module Examples2
where

import Prelude hiding (and, or)
import qualified Prelude as P (and, or)

import DataTypes
import BoolExprStep2

a, b, c :: BoolExpr

a = var "a"
b = var "b"
c = var "c"

deMorgan, modusPonens :: BoolExpr

deMorgan
    = (neg (a `and` b)) `equiv` (neg a `or` neg b)

modusPonens
    = (a `and` (a `impl` b)) `impl` b

true1
    = (a `and` true) `or` (b `or` true)

equiv1
    = ((a `equiv` a) `equiv` a) `equiv` false `equiv` false

t1 = showEx . simplifyExpr $ modusPonens
t2 = showEx . simplifyExpr $ deMorgan
t3 = showEx . simplifyExpr $ equiv1