a // th // ph) (body // th // ph) loc
|
||||
pushSubstsWith th ph (Lam body loc) =
|
||||
nclo $ Lam (body // th // ph) loc
|
||||
pushSubstsWith th ph (Sig a b loc) =
|
||||
nclo $ Sig (a // th // ph) (b // th // ph) loc
|
||||
pushSubstsWith th ph (Pair s t loc) =
|
||||
nclo $ Pair (s // th // ph) (t // th // ph) loc
|
||||
pushSubstsWith th ph (Enum tags loc) =
|
||||
nclo $ Enum tags loc
|
||||
pushSubstsWith th ph (Tag tag loc) =
|
||||
nclo $ Tag tag loc
|
||||
pushSubstsWith th ph (Eq ty l r loc) =
|
||||
nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
|
||||
pushSubstsWith th ph (DLam body loc) =
|
||||
nclo $ DLam (body // th // ph) loc
|
||||
pushSubstsWith _ _ (Nat loc) =
|
||||
nclo $ Nat loc
|
||||
pushSubstsWith _ _ (Zero loc) =
|
||||
nclo $ Zero loc
|
||||
pushSubstsWith th ph (Succ n loc) =
|
||||
nclo $ Succ (n // th // ph) loc
|
||||
pushSubstsWith th ph (BOX pi ty loc) =
|
||||
nclo $ BOX pi (ty // th // ph) loc
|
||||
pushSubstsWith th ph (Box val loc) =
|
||||
nclo $ Box (val // th // ph) loc
|
||||
pushSubstsWith th ph (E e) =
|
||||
let Element e nc = pushSubstsWith th ph e in nclo $ E e
|
||||
pushSubstsWith th ph (CloT (Sub s ps)) =
|
||||
pushSubstsWith th (comp th ps ph) s
|
||||
pushSubstsWith th ph (DCloT (Sub s ps)) =
|
||||
pushSubstsWith (ps . th) ph s
|
||||
|
||||
export
|
||||
PushSubsts Elim Subst.isCloE where
|
||||
pushSubstsWith th ph (F x u loc) =
|
||||
nclo $ F x u loc
|
||||
pushSubstsWith th ph (B i loc) =
|
||||
let res = getLoc ph i loc in
|
||||
case nchoose $ isCloE res of
|
||||
Left yes => assert_total pushSubsts res
|
||||
Right no => Element res no
|
||||
pushSubstsWith th ph (App f s loc) =
|
||||
nclo $ App (f // th // ph) (s // th // ph) loc
|
||||
pushSubstsWith th ph (CasePair pi p r b loc) =
|
||||
nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
|
||||
pushSubstsWith th ph (CaseEnum pi t r arms loc) =
|
||||
nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
|
||||
(map (\b => b // th // ph) arms) loc
|
||||
pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
|
||||
nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
|
||||
(z // th // ph) (s // th // ph) loc
|
||||
pushSubstsWith th ph (CaseBox pi x r b loc) =
|
||||
nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
|
||||
pushSubstsWith th ph (DApp f d loc) =
|
||||
nclo $ DApp (f // th // ph) (d // th) loc
|
||||
pushSubstsWith th ph (Ann s a loc) =
|
||||
nclo $ Ann (s // th // ph) (a // th // ph) loc
|
||||
pushSubstsWith th ph (Coe ty p q val loc) =
|
||||
nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
|
||||
pushSubstsWith th ph (Comp ty p q val r zero one loc) =
|
||||
nclo $ Comp (ty // th // ph) (p // th) (q // th)
|
||||
(val // th // ph) (r // th)
|
||||
(zero // th // ph) (one // th // ph) loc
|
||||
pushSubstsWith th ph (TypeCase ty ret arms def loc) =
|
||||
nclo $ TypeCase (ty // th // ph) (ret // th // ph)
|
||||
(map (\t => t // th // ph) arms) (def // th // ph) loc
|
||||
pushSubstsWith th ph (CloE (Sub e ps)) =
|
||||
pushSubstsWith th (comp th ps ph) e
|
||||
pushSubstsWith th ph (DCloE (Sub e ps)) =
|
||||
pushSubstsWith (ps . th) ph e
|
||||
namespace Elim
|
||||
export
|
||||
(///) : {d1, d2, n : Nat} -> ElimT d1 n -> DSubst d1 d2 -> ElimT d2 n
|
||||
Th2 dope tope elim /// th =
|
||||
let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
|
||||
Th2 dope' tope' elim' = dsubElim elim (select dope th)
|
||||
in
|
||||
Th2 dope' (tope . tope') elim'
|
||||
|
||||
|
||||
private %inline
|
||||
CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
|
||||
(r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
|
||||
CompHY {ty, p, q, val, r, zero, one, loc} =
|
||||
let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in
|
||||
Comp {
|
||||
ty = dsub1 ty q, p, q,
|
||||
val = E $ Coe ty p q val val.loc, r,
|
||||
-- [fixme] better locations for these vars?
|
||||
zero = SY zero.names $ E $
|
||||
Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
|
||||
one = SY one.names $ E $
|
||||
Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
|
||||
loc
|
||||
}
|
||||
public export
|
||||
TSubst : Nat -> Nat -> Nat -> Type
|
||||
TSubst = Subst2 Elim
|
||||
|
||||
public export %inline
|
||||
CompH' : (ty : DScopeTerm d n) ->
|
||||
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||||
(zero : DScopeTerm d n) ->
|
||||
(one : DScopeTerm d n) ->
|
||||
(loc : Loc) ->
|
||||
Elim d n
|
||||
CompH' {ty, p, q, val, r, zero, one, loc} =
|
||||
case dsqueeze ty of
|
||||
S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc}
|
||||
S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc}
|
||||
|
||||
||| heterogeneous composition, using Comp and Coe (and subst)
|
||||
|||
|
||||
||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
|
||||
||| ≔
|
||||
||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
|
||||
||| 0 j ⇒ coe [i ⇒ A] @j @q t₀;
|
||||
||| 1 j ⇒ coe [i ⇒ A] @j @q t₁
|
||||
||| }
|
||||
public export %inline
|
||||
CompH : (i : BindName) -> (ty : Term (S d) n) ->
|
||||
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||||
(j0 : BindName) -> (zero : Term (S d) n) ->
|
||||
(j1 : BindName) -> (one : Term (S d) n) ->
|
||||
(loc : Loc) ->
|
||||
Elim d n
|
||||
CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
|
||||
CompH' {ty = SY [< i] ty, p, q, val, r,
|
||||
zero = SY [< j0] zero, one = SY [< j0] one, loc}
|
||||
public export %inline FromVar (Elim 0) where var = B
|
||||
|
||||
export CanSubstSelf2 Elim
|
||||
|
||||
private subTerm : {d, n1, n2 : Nat} -> Term d n1 -> TSubst d n1 n2 -> TermT d n2
|
||||
private subElim : {d, n1, n2 : Nat} -> Elim d n1 -> TSubst d n1 n2 -> ElimT d n2
|
||||
|
||||
subTerm (TYPE l loc) th = th0 $ TYPE l loc
|
||||
subTerm (Nat loc) th = th0 $ Nat loc
|
||||
subTerm (Zero loc) th = th0 $ Zero loc
|
||||
subTerm (E e) th = let Th2 dope tope e' = subElim e th in Th2 dope tope $ E e'
|
||||
subTerm (CloT (Sub2 s ph)) th = th1 $ CloT $ Sub2 s $ ph .% th
|
||||
subTerm s th = th1 $ CloT $ Sub2 s th
|
||||
|
||||
subElim (F x k loc) th = th0 $ F x k loc
|
||||
subElim (B loc) [< e] = e
|
||||
subElim (CloE (Sub2 e ph)) th = th1 $ CloE $ Sub2 e $ ph .% th
|
||||
subElim e th = th1 $ CloE $ Sub2 e th
|
||||
|
||||
|
||||
|
||||
export
|
||||
CanSubstSelf2 Elim where
|
||||
Th2 dope tope elim // th =
|
||||
let
|
||||
th' = select tope th
|
||||
in
|
||||
?sube2
|
||||
|
||||
-- namespace CanDSubst
|
||||
-- public export
|
||||
-- interface CanDSubst (0 tm : TermLike) where
|
||||
-- (//) : {d1 : Nat} -> Thinned2 tm d1 n -> Lazy (DSubst d1 d2) ->
|
||||
-- Thinned2 tm d2 n
|
||||
|
||||
-- ||| does the minimal reasonable work:
|
||||
-- ||| - deletes the closure around an atomic constant like `TYPE`
|
||||
-- ||| - deletes an identity substitution
|
||||
-- ||| - composes (lazily) with an existing top-level dim-closure
|
||||
-- ||| - otherwise, wraps in a new closure
|
||||
-- export
|
||||
-- CanDSubst Term where
|
||||
-- Th2 _ _ (TYPE l loc) // _ = Th2 zero zero $ TYPE l loc
|
||||
-- Th2 i j (DCloT (Sub s ph)) // th =
|
||||
-- Th2 ?i' j $ DCloT $ Sub s $ ph . ?th'
|
||||
-- Th2 i j s // th = ?sdf -- DCloT $ Sub s th
|
||||
|
||||
-- -- private
|
||||
-- -- subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
|
||||
-- -- subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
|
||||
-- -- subDArgs e th = DCloE $ Sub e th
|
||||
|
||||
-- -- ||| does the minimal reasonable work:
|
||||
-- -- ||| - deletes the closure around a term variable
|
||||
-- -- ||| - deletes an identity substitution
|
||||
-- -- ||| - composes (lazily) with an existing top-level dim-closure
|
||||
-- -- ||| - immediately looks up bound variables in a
|
||||
-- -- ||| top-level sequence of dimension applications
|
||||
-- -- ||| - otherwise, wraps in a new closure
|
||||
-- -- export
|
||||
-- -- CanDSubst Elim where
|
||||
-- -- e // Shift SZ = e
|
||||
-- -- F x u loc // _ = F x u loc
|
||||
-- -- B i loc // _ = B i loc
|
||||
-- -- e@(DApp {}) // th = subDArgs e th
|
||||
-- -- DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th
|
||||
-- -- e // th = DCloE $ Sub e th
|
||||
|
||||
-- -- namespace DSubst.ScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
|
||||
-- -- ScopeTermN s d2 n
|
||||
-- -- S ns (Y body) // th = S ns $ Y $ body // th
|
||||
-- -- S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
-- -- namespace DSubst.DScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (//) : {s : Nat} ->
|
||||
-- -- DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
|
||||
-- -- DScopeTermN s d2 n
|
||||
-- -- S ns (Y body) // th = S ns $ Y $ body // pushN s th
|
||||
-- -- S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
|
||||
-- -- export %inline FromVar (Elim d) where fromVarLoc = B
|
||||
-- -- export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
|
||||
|
||||
|
||||
-- -- ||| does the minimal reasonable work:
|
||||
-- -- ||| - deletes the closure around a *free* name
|
||||
-- -- ||| - deletes an identity substitution
|
||||
-- -- ||| - composes (lazily) with an existing top-level closure
|
||||
-- -- ||| - immediately looks up a bound variable
|
||||
-- -- ||| - otherwise, wraps in a new closure
|
||||
-- -- export
|
||||
-- -- CanSubstSelf (Elim d) where
|
||||
-- -- F x u loc // _ = F x u loc
|
||||
-- -- B i loc // th = getLoc th i loc
|
||||
-- -- CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
|
||||
-- -- e // th = case force th of
|
||||
-- -- Shift SZ => e
|
||||
-- -- th => CloE $ Sub e th
|
||||
|
||||
-- -- namespace CanTSubst
|
||||
-- -- public export
|
||||
-- -- interface CanTSubst (0 tm : TermLike) where
|
||||
-- -- (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
|
||||
|
||||
-- -- ||| does the minimal reasonable work:
|
||||
-- -- ||| - deletes the closure around an atomic constant like `TYPE`
|
||||
-- -- ||| - deletes an identity substitution
|
||||
-- -- ||| - composes (lazily) with an existing top-level closure
|
||||
-- -- ||| - goes inside `E` in case it is a simple variable or something
|
||||
-- -- ||| - otherwise, wraps in a new closure
|
||||
-- -- export
|
||||
-- -- CanTSubst Term where
|
||||
-- -- TYPE l loc // _ = TYPE l loc
|
||||
-- -- E e // th = E $ e // th
|
||||
-- -- CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
|
||||
-- -- s // th = case force th of
|
||||
-- -- Shift SZ => s
|
||||
-- -- th => CloT $ Sub s th
|
||||
|
||||
-- -- namespace ScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (//) : {s : Nat} ->
|
||||
-- -- ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
|
||||
-- -- ScopeTermN s d n2
|
||||
-- -- S ns (Y body) // th = S ns $ Y $ body // pushN s th
|
||||
-- -- S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
-- -- namespace DScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (//) : {s : Nat} ->
|
||||
-- -- DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
|
||||
-- -- S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
|
||||
-- -- S ns (N body) // th = S ns $ N $ body // th
|
||||
|
||||
-- -- export %inline CanShift (Term d) where s // by = s // Shift by
|
||||
-- -- export %inline CanShift (Elim d) where e // by = e // Shift by
|
||||
|
||||
-- -- export %inline
|
||||
-- -- {s : Nat} -> CanShift (ScopeTermN s d) where
|
||||
-- -- b // by = b // Shift by
|
||||
|
||||
|
||||
-- -- export %inline
|
||||
-- -- comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
|
||||
-- -- comp th ps ph = map (// th) ps . ph
|
||||
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- dweakT : (by : Nat) -> Term d n -> Term (by + d) n
|
||||
-- -- dweakT by t = t // shift by
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
|
||||
-- -- dweakE by t = t // shift by
|
||||
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- weakT : (by : Nat) -> Term d n -> Term d (by + n)
|
||||
-- -- weakT by t = t // shift by
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
|
||||
-- -- weakE by t = t // shift by
|
||||
|
||||
|
||||
-- -- parameters {s : Nat}
|
||||
-- -- namespace ScopeTermBody
|
||||
-- -- export %inline
|
||||
-- -- (.term) : ScopedBody s (Term d) n -> Term d (s + n)
|
||||
-- -- (Y b).term = b
|
||||
-- -- (N b).term = weakT s b
|
||||
|
||||
-- -- namespace ScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (.term) : ScopeTermN s d n -> Term d (s + n)
|
||||
-- -- t.term = t.body.term
|
||||
|
||||
-- -- namespace DScopeTermBody
|
||||
-- -- export %inline
|
||||
-- -- (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
|
||||
-- -- (Y b).term = b
|
||||
-- -- (N b).term = dweakT s b
|
||||
|
||||
-- -- namespace DScopeTermN
|
||||
-- -- export %inline
|
||||
-- -- (.term) : DScopeTermN s d n -> Term (s + d) n
|
||||
-- -- t.term = t.body.term
|
||||
|
||||
|
||||
-- -- export %inline
|
||||
-- -- subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
|
||||
-- -- subN (S _ (Y body)) es = body // fromSnocVect es
|
||||
-- -- subN (S _ (N body)) _ = body
|
||||
|
||||
-- -- export %inline
|
||||
-- -- sub1 : ScopeTerm d n -> Elim d n -> Term d n
|
||||
-- -- sub1 t e = subN t [< e]
|
||||
|
||||
-- -- export %inline
|
||||
-- -- dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
|
||||
-- -- dsubN (S _ (Y body)) ps = body // fromSnocVect ps
|
||||
-- -- dsubN (S _ (N body)) _ = body
|
||||
|
||||
-- -- export %inline
|
||||
-- -- dsub1 : DScopeTerm d n -> Dim d -> Term d n
|
||||
-- -- dsub1 t p = dsubN t [< p]
|
||||
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- (.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
|
||||
-- -- body.zero = dsub1 body $ K Zero loc
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- (.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
|
||||
-- -- body.one = dsub1 body $ K One loc
|
||||
|
||||
|
||||
-- -- public export
|
||||
-- -- 0 CloTest : TermLike -> Type
|
||||
-- -- CloTest tm = forall d, n. tm d n -> Bool
|
||||
|
||||
-- -- interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
|
||||
-- -- pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
|
||||
-- -- tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
|
||||
|
||||
-- -- public export
|
||||
-- -- 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
|
||||
-- -- NotClo = No . isClo
|
||||
|
||||
-- -- public export
|
||||
-- -- 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
|
||||
-- -- PushSubsts tm isClo => TermLike
|
||||
-- -- NonClo tm d n = Subset (tm d n) NotClo
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
|
||||
-- -- (t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n
|
||||
-- -- nclo t = Element t nc
|
||||
|
||||
-- -- parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
|
||||
-- -- ||| if the input term has any top-level closures, push them under one layer of
|
||||
-- -- ||| syntax
|
||||
-- -- export %inline
|
||||
-- -- pushSubsts : tm d n -> NonClo tm d n
|
||||
-- -- pushSubsts s = pushSubstsWith id id s
|
||||
|
||||
-- -- export %inline
|
||||
-- -- pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
|
||||
-- -- pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
|
||||
|
||||
-- -- export %inline
|
||||
-- -- pushSubsts' : tm d n -> tm d n
|
||||
-- -- pushSubsts' s = fst $ pushSubsts s
|
||||
|
||||
-- -- mutual
|
||||
-- -- public export
|
||||
-- -- isCloT : CloTest Term
|
||||
-- -- isCloT (CloT {}) = True
|
||||
-- -- isCloT (DCloT {}) = True
|
||||
-- -- isCloT (E e) = isCloE e
|
||||
-- -- isCloT _ = False
|
||||
|
||||
-- -- public export
|
||||
-- -- isCloE : CloTest Elim
|
||||
-- -- isCloE (CloE {}) = True
|
||||
-- -- isCloE (DCloE {}) = True
|
||||
-- -- isCloE _ = False
|
||||
|
||||
-- -- mutual
|
||||
-- -- export
|
||||
-- -- PushSubsts Term Subst.isCloT where
|
||||
-- -- pushSubstsWith th ph (TYPE l loc) =
|
||||
-- -- nclo $ TYPE l loc
|
||||
-- -- pushSubstsWith th ph (Pi qty a body loc) =
|
||||
-- -- nclo $ Pi qty (a // th // ph) (body // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Lam body loc) =
|
||||
-- -- nclo $ Lam (body // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Sig a b loc) =
|
||||
-- -- nclo $ Sig (a // th // ph) (b // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Pair s t loc) =
|
||||
-- -- nclo $ Pair (s // th // ph) (t // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Enum tags loc) =
|
||||
-- -- nclo $ Enum tags loc
|
||||
-- -- pushSubstsWith th ph (Tag tag loc) =
|
||||
-- -- nclo $ Tag tag loc
|
||||
-- -- pushSubstsWith th ph (Eq ty l r loc) =
|
||||
-- -- nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (DLam body loc) =
|
||||
-- -- nclo $ DLam (body // th // ph) loc
|
||||
-- -- pushSubstsWith _ _ (Nat loc) =
|
||||
-- -- nclo $ Nat loc
|
||||
-- -- pushSubstsWith _ _ (Zero loc) =
|
||||
-- -- nclo $ Zero loc
|
||||
-- -- pushSubstsWith th ph (Succ n loc) =
|
||||
-- -- nclo $ Succ (n // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (BOX pi ty loc) =
|
||||
-- -- nclo $ BOX pi (ty // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Box val loc) =
|
||||
-- -- nclo $ Box (val // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (E e) =
|
||||
-- -- let Element e nc = pushSubstsWith th ph e in nclo $ E e
|
||||
-- -- pushSubstsWith th ph (CloT (Sub s ps)) =
|
||||
-- -- pushSubstsWith th (comp th ps ph) s
|
||||
-- -- pushSubstsWith th ph (DCloT (Sub s ps)) =
|
||||
-- -- pushSubstsWith (ps . th) ph s
|
||||
|
||||
-- -- export
|
||||
-- -- PushSubsts Elim Subst.isCloE where
|
||||
-- -- pushSubstsWith th ph (F x u loc) =
|
||||
-- -- nclo $ F x u loc
|
||||
-- -- pushSubstsWith th ph (B i loc) =
|
||||
-- -- let res = getLoc ph i loc in
|
||||
-- -- case nchoose $ isCloE res of
|
||||
-- -- Left yes => assert_total pushSubsts res
|
||||
-- -- Right no => Element res no
|
||||
-- -- pushSubstsWith th ph (App f s loc) =
|
||||
-- -- nclo $ App (f // th // ph) (s // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (CasePair pi p r b loc) =
|
||||
-- -- nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (CaseEnum pi t r arms loc) =
|
||||
-- -- nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
|
||||
-- -- (map (\b => b // th // ph) arms) loc
|
||||
-- -- pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
|
||||
-- -- nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
|
||||
-- -- (z // th // ph) (s // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (CaseBox pi x r b loc) =
|
||||
-- -- nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (DApp f d loc) =
|
||||
-- -- nclo $ DApp (f // th // ph) (d // th) loc
|
||||
-- -- pushSubstsWith th ph (Ann s a loc) =
|
||||
-- -- nclo $ Ann (s // th // ph) (a // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Coe ty p q val loc) =
|
||||
-- -- nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (Comp ty p q val r zero one loc) =
|
||||
-- -- nclo $ Comp (ty // th // ph) (p // th) (q // th)
|
||||
-- -- (val // th // ph) (r // th)
|
||||
-- -- (zero // th // ph) (one // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (TypeCase ty ret arms def loc) =
|
||||
-- -- nclo $ TypeCase (ty // th // ph) (ret // th // ph)
|
||||
-- -- (map (\t => t // th // ph) arms) (def // th // ph) loc
|
||||
-- -- pushSubstsWith th ph (CloE (Sub e ps)) =
|
||||
-- -- pushSubstsWith th (comp th ps ph) e
|
||||
-- -- pushSubstsWith th ph (DCloE (Sub e ps)) =
|
||||
-- -- pushSubstsWith (ps . th) ph e
|
||||
|
||||
|
||||
-- -- private %inline
|
||||
-- -- CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
|
||||
-- -- (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
|
||||
-- -- CompHY {ty, p, q, val, r, zero, one, loc} =
|
||||
-- -- let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in
|
||||
-- -- Comp {
|
||||
-- -- ty = dsub1 ty q, p, q,
|
||||
-- -- val = E $ Coe ty p q val val.loc, r,
|
||||
-- -- -- [fixme] better locations for these vars?
|
||||
-- -- zero = SY zero.names $ E $
|
||||
-- -- Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
|
||||
-- -- one = SY one.names $ E $
|
||||
-- -- Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
|
||||
-- -- loc
|
||||
-- -- }
|
||||
|
||||
-- -- public export %inline
|
||||
-- -- CompH' : (ty : DScopeTerm d n) ->
|
||||
-- -- (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||||
-- -- (zero : DScopeTerm d n) ->
|
||||
-- -- (one : DScopeTerm d n) ->
|
||||
-- -- (loc : Loc) ->
|
||||
-- -- Elim d n
|
||||
-- -- CompH' {ty, p, q, val, r, zero, one, loc} =
|
||||
-- -- case dsqueeze ty of
|
||||
-- -- S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc}
|
||||
-- -- S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc}
|
||||
|
||||
-- -- ||| heterogeneous composition, using Comp and Coe (and subst)
|
||||
-- -- |||
|
||||
-- -- ||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
|
||||
-- -- ||| ≔
|
||||
-- -- ||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
|
||||
-- -- ||| 0 j ⇒ coe [i ⇒ A] @j @q t₀;
|
||||
-- -- ||| 1 j ⇒ coe [i ⇒ A] @j @q t₁
|
||||
-- -- ||| }
|
||||
-- -- public export %inline
|
||||
-- -- CompH : (i : BindName) -> (ty : Term (S d) n) ->
|
||||
-- -- (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||||
-- -- (j0 : BindName) -> (zero : Term (S d) n) ->
|
||||
-- -- (j1 : BindName) -> (one : Term (S d) n) ->
|
||||
-- -- (loc : Loc) ->
|
||||
-- -- Elim d n
|
||||
-- -- CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
|
||||
-- -- CompH' {ty = SY [< i] ty, p, q, val, r,
|
||||
-- -- zero = SY [< j0] zero, one = SY [< j0] one, loc}
|
||||
|
|
|
@ -138,15 +138,6 @@ export
|
|||
weakIsSpec p i = toNatInj $ trans (weakCorrect p i) (sym $ weakSpecCorrect p i)
|
||||
|
||||
|
||||
public export
|
||||
interface FromVar f where %inline fromVarLoc : Var n -> Loc -> f n
|
||||
|
||||
public export %inline
|
||||
fromVar : FromVar f => Var n -> {default noLoc loc : Loc} -> f n
|
||||
fromVar x = fromVarLoc x loc
|
||||
|
||||
public export FromVar Var where fromVarLoc x _ = x
|
||||
|
||||
export
|
||||
tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->
|
||||
(n : Nat) -> Vect n (tm n)
|
||||
|
|
|
@ -53,7 +53,7 @@ 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
|
||||
0 id' : {m : Nat} -> OPE m m (fst (Base.id {m}))
|
||||
id' = id.snd
|
||||
|
||||
||| nothing selected
|
||||
|
|
|
@ -2,6 +2,7 @@ module Quox.Thin.Comp
|
|||
|
||||
import public Quox.Thin.Base
|
||||
import public Quox.Thin.View
|
||||
import Quox.NatExtra
|
||||
import Data.Singleton
|
||||
|
||||
%default total
|
||||
|
@ -52,8 +53,3 @@ 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
|
||||
|
|
|
@ -5,6 +5,7 @@ import public Quox.Thin.Comp
|
|||
import public Quox.Thin.List
|
||||
import Quox.Thin.Eqv
|
||||
import public Quox.Thin.Cover
|
||||
import Quox.Thin.Append
|
||||
import Quox.Name
|
||||
import Quox.Loc
|
||||
import Data.DPair
|
||||
|
@ -15,6 +16,13 @@ import Decidable.Equality
|
|||
|
||||
%default total
|
||||
|
||||
private
|
||||
cmpMask : (m, n : Nat) -> Either Ordering (m = n)
|
||||
cmpMask 0 0 = Right Refl
|
||||
cmpMask 0 (S n) = Left LT
|
||||
cmpMask (S m) 0 = Left GT
|
||||
cmpMask (S m) (S n) = map (cong S) $ cmpMask m n
|
||||
|
||||
public export
|
||||
record Thinned f n where
|
||||
constructor Th
|
||||
|
@ -26,9 +34,20 @@ record Thinned f n where
|
|||
|
||||
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
|
||||
s == t = case cmpMask s.scopeMask t.scopeMask of
|
||||
Left _ => False
|
||||
Right eq => s.term == (rewrite maskEqInner s.ope t.ope eq in t.term)
|
||||
|
||||
export
|
||||
(forall n. Ord (f n)) => Ord (Thinned f n) where
|
||||
compare s t = case cmpMask s.scopeMask t.scopeMask of
|
||||
Left o => o
|
||||
Right eq => compare s.term (rewrite maskEqInner s.ope t.ope eq in t.term)
|
||||
|
||||
export
|
||||
{n : Nat} -> (forall s. Show (f s)) => Show (Thinned f n) where
|
||||
showPrec d (Th ope term) =
|
||||
showCon d "Th" $ showArg (unVal $ maskToOpe ope) ++ showArg term
|
||||
|
||||
export
|
||||
(forall n. Located (f n)) => Located (Thinned f n) where
|
||||
|
@ -47,6 +66,10 @@ namespace Thinned
|
|||
join : {n : Nat} -> Thinned (Thinned f) n -> Thinned f n
|
||||
join (Th ope1 (Th ope2 term)) = Th (ope1 . ope2) term
|
||||
|
||||
export
|
||||
weak : {n : Nat} -> (by : Nat) -> Thinned f n -> Thinned f (by + n)
|
||||
weak by (Th ope term) = Th (zero ++ ope).snd term
|
||||
|
||||
|
||||
public export
|
||||
record ScopedN (s : Nat) (f : Nat -> Type) (n : Nat) where
|
||||
|
@ -104,6 +127,14 @@ export
|
|||
rewrite maskEqInner s.tope t.tope teq in t.term)
|
||||
_ => False
|
||||
|
||||
export
|
||||
{d, n : Nat} -> (forall sd, sn. Show (f sd sn)) => Show (Thinned2 f d n) where
|
||||
showPrec d (Th2 dope tope term) =
|
||||
showCon d "Th2" $
|
||||
showArg (unVal $ maskToOpe dope) ++
|
||||
showArg (unVal $ maskToOpe tope) ++
|
||||
showArg term
|
||||
|
||||
export
|
||||
(forall d, n. Located (f d n)) => Located (Thinned2 f d n) where
|
||||
term.loc = term.term.loc
|
||||
|
@ -122,6 +153,12 @@ namespace Thinned2
|
|||
join (Th2 dope1 tope1 (Th2 dope2 tope2 term)) =
|
||||
Th2 (dope1 . dope2) (tope1 . tope2) term
|
||||
|
||||
export
|
||||
weak : {d, n : Nat} -> (dby, nby : Nat) ->
|
||||
Thinned2 f d n -> Thinned2 f (dby + d) (nby + n)
|
||||
weak dby nby (Th2 dope tope term) =
|
||||
Th2 (zero ++ dope).snd (zero ++ tope).snd term
|
||||
|
||||
|
||||
namespace TermList
|
||||
public export
|
||||
|
|
|
@ -4,6 +4,7 @@ import public Quox.Thin.Base
|
|||
import Quox.NatExtra
|
||||
import Data.Singleton
|
||||
import Data.SnocVect
|
||||
import Data.Fin
|
||||
|
||||
%default total
|
||||
|
||||
|
@ -52,6 +53,12 @@ view {n = S n} ope with %syntactic (half mask)
|
|||
_ | HalfEven mask' with %syntactic 0 (fromDrop ope)
|
||||
_ | (ope' ** eq) = rewrite eq in DropV mask' ope'
|
||||
|
||||
export
|
||||
(.fin) : {n, mask : Nat} -> (0 ope : OPE 1 n mask) -> Fin n
|
||||
ope.fin with (view ope)
|
||||
_.fin | DropV _ ope = FS ope.fin
|
||||
_.fin | KeepV _ ope = FZ
|
||||
|
||||
|
||||
export
|
||||
appOpe : {0 m : Nat} -> (n : Nat) -> {mask : Nat} ->
|
||||
|
@ -83,21 +90,11 @@ viewStop = Refl
|
|||
export
|
||||
0 viewDrop : (ope : OPE m n mask) -> (eq : mask2 = mask + mask) ->
|
||||
view (Drop {mask} ope eq) = DropV mask ope
|
||||
viewDrop ope eq with (view (Drop ope eq))
|
||||
viewDrop ope eq with %syntactic (view (Drop ope eq))
|
||||
viewDrop ope Refl | DropV _ ope = Refl
|
||||
|
||||
export
|
||||
0 viewKeep : (ope : OPE m n mask) -> (eq : mask2 = S (mask + mask)) ->
|
||||
view (Keep {mask} ope eq) = KeepV mask ope
|
||||
viewKeep ope eq with (view (Keep ope eq))
|
||||
viewKeep ope eq with %syntactic (view (Keep ope eq))
|
||||
viewKeep ope Refl | KeepV _ ope = Refl
|
||||
|
||||
|
||||
namespace SnocVect
|
||||
export
|
||||
select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
|
||||
SnocVect n a -> SnocVect m a
|
||||
select ope sx with (view ope)
|
||||
select _ [<] | StopV = [<]
|
||||
select _ (sx :< x) | DropV _ ope = select ope sx
|
||||
select _ (sx :< x) | KeepV _ ope = select ope sx :< x
|
||||
|
|
Loading…
Reference in a new issue