-- SPDX-FileCopyrightText: 2020 Tocqueville Group
--
-- SPDX-License-Identifier: LicenseRef-MIT-TQ

-- | Type families from 'Michelson.Typed.Arith' lifted to Haskell types.
module Lorentz.Arith
  ( ArithOpHs (..)
  , UnaryArithOpHs (..)
  , ToIntegerArithOpHs
  ) where

import Lorentz.Value
import Michelson.Typed.Arith

-- | Lifted 'ArithOp'.
class ( ArithOp aop (ToT n) (ToT m)
      , ToT (ArithResHs aop n m) ~ ArithRes aop (ToT n) (ToT m)
      ) => ArithOpHs (aop :: Type) (n :: Type) (m :: Type) where
  type ArithResHs aop n m :: Type

-- | Lifted 'UnaryArithOp'.
class ( UnaryArithOp aop (ToT n)
      , ToT (UnaryArithResHs aop n) ~ UnaryArithRes aop (ToT n)
      ) => UnaryArithOpHs (aop :: Type) (n :: Type) where
  type UnaryArithResHs aop n :: Type

class ( ToIntArithOp (ToT n)
      ) =>
      ToIntegerArithOpHs (n :: Type)

instance ArithOpHs Add Natural Integer where
  type ArithResHs Add Natural Integer = Integer
instance ArithOpHs Add Integer Natural where
  type ArithResHs Add Integer Natural = Integer
instance ArithOpHs Add Natural Natural where
  type ArithResHs Add Natural Natural = Natural
instance ArithOpHs Add Integer Integer where
  type ArithResHs Add Integer Integer = Integer
instance ArithOpHs Add Timestamp Integer where
  type ArithResHs Add Timestamp Integer = Timestamp
instance ArithOpHs Add Integer Timestamp where
  type ArithResHs Add Integer Timestamp = Timestamp
instance ArithOpHs Add Mutez Mutez where
  type ArithResHs Add Mutez Mutez = Mutez
instance ArithOpHs Add Bls12381Fr Bls12381Fr where
  type ArithResHs Add Bls12381Fr Bls12381Fr = Bls12381Fr
instance ArithOpHs Add Bls12381G1 Bls12381G1 where
  type ArithResHs Add Bls12381G1 Bls12381G1 = Bls12381G1
instance ArithOpHs Add Bls12381G2 Bls12381G2 where
  type ArithResHs Add Bls12381G2 Bls12381G2 = Bls12381G2

instance ArithOpHs Sub Natural Integer where
  type ArithResHs Sub Natural Integer = Integer
instance ArithOpHs Sub Integer Natural where
  type ArithResHs Sub Integer Natural = Integer
instance ArithOpHs Sub Natural Natural where
  type ArithResHs Sub Natural Natural = Integer
instance ArithOpHs Sub Integer Integer where
  type ArithResHs Sub Integer Integer = Integer
instance ArithOpHs Sub Timestamp Integer where
  type ArithResHs Sub Timestamp Integer = Timestamp
instance ArithOpHs Sub Timestamp Timestamp where
  type ArithResHs Sub Timestamp Timestamp = Integer
instance ArithOpHs Sub Mutez Mutez where
  type ArithResHs Sub Mutez Mutez = Mutez

instance ArithOpHs Mul Natural Integer where
  type ArithResHs Mul Natural Integer = Integer
instance ArithOpHs Mul Integer Natural where
  type ArithResHs Mul Integer Natural = Integer
instance ArithOpHs Mul Natural Natural where
  type ArithResHs Mul Natural Natural = Natural
instance ArithOpHs Mul Integer Integer where
  type ArithResHs Mul Integer Integer = Integer
instance ArithOpHs Mul Natural Mutez where
  type ArithResHs Mul Natural Mutez = Mutez
instance ArithOpHs Mul Mutez Natural where
  type ArithResHs Mul Mutez Natural = Mutez
instance ArithOpHs Mul Integer Bls12381Fr where
  type ArithResHs Mul Integer Bls12381Fr = Bls12381Fr
instance ArithOpHs Mul Natural Bls12381Fr where
  type ArithResHs Mul Natural Bls12381Fr = Bls12381Fr
instance ArithOpHs Mul Bls12381Fr Integer where
  type ArithResHs Mul Bls12381Fr Integer = Bls12381Fr
instance ArithOpHs Mul Bls12381Fr Natural where
  type ArithResHs Mul Bls12381Fr Natural = Bls12381Fr
instance ArithOpHs Mul Bls12381Fr Bls12381Fr where
  type ArithResHs Mul Bls12381Fr Bls12381Fr = Bls12381Fr
instance ArithOpHs Mul Bls12381G1 Bls12381Fr where
  type ArithResHs Mul Bls12381G1 Bls12381Fr = Bls12381G1
instance ArithOpHs Mul Bls12381G2 Bls12381Fr where
  type ArithResHs Mul Bls12381G2 Bls12381Fr = Bls12381G2
instance Bls12381MulBadOrder Bls12381Fr Bls12381G1 =>
         ArithOpHs Mul Bls12381Fr Bls12381G1 where
  type ArithResHs Mul Bls12381Fr Bls12381G1 = Bls12381G1
instance Bls12381MulBadOrder Bls12381Fr Bls12381G2 =>
         ArithOpHs Mul Bls12381Fr Bls12381G2 where
  type ArithResHs Mul Bls12381Fr Bls12381G2 = Bls12381G2

instance UnaryArithOpHs Neg Integer where
  type UnaryArithResHs Neg Integer = Integer
instance UnaryArithOpHs Neg Natural where
  type UnaryArithResHs Neg Natural = Integer
instance UnaryArithOpHs Neg Bls12381Fr where
  type UnaryArithResHs Neg Bls12381Fr = Bls12381Fr
instance UnaryArithOpHs Neg Bls12381G1 where
  type UnaryArithResHs Neg Bls12381G1 = Bls12381G1
instance UnaryArithOpHs Neg Bls12381G2 where
  type UnaryArithResHs Neg Bls12381G2 = Bls12381G2

instance ArithOpHs Or Natural Natural where
  type ArithResHs Or Natural Natural = Natural
instance ArithOpHs Or Bool Bool where
  type ArithResHs Or Bool Bool = Bool

instance ArithOpHs And Integer Natural where
  type ArithResHs And Integer Natural = Natural
instance ArithOpHs And Natural Natural where
  type ArithResHs And Natural Natural = Natural
instance ArithOpHs And Bool Bool where
  type ArithResHs And Bool Bool = Bool

instance ArithOpHs Xor Natural Natural where
  type ArithResHs Xor Natural Natural = Natural
instance ArithOpHs Xor Bool Bool where
  type ArithResHs Xor Bool Bool = Bool

instance ArithOpHs Lsl Natural Natural where
  type ArithResHs Lsl Natural Natural = Natural

instance ArithOpHs Lsr Natural Natural where
  type ArithResHs Lsr Natural Natural = Natural

instance UnaryArithOpHs Abs Integer where
  type UnaryArithResHs Abs Integer = Natural

instance UnaryArithOpHs Not Integer where
  type UnaryArithResHs Not Integer = Integer
instance UnaryArithOpHs Not Natural where
  type UnaryArithResHs Not Natural = Integer
instance UnaryArithOpHs Not Bool where
  type UnaryArithResHs Not Bool = Bool

instance UnaryArithOpHs Eq' Integer where
  type UnaryArithResHs Eq' Integer = Bool

instance UnaryArithOpHs Neq Integer where
  type UnaryArithResHs Neq Integer = Bool

instance UnaryArithOpHs Lt Integer where
  type UnaryArithResHs Lt Integer = Bool

instance UnaryArithOpHs Gt Integer where
  type UnaryArithResHs Gt Integer = Bool

instance UnaryArithOpHs Le Integer where
  type UnaryArithResHs Le Integer = Bool

instance UnaryArithOpHs Ge Integer where
  type UnaryArithResHs Ge Integer = Bool

instance ToIntegerArithOpHs Natural
instance ToIntegerArithOpHs Bls12381Fr