{-# LANGUAGE GeneralizedNewtypeDeriving #-}

module Lattices.UnitInterval(
    UnitInterval(..),
    mkUnitInterval
) where

import Lattices.ResiduatedLattice

-- | unit interval on real numbers [0,1]

newtype UnitInterval = UnitInterval Double 
    deriving (UnitInterval -> UnitInterval -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: UnitInterval -> UnitInterval -> Bool
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fromInteger :: Integer -> UnitInterval
$cfromInteger :: Integer -> UnitInterval
signum :: UnitInterval -> UnitInterval
$csignum :: UnitInterval -> UnitInterval
abs :: UnitInterval -> UnitInterval
$cabs :: UnitInterval -> UnitInterval
negate :: UnitInterval -> UnitInterval
$cnegate :: UnitInterval -> UnitInterval
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$c* :: UnitInterval -> UnitInterval -> UnitInterval
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floor :: forall b. Integral b => UnitInterval -> b
$cfloor :: forall b. Integral b => UnitInterval -> b
ceiling :: forall b. Integral b => UnitInterval -> b
$cceiling :: forall b. Integral b => UnitInterval -> b
round :: forall b. Integral b => UnitInterval -> b
$cround :: forall b. Integral b => UnitInterval -> b
truncate :: forall b. Integral b => UnitInterval -> b
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instance BoundedLattice UnitInterval where
    /\ :: UnitInterval -> UnitInterval -> UnitInterval
(/\) = forall a. Ord a => a -> a -> a
min
    \/ :: UnitInterval -> UnitInterval -> UnitInterval
(\/) = forall a. Ord a => a -> a -> a
max
    top :: UnitInterval
top = UnitInterval
1
    bot :: UnitInterval
bot = UnitInterval
0
    mkLattice :: Double -> UnitInterval
mkLattice = Double -> UnitInterval
mkUnitInterval

instance Show UnitInterval where
    show :: UnitInterval -> String
show (UnitInterval Double
x) = forall a. Show a => a -> String
show Double
x

-- | Unit interval constructor. Ensures values are in bounds

mkUnitInterval :: Double -> UnitInterval
mkUnitInterval :: Double -> UnitInterval
mkUnitInterval Double
x = Double -> UnitInterval
UnitInterval forall a b. (a -> b) -> a -> b
$ forall a. Ord a => a -> a -> a
max Double
0 forall a b. (a -> b) -> a -> b
$ forall a. Ord a => a -> a -> a
min Double
1 Double
x