368 lines
10 KiB
Idris
368 lines
10 KiB
Idris
module Quox.Context
|
|
|
|
import Quox.Syntax.Shift
|
|
import Quox.Pretty
|
|
import Quox.Name
|
|
|
|
import Data.DPair
|
|
import Data.Nat
|
|
import Data.Singleton
|
|
import Data.SnocList
|
|
import Data.SnocVect
|
|
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
|
|
NContext : Nat -> Type
|
|
NContext = Context' BaseName
|
|
|
|
public export
|
|
BContext : Nat -> Type
|
|
BContext = Context' BindName
|
|
|
|
|
|
public export
|
|
unsnoc : Context tm (S n) -> (Context tm n, tm n)
|
|
unsnoc (tel :< x) = (tel, x)
|
|
|
|
public export
|
|
head : Context tm (S n) -> tm n
|
|
head = snd . unsnoc
|
|
|
|
public export
|
|
tail : Context tm (S n) -> Context tm n
|
|
tail = fst . unsnoc
|
|
|
|
|
|
parameters {0 tm : Nat -> Type} (f : forall n. tm n -> a)
|
|
export
|
|
toSnocListWith : Telescope tm _ _ -> SnocList a
|
|
toSnocListWith [<] = [<]
|
|
toSnocListWith (tel :< t) = toSnocListWith tel :< f t
|
|
|
|
export
|
|
toListWith : Telescope tm _ _ -> List a
|
|
toListWith tel = toListAcc tel [] where
|
|
toListAcc : Telescope tm _ _ -> List a -> List a
|
|
toListAcc [<] acc = acc
|
|
toListAcc (tel :< t) acc = toListAcc tel (f t :: acc)
|
|
|
|
export
|
|
toSnocVectWith : Context tm n -> SnocVect n a
|
|
toSnocVectWith [<] = [<]
|
|
toSnocVectWith (tel :< t) = toSnocVectWith tel :< f t
|
|
|
|
export %inline
|
|
toSnocList : Telescope tm _ _ -> SnocList (Exists tm)
|
|
toSnocList = toSnocListWith (Evidence _)
|
|
|
|
export %inline
|
|
toSnocList' : Telescope' a _ _ -> SnocList a
|
|
toSnocList' = toSnocListWith id
|
|
|
|
export %inline
|
|
toList : Telescope tm _ _ -> List (Exists tm)
|
|
toList = toListWith (Evidence _)
|
|
|
|
export %inline
|
|
toList' : Telescope' a _ _ -> List a
|
|
toList' = toListWith id
|
|
|
|
export %inline
|
|
toSnocVect : Context tm n -> SnocVect n (Exists tm)
|
|
toSnocVect = toSnocVectWith (Evidence _)
|
|
|
|
export %inline
|
|
toSnocVect' : Context' a n -> SnocVect n a
|
|
toSnocVect' = toSnocVectWith id
|
|
|
|
|
|
|
|
export
|
|
fromSnocVect : SnocVect n a -> Context' a n
|
|
fromSnocVect [<] = [<]
|
|
fromSnocVect (sx :< x) = fromSnocVect sx :< x
|
|
|
|
|
|
public export
|
|
tabulateLT : (n : Nat) -> ((i : Nat) -> (0 p : i `LT` n) => tm i) ->
|
|
Context tm n
|
|
tabulateLT 0 f = [<]
|
|
tabulateLT (S k) f =
|
|
tabulateLT k (\i => f i @{lteSuccRight %search}) :< f k @{reflexive}
|
|
|
|
public export
|
|
tabulate : ((n : Nat) -> tm n) -> (n : Nat) -> Context tm n
|
|
tabulate f n = tabulateLT n (\i => f i)
|
|
-- [todo] fixup argument order lol
|
|
|
|
public export
|
|
replicate : (n : Nat) -> a -> Context' a n
|
|
replicate n x = tabulate (const x) n
|
|
|
|
|
|
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
|
|
|
|
export
|
|
(++) : Telescope' a from to -> SnocVect n a -> Telescope' a from (n + to)
|
|
tel ++ [<] = tel
|
|
tel ++ (sx :< x) = (tel ++ sx) :< x
|
|
|
|
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
|
|
|
|
|
|
public export
|
|
drop : (m : Nat) -> Context term (m + n) -> Context term n
|
|
drop 0 ctx = ctx
|
|
drop (S m) (ctx :< _) = drop m ctx
|
|
|
|
|
|
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|]
|
|
|
|
export %inline
|
|
traverse' : (a -> f b) -> Telescope' a from to -> f (Telescope' b from to)
|
|
traverse' f = traverse f
|
|
|
|
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
|
|
unzip : Telescope (\n => (tm1 n, tm2 n)) from to ->
|
|
(Telescope tm1 from to, Telescope tm2 from to)
|
|
unzip [<] = ([<], [<])
|
|
unzip (tel :< (x, y)) = let (xs, ys) = unzip tel in (xs :< x, ys :< y)
|
|
|
|
export
|
|
unzip3 : Telescope (\n => (tm1 n, tm2 n, tm3 n)) from to ->
|
|
(Telescope tm1 from to, Telescope tm2 from to, Telescope tm3 from to)
|
|
unzip3 [<] = ([<], [<], [<])
|
|
unzip3 (tel :< (x, y, z)) =
|
|
let (xs, ys, zs) = unzip3 tel in (xs :< x, ys :< y, zs :< z)
|
|
|
|
|
|
|
|
public 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 -> Singleton to
|
|
lengthPrf0 ctx =
|
|
let Element len prf = lengthPrf ctx in
|
|
rewrite sym prf `trans` plusZeroRightNeutral len in
|
|
[|len|]
|
|
|
|
public export %inline
|
|
length : Telescope {} -> Nat
|
|
length = fst . lengthPrf
|
|
|
|
public export
|
|
null : Telescope _ from to -> Bool
|
|
null [<] = True
|
|
null _ = False
|
|
|
|
|
|
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
|
|
foldl_ : (acc -> tm -> acc) -> acc -> Telescope' tm from to -> acc
|
|
foldl_ f z tel = foldl f z tel
|
|
|
|
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
|
|
all, any : (forall n. tm n -> Bool) -> Telescope tm from to -> Bool
|
|
all p = foldMap @{All} p
|
|
any p = foldMap @{Any} p
|
|
|
|
|
|
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
|
|
|
|
|
|
parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
|
|
(nameHL : HL)
|
|
(pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts))
|
|
private
|
|
prettyOne : BindName -> BContext to -> tm to -> Eff Pretty (Doc opts)
|
|
prettyOne x xs tm = hsep <$> sequence
|
|
[hl nameHL $ prettyBind' x, hl Delim $ text ":", pterm xs tm]
|
|
|
|
private
|
|
prettyEach : BContext to -> Telescope tm from to ->
|
|
Eff Pretty (Telescope' (Doc opts) from to)
|
|
prettyEach _ [<] = pure [<]
|
|
prettyEach (xs :< x) (ts :< t) = [|prettyEach xs ts :< prettyOne x xs t|]
|
|
|
|
export
|
|
prettyTel : BContext to -> Telescope tm from to -> Eff Pretty (Doc opts)
|
|
prettyTel names tel = do
|
|
docs <- prettyEach names tel
|
|
comma <- hl Delim $ text ","
|
|
pure $ separateTight comma $ toList' docs
|
|
|
|
|
|
namespace BContext
|
|
export
|
|
toNames : BContext n -> SnocList BaseName
|
|
toNames = foldl (\xs, x => xs :< x.name) [<]
|