module Quox.Syntax.Dim

import Quox.Syntax.Var
import Quox.Syntax.Subst
import Quox.Pretty

%default total


public export
data Dim : Nat -> Type where
  DZero, DOne : Dim d
  DBound : Var d -> Dim d
%name Dim.Dim p, q

private DRepr : Type
DRepr = Nat

private %inline drepr : Dim n -> DRepr
drepr d = case d of DZero => 0; DOne => 1; DBound i => 2 + i.nat

export Eq  (Dim n) where (==) = (==) `on` drepr
export Ord (Dim n) where compare = compare `on` drepr

export
PrettyHL (Dim n) where
  prettyM DZero      = hl Dim <$> ifUnicode "𝟬" "0"
  prettyM DOne       = hl Dim <$> ifUnicode "𝟭" "1"
  prettyM (DBound i) = prettyVar DVar DVarErr (!ask).dnames i


public export
0 DSubst : Nat -> Nat -> Type
DSubst = Subst Dim


export %inline
prettyDSubst : Pretty.HasEnv m => DSubst from to -> m (Doc HL)
prettyDSubst th =
  prettySubstM prettyM (dnames !ask) DVar
    !(ifUnicode "⟨" "<") !(ifUnicode "⟩" ">") th


export FromVar Dim where fromVar = DBound

export
CanSubst Dim Dim where
  DZero    // _  = DZero
  DOne     // _  = DOne
  DBound i // th = th !! i