module Quox.Syntax.Qty

import Quox.Pretty

import Data.Fin


public export
data Qty = Zero | One | Many
%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; Many => 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"
      Many => ifUnicode "𝛚" "*"

export %inline
prettyQtyBinds : List Qty -> M (Doc HL)
prettyQtyBinds =
  map (align . sep) .
  traverse (\pi => [|pretty0M pi <++> pure (hl Delim "|")|])


public export
(+) : Qty -> Qty -> Qty
Zero + rh   = rh
pi   + Zero = pi
_    + _    = Many

public export
(*) : Qty -> Qty -> Qty
Zero * _    = Zero
_    * Zero = Zero
One  * rh   = rh
pi   * One  = pi
Many * Many = Many

infix 6 <=.
public export
(<=.) : Qty -> Qty -> Bool
pi <=. rh = rh == Many || pi == rh