module Quox.Syntax.Qty

import Quox.Pretty

import Data.Fin


public export
data Qty = Zero | One | Any
%name Qty.Qty pi, rh

private Repr : Type
Repr = Fin 3

private %inline repr : Qty -> Repr
repr pi = case pi of Zero => 0; One => 1; Any => 2

export Eq  Qty where (==) = (==) `on` repr
export Ord Qty where compare = compare `on` repr


export
PrettyHL Qty where
  prettyM pi = hl Qty <$>
    case pi of
      Zero => ifUnicode "𝟬" "0"
      One  => ifUnicode "𝟭" "1"
      Any  => ifUnicode "𝛚" "*"

private
commas : List (Doc HL) -> List (Doc HL)
commas [] = []
commas [x] = [x]
commas (x::xs) = (x <+> hl Delim ",") :: commas xs

export %inline
prettyQtyBinds : Pretty.HasEnv m => List Qty -> m (Doc HL)
prettyQtyBinds =
  map ((hl Delim "@" <++>) . align . sep . commas) . traverse pretty0M


public export
plus : Qty -> Qty -> Qty
plus Zero rh   = rh
plus pi   Zero = pi
plus _    _    = Any

public export
times : Qty -> Qty -> Qty
times Zero _    = Zero
times _    Zero = Zero
times One  rh   = rh
times pi   One  = pi
times Any  Any  = Any

infix 6 <=.
public export
compat : Qty -> Qty -> Bool
compat pi rh = rh == Any || pi == rh


public export
interface IsQty q where
  zero, one : q
  (+),  (*) : q -> q -> q
  (<=.)     : q -> q -> Bool

public export
IsQty Qty where
  zero  = Zero; one = One
  (+)   = plus; (*) = times
  (<=.) = compat


public export
data IsSubj : Qty -> Type where
  SZero : IsSubj Zero
  SOne  : IsSubj One

public export
data IsGlobal : Qty -> Type where
  GZero : IsGlobal Zero
  GAny  : IsGlobal Any