module Quox.Context import Quox.Syntax.Shift import Quox.Pretty import Data.DPair import Data.Nat import Data.SnocList import Data.Vect import Control.Monad.Identity %default total ||| a sequence of bindings under an existing context. each successive element ||| has one more bound variable, which correspond to all previous elements ||| as well as the surrounding context. public export data Telescope : (tm : Nat -> Type) -> (from, to : Nat) -> Type where Lin : Telescope tm from from (:<) : Telescope tm from to -> tm to -> Telescope tm from (S to) %name Telescope tel public export Telescope' : (a : Type) -> (from, to : Nat) -> Type Telescope' a = Telescope (\_ => a) ||| a top level context is actually just a telescope over no existing bindings public export Context : (tm : Nat -> Type) -> (len : Nat) -> Type Context tm len = Telescope tm 0 len public export Context' : (a : Type) -> (len : Nat) -> Type Context' a = Context (\_ => a) public export tail : Context tm (S n) -> Context tm n tail (tel :< _) = tel export toSnocList : Telescope tm _ _ -> SnocList (Exists tm) toSnocList [<] = [<] toSnocList (tel :< t) = toSnocList tel :< Evidence _ t export %inline toList : Telescope tm _ _ -> List (Exists tm) toList tel = toListAcc tel [] where toListAcc : Telescope tm _ _ -> List (Exists tm) -> List (Exists tm) toListAcc [<] acc = acc toListAcc (tel :< t) acc = toListAcc tel (Evidence _ t :: acc) export %inline toSnocList' : Telescope' a _ _ -> SnocList a toSnocList' = map snd . toSnocList export %inline toList' : Telescope' a _ _ -> List a toList' = map snd . toList public export (.) : Telescope tm from mid -> Telescope tm mid to -> Telescope tm from to tel1 . [<] = tel1 tel1 . (tel2 :< s) = (tel1 . tel2) :< s export (<><) : Telescope' a from to -> Vect n a -> Telescope' a from (n + to) (<><) tel [] = tel (<><) tel (x :: xs) {n = S n} = rewrite plusSuccRightSucc n to in (tel :< x) <>< xs public export getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) -> Shift len out -> Context tm len -> Var len -> tm out getShiftWith shft by (ctx :< t) VZ = t `shft` ssDown by getShiftWith shft by (ctx :< t) (VS i) = getShiftWith shft (ssDown by) ctx i public export %inline getShift : CanShift tm => Shift len out -> Context tm len -> Var len -> tm out getShift = getShiftWith (//) public export %inline getWith : (forall from, to. tm from -> Shift from to -> tm to) -> Context tm len -> Var len -> tm len getWith shft = getShiftWith shft SZ infixl 8 !! public export %inline (!!) : CanShift tm => Context tm len -> Var len -> tm len (!!) = getWith (//) infixl 8 !!! public export %inline (!!!) : Context' tm len -> Var len -> tm (!!!) = getWith const public export find : Alternative f => (forall n. tm n -> Bool) -> Context tm len -> f (Var len) find p [<] = empty find p (ctx :< x) = (guard (p x) $> VZ) <|> (VS <$> find p ctx) export 0 telescopeLTE : Telescope _ from to -> from `LTE` to telescopeLTE [<] = reflexive telescopeLTE (tel :< _) = lteSuccRight $ telescopeLTE tel export (gt : from `GT` to) => Uninhabited (Telescope _ from to) where uninhabited tel = void $ LTEImpliesNotGT (telescopeLTE tel) gt export %hint 0 succGT : S n `GT` n succGT = LTESucc reflexive parameters {auto _ : Applicative f} export traverse : (forall n. tm1 n -> f (tm2 n)) -> Telescope tm1 from to -> f (Telescope tm2 from to) traverse f [<] = pure [<] traverse f (tel :< x) = [|traverse f tel :< f x|] infixl 3 `app` ||| like `(<*>)` but with effects export app : Telescope (\n => tm1 n -> f (tm2 n)) from to -> Telescope tm1 from to -> f (Telescope tm2 from to) app [<] [<] = pure [<] app (ftel :< f) (xtel :< x) = [|app ftel xtel :< f x|] app [<] (xtel :< _) = void $ uninhabited xtel app (ftel :< _) [<] = void $ uninhabited ftel export %inline sequence : Telescope (f . tm) from to -> f (Telescope tm from to) sequence = traverse id parameters {0 tm1, tm2 : Nat -> Type} (f : forall n. tm1 n -> tm2 n) export %inline map : Telescope tm1 from to -> Telescope tm2 from to map = runIdentity . traverse (pure . f) export %inline (<$>) : Telescope tm1 from to -> Telescope tm2 from to (<$>) = map export %inline (<*>) : Telescope (\n => tm1 n -> tm2 n) from to -> Telescope tm1 from to -> Telescope tm2 from to ftel <*> xtel = runIdentity $ (pure .) <$> ftel `app` xtel -- ...but can't write pure without `from,to` being ω, so no idiom brackets ☹ export %inline (<$) : (forall n. tm1 n) -> Telescope tm2 from to -> Telescope tm1 from to x <$ tel = const x <$> tel export %inline zipWith : (forall n. tm1 n -> tm2 n -> tm3 n) -> Telescope tm1 from to -> Telescope tm2 from to -> Telescope tm3 from to zipWith f tel1 tel2 = f <$> tel1 <*> tel2 export %inline zipWithLazy : forall tm1, tm2, tm3. (forall n. tm1 n -> tm2 n -> tm3 n) -> Telescope tm1 from to -> Telescope tm2 from to -> Telescope (\n => Lazy (tm3 n)) from to zipWithLazy f = zipWith $ delay .: f export lengthPrf : Telescope _ from to -> Subset Nat (\len => len + from = to) lengthPrf [<] = Element 0 Refl lengthPrf (tel :< _) = let len = lengthPrf tel in Element (S len.fst) (cong S len.snd) export lengthPrf0 : Context _ to -> Subset Nat (\len => len = to) lengthPrf0 ctx = let len = lengthPrf ctx in Element len.fst (rewrite sym $ plusZeroRightNeutral len.fst in len.snd) public export %inline length : Telescope {} -> Nat length = fst . lengthPrf export foldl : {0 acc : Nat -> Type} -> (f : forall n. acc n -> tm (n + from) -> acc (S n)) -> (z : acc 0) -> (tel : Telescope tm from to) -> acc (length tel) foldl f z [<] = z foldl f z (tel :< t) = f (foldl f z tel) (rewrite (lengthPrf tel).snd in t) export %inline foldMap : Monoid a => (forall n. tm n -> a) -> Telescope tm from to -> a foldMap f = foldl (\acc, tm => acc <+> f tm) neutral export %inline fold : Monoid a => Telescope' a from to -> a fold = foldMap id ||| like `fold` but calculate the elements only when actually appending export %inline foldLazy : Monoid a => Telescope' (Lazy a) from to -> a foldLazy = foldMap force export %inline (forall n. Eq (tm n)) => Eq (Telescope tm from to) where (==) = foldLazy @{All} .: zipWithLazy (==) export %inline (forall n. Ord (tm n)) => Ord (Telescope tm from to) where compare = foldLazy .: zipWithLazy compare export %inline (forall n. Show (tm n)) => Show (Telescope tm from to) where showPrec d = showPrec d . toSnocList where Show (Exists tm) where showPrec d t = showPrec d t.snd export %inline (forall n. PrettyHL (tm n)) => PrettyHL (Telescope tm from to) where prettyM tel = separate (hl Delim ";") <$> traverse prettyM (toList tel)