144 lines
3.9 KiB
Idris
144 lines
3.9 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 Quox.Pretty
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import Data.Nat
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import Data.List
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import Data.Vect
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%default total
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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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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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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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infixl 8 !!
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public export
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(!!) : FromVar term => Subst term from to -> Var from -> term to
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(Shift by) !! i = fromVar $ shift by i
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(t ::: th) !! VZ = t
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(t ::: th) !! (VS i) = th !! i
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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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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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fromVect : Vect s (f n) -> Subst f (s + n) n
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fromVect [] = id
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fromVect (x :: xs) = x ::: fromVect 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 = fromVect [x]
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||| `prettySubst pr names bnd op cl th` pretty-prints the substitution `th`,
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||| with the following arguments:
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||| * `th : Subst f from to`
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||| * `pr : f to -> m (Doc HL)` prints a single element
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||| * `names : List Name` is a list of known bound var names
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||| * `bnd : HL` is the highlight to use for bound variables being subsituted
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||| * `op, cl : Doc HL` are the opening and closing brackets
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export
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prettySubstM : Pretty.HasEnv m =>
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(pr : f to -> m (Doc HL)) ->
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(names : List Name) -> (bnd : HL) -> (op, cl : Doc HL) ->
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Subst f from to -> m (Doc HL)
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prettySubstM pr names bnd op cl th =
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encloseSep (hl Delim op) (hl Delim cl) (hl Delim "; ") <$>
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withPrec Outer (go 0 th)
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where
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go1 : Nat -> f to -> m (Doc HL)
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go1 i t = pure $ hang 2 $ sep
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[hsep [!(prettyVar' bnd bnd names i),
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hl Delim !(ifUnicode "≔" ":=")],
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!(pr t)]
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go : forall from. Nat -> Subst f from to -> m (List (Doc HL))
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go _ (Shift SZ) = pure []
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go _ (Shift by) = [|pure (prettyShift bnd by)|]
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go i (t ::: th) = [|go1 i t :: go (S i) th|]
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||| prints with [square brackets] and the `TVar` highlight for variables
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export
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PrettyHL (f to) => PrettyHL (Subst f from to) where
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prettyM th = prettySubstM prettyM (!ask).tnames TVar "[" "]" th
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