VerifiedNum.hs

module VerifiedNum where

-- Hiding numeric operations, because they get by default translated to SMT equivalent
import Prelude hiding (Num(..))

import qualified Prelude as Prelude

class VerifiedNum a where
  (+) :: a -> a -> a
  (-) :: a -> a -> a

{-@ predicate BoundInt X = 0 < X + 10000 && X < 10000 @-}

{-@ type OkInt N = {v:Int | BoundInt N => v == N} @-}

{-@ type ValidInt = {v:Int | BoundInt v} @-}


instance VerifiedNum Int where
{-@ instance VerifiedNum Int where
      + :: x:Int -> y:Int -> OkInt {x + y}
  @-}
    x + y = (Prelude.+) x y
{-@ instance VerifiedNum Int where
      - :: x:Int -> y:Int -> OkInt {x - y}
  @-}
    x - y = (Prelude.-) x y