{-# LANGUAGE GADTs #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE EmptyDataDecls #-}

-- | A simple arithmetic expression, its family and some instances.
module Expr (Expr(..), ExprFam(..)) where

import Prelude hiding (Num)

import Eq1
import ShowFam
import Generics.MultiRec.Base
import Generics.MultiRec.TH


-- | A simple arithmetic expression.
data Expr
  = Num Int
  | Add Expr Expr
  | Sub Expr Expr
  | Mul Expr Expr
  | Div Expr Expr
  deriving (Eq, Show)


-- | The singleton data family for arithmetic expressions. Implements 'PF'.
data ExprFam :: * -> * where
  Expr :: ExprFam Expr

instance Show (ExprFam a) where
  show Expr = "Expr"

instance ShowFam ExprFam where
  showFam Expr = show

instance Eq1 ExprFam where
  eq1 Expr Expr = Just Refl


$(deriveConstructors [''Expr])
$(deriveSystem ''ExprFam [''Expr] "PFExprFam")
type instance PF ExprFam = PFExprFam