163 lines
4.3 KiB
Idris
163 lines
4.3 KiB
Idris
module Quox.Syntax.Subst
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import public Quox.Syntax.Shift
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import Quox.Syntax.Var
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import Quox.Name
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import Data.Nat
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import Data.List
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import Data.SnocVect
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import Derive.Prelude
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%default total
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%language ElabReflection
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public export
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data Subst : (Nat -> Type) -> Nat -> Nat -> Type where
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Shift : Shift from to -> Subst env from to
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(:::) : (t : Lazy (env to)) -> Subst env from to -> Subst env (S from) to
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%name Subst th, ph, ps
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infixr 7 !:::
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||| in case the automatic laziness insertion gets confused
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public export
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(!:::) : env to -> Subst env from to -> Subst env (S from) to
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t !::: ts = t ::: ts
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private
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Repr : (Nat -> Type) -> Nat -> Type
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Repr f to = (List (f to), Nat)
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private
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repr : Subst f from to -> Repr f to
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repr (Shift by) = ([], by.nat)
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repr (t ::: th) = let (ts, i) = repr th in (t::ts, i)
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export Eq (f to) => Eq (Subst f from to) where (==) = (==) `on` repr
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export Ord (f to) => Ord (Subst f from to) where compare = compare `on` repr
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export Show (f to) => Show (Subst f from to) where show = show . repr
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infixl 8 //
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public export
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interface FromVar term => CanSubstSelf term where
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(//) : term from -> Lazy (Subst term from to) -> term to
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public export
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getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
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getLoc (Shift by) i loc = fromVarLoc (shift by i) loc
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getLoc (t ::: th) VZ _ = t
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getLoc (t ::: th) (VS i) loc = getLoc th i loc
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public export
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CanSubstSelf Var where
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i // Shift by = shift by i
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VZ // (t ::: th) = t
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VS i // (t ::: th) = i // th
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public export %inline
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shift : (by : Nat) -> Subst env from (by + from)
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shift by = Shift $ fromNat by
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public export %inline
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shift0 : (by : Nat) -> Subst env 0 by
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shift0 by = rewrite sym $ plusZeroRightNeutral by in Shift $ fromNat by
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public export
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(.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to
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Shift by . Shift bz = Shift $ by . bz
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Shift SZ . ph = ph
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Shift (SS by) . (t ::: th) = Shift by . th
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(t ::: th) . ph = (t // ph) ::: (th . ph)
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public export %inline
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id : Subst f n n
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id = shift 0
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public export
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traverse : Applicative m =>
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(f to -> m (g to)) -> Subst f from to -> m (Subst g from to)
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traverse f (Shift by) = pure $ Shift by
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traverse f (t ::: th) = [|f t !::: traverse f th|]
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-- not in terms of traverse because this map can maintain laziness better
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public export
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map : (f to -> g to) -> Subst f from to -> Subst g from to
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map f (Shift by) = Shift by
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map f (t ::: th) = f t ::: map f th
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public export %inline
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push : CanSubstSelf f => Subst f from to -> Subst f (S from) (S to)
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push th = fromVar VZ ::: (th . shift 1)
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-- [fixme] a better way to do this?
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public export
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pushN : CanSubstSelf f => (s : Nat) ->
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Subst f from to -> Subst f (s + from) (s + to)
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pushN 0 th = th
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pushN (S s) th =
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rewrite plusSuccRightSucc s from in
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rewrite plusSuccRightSucc s to in
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pushN s $ fromVar VZ ::: (th . shift 1)
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public export
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drop1 : Subst f (S from) to -> Subst f from to
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drop1 (Shift by) = Shift $ ssDown by
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drop1 (t ::: th) = th
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public export
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fromSnocVect : SnocVect s (f n) -> Subst f (s + n) n
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fromSnocVect [<] = id
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fromSnocVect (xs :< x) = x ::: fromSnocVect xs
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public export %inline
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one : f n -> Subst f (S n) n
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one x = fromSnocVect [< x]
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||| whether two substitutions with the same codomain have the same shape
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||| (the same number of terms and the same shift at the end). if so, they
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||| also have the same domain
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export
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cmpShape : Subst env from1 to -> Subst env from2 to ->
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Either Ordering (from1 = from2)
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cmpShape (Shift by) (Shift bz) = cmpLen by bz
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cmpShape (Shift _) (_ ::: _) = Left LT
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cmpShape (_ ::: _) (Shift _) = Left GT
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cmpShape (_ ::: th) (_ ::: ph) = cong S <$> cmpShape th ph
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public export
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record WithSubst tm env n where
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constructor Sub
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term : tm from
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subst : Lazy (Subst env from n)
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export
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(Eq (env n), forall n. Eq (tm n)) => Eq (WithSubst tm env n) where
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Sub t1 s1 == Sub t2 s2 =
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case cmpShape s1 s2 of
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Left _ => False
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Right Refl => t1 == t2 && s1 == s2
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export
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(Ord (env n), forall n. Ord (tm n)) => Ord (WithSubst tm env n) where
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Sub t1 s1 `compare` Sub t2 s2 =
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case cmpShape s1 s2 of
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Left o => o
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Right Refl => compare (t1, s1) (t2, s2)
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export %hint
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ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
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Show (WithSubst tm env n)
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ShowWithSubst = deriveShow
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