--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.Small.AtMostTwo
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--
-- A type expressing that some value may have at most two values
--
--------------------------------------------------------------------------------
module HGeometry.Small.AtMostTwo
  ( AtMostTwo(..)
  ) where

import           Data.Functor.Classes

--------------------------------------------------------------------------------

-- | At most two elements
data AtMostTwo a = Zero | One !a | Two !a !a
  deriving (Int -> AtMostTwo a -> ShowS
[AtMostTwo a] -> ShowS
AtMostTwo a -> String
(Int -> AtMostTwo a -> ShowS)
-> (AtMostTwo a -> String)
-> ([AtMostTwo a] -> ShowS)
-> Show (AtMostTwo a)
forall a. Show a => Int -> AtMostTwo a -> ShowS
forall a. Show a => [AtMostTwo a] -> ShowS
forall a. Show a => AtMostTwo a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> AtMostTwo a -> ShowS
showsPrec :: Int -> AtMostTwo a -> ShowS
$cshow :: forall a. Show a => AtMostTwo a -> String
show :: AtMostTwo a -> String
$cshowList :: forall a. Show a => [AtMostTwo a] -> ShowS
showList :: [AtMostTwo a] -> ShowS
Show,ReadPrec [AtMostTwo a]
ReadPrec (AtMostTwo a)
Int -> ReadS (AtMostTwo a)
ReadS [AtMostTwo a]
(Int -> ReadS (AtMostTwo a))
-> ReadS [AtMostTwo a]
-> ReadPrec (AtMostTwo a)
-> ReadPrec [AtMostTwo a]
-> Read (AtMostTwo a)
forall a. Read a => ReadPrec [AtMostTwo a]
forall a. Read a => ReadPrec (AtMostTwo a)
forall a. Read a => Int -> ReadS (AtMostTwo a)
forall a. Read a => ReadS [AtMostTwo a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
$creadsPrec :: forall a. Read a => Int -> ReadS (AtMostTwo a)
readsPrec :: Int -> ReadS (AtMostTwo a)
$creadList :: forall a. Read a => ReadS [AtMostTwo a]
readList :: ReadS [AtMostTwo a]
$creadPrec :: forall a. Read a => ReadPrec (AtMostTwo a)
readPrec :: ReadPrec (AtMostTwo a)
$creadListPrec :: forall a. Read a => ReadPrec [AtMostTwo a]
readListPrec :: ReadPrec [AtMostTwo a]
Read,AtMostTwo a -> AtMostTwo a -> Bool
(AtMostTwo a -> AtMostTwo a -> Bool)
-> (AtMostTwo a -> AtMostTwo a -> Bool) -> Eq (AtMostTwo a)
forall a. Eq a => AtMostTwo a -> AtMostTwo a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall a. Eq a => AtMostTwo a -> AtMostTwo a -> Bool
== :: AtMostTwo a -> AtMostTwo a -> Bool
$c/= :: forall a. Eq a => AtMostTwo a -> AtMostTwo a -> Bool
/= :: AtMostTwo a -> AtMostTwo a -> Bool
Eq,Eq (AtMostTwo a)
Eq (AtMostTwo a) =>
(AtMostTwo a -> AtMostTwo a -> Ordering)
-> (AtMostTwo a -> AtMostTwo a -> Bool)
-> (AtMostTwo a -> AtMostTwo a -> Bool)
-> (AtMostTwo a -> AtMostTwo a -> Bool)
-> (AtMostTwo a -> AtMostTwo a -> Bool)
-> (AtMostTwo a -> AtMostTwo a -> AtMostTwo a)
-> (AtMostTwo a -> AtMostTwo a -> AtMostTwo a)
-> Ord (AtMostTwo a)
AtMostTwo a -> AtMostTwo a -> Bool
AtMostTwo a -> AtMostTwo a -> Ordering
AtMostTwo a -> AtMostTwo a -> AtMostTwo a
forall a.
Eq a =>
(a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (AtMostTwo a)
forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Bool
forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Ordering
forall a. Ord a => AtMostTwo a -> AtMostTwo a -> AtMostTwo a
$ccompare :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Ordering
compare :: AtMostTwo a -> AtMostTwo a -> Ordering
$c< :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Bool
< :: AtMostTwo a -> AtMostTwo a -> Bool
$c<= :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Bool
<= :: AtMostTwo a -> AtMostTwo a -> Bool
$c> :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Bool
> :: AtMostTwo a -> AtMostTwo a -> Bool
$c>= :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> Bool
>= :: AtMostTwo a -> AtMostTwo a -> Bool
$cmax :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> AtMostTwo a
max :: AtMostTwo a -> AtMostTwo a -> AtMostTwo a
$cmin :: forall a. Ord a => AtMostTwo a -> AtMostTwo a -> AtMostTwo a
min :: AtMostTwo a -> AtMostTwo a -> AtMostTwo a
Ord,(forall a b. (a -> b) -> AtMostTwo a -> AtMostTwo b)
-> (forall a b. a -> AtMostTwo b -> AtMostTwo a)
-> Functor AtMostTwo
forall a b. a -> AtMostTwo b -> AtMostTwo a
forall a b. (a -> b) -> AtMostTwo a -> AtMostTwo b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
$cfmap :: forall a b. (a -> b) -> AtMostTwo a -> AtMostTwo b
fmap :: forall a b. (a -> b) -> AtMostTwo a -> AtMostTwo b
$c<$ :: forall a b. a -> AtMostTwo b -> AtMostTwo a
<$ :: forall a b. a -> AtMostTwo b -> AtMostTwo a
Functor,(forall m. Monoid m => AtMostTwo m -> m)
-> (forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m)
-> (forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m)
-> (forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b)
-> (forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b)
-> (forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b)
-> (forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b)
-> (forall a. (a -> a -> a) -> AtMostTwo a -> a)
-> (forall a. (a -> a -> a) -> AtMostTwo a -> a)
-> (forall a. AtMostTwo a -> [a])
-> (forall a. AtMostTwo a -> Bool)
-> (forall a. AtMostTwo a -> Int)
-> (forall a. Eq a => a -> AtMostTwo a -> Bool)
-> (forall a. Ord a => AtMostTwo a -> a)
-> (forall a. Ord a => AtMostTwo a -> a)
-> (forall a. Num a => AtMostTwo a -> a)
-> (forall a. Num a => AtMostTwo a -> a)
-> Foldable AtMostTwo
forall a. Eq a => a -> AtMostTwo a -> Bool
forall a. Num a => AtMostTwo a -> a
forall a. Ord a => AtMostTwo a -> a
forall m. Monoid m => AtMostTwo m -> m
forall a. AtMostTwo a -> Bool
forall a. AtMostTwo a -> Int
forall a. AtMostTwo a -> [a]
forall a. (a -> a -> a) -> AtMostTwo a -> a
forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m
forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b
forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
$cfold :: forall m. Monoid m => AtMostTwo m -> m
fold :: forall m. Monoid m => AtMostTwo m -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m
foldMap' :: forall m a. Monoid m => (a -> m) -> AtMostTwo a -> m
$cfoldr :: forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b
foldr :: forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> AtMostTwo a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b
foldl :: forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b
foldl' :: forall b a. (b -> a -> b) -> b -> AtMostTwo a -> b
$cfoldr1 :: forall a. (a -> a -> a) -> AtMostTwo a -> a
foldr1 :: forall a. (a -> a -> a) -> AtMostTwo a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> AtMostTwo a -> a
foldl1 :: forall a. (a -> a -> a) -> AtMostTwo a -> a
$ctoList :: forall a. AtMostTwo a -> [a]
toList :: forall a. AtMostTwo a -> [a]
$cnull :: forall a. AtMostTwo a -> Bool
null :: forall a. AtMostTwo a -> Bool
$clength :: forall a. AtMostTwo a -> Int
length :: forall a. AtMostTwo a -> Int
$celem :: forall a. Eq a => a -> AtMostTwo a -> Bool
elem :: forall a. Eq a => a -> AtMostTwo a -> Bool
$cmaximum :: forall a. Ord a => AtMostTwo a -> a
maximum :: forall a. Ord a => AtMostTwo a -> a
$cminimum :: forall a. Ord a => AtMostTwo a -> a
minimum :: forall a. Ord a => AtMostTwo a -> a
$csum :: forall a. Num a => AtMostTwo a -> a
sum :: forall a. Num a => AtMostTwo a -> a
$cproduct :: forall a. Num a => AtMostTwo a -> a
product :: forall a. Num a => AtMostTwo a -> a
Foldable,Functor AtMostTwo
Foldable AtMostTwo
(Functor AtMostTwo, Foldable AtMostTwo) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> AtMostTwo a -> f (AtMostTwo b))
-> (forall (f :: * -> *) a.
    Applicative f =>
    AtMostTwo (f a) -> f (AtMostTwo a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> AtMostTwo a -> m (AtMostTwo b))
-> (forall (m :: * -> *) a.
    Monad m =>
    AtMostTwo (m a) -> m (AtMostTwo a))
-> Traversable AtMostTwo
forall (t :: * -> *).
(Functor t, Foldable t) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a.
Monad m =>
AtMostTwo (m a) -> m (AtMostTwo a)
forall (f :: * -> *) a.
Applicative f =>
AtMostTwo (f a) -> f (AtMostTwo a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> AtMostTwo a -> m (AtMostTwo b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> AtMostTwo a -> f (AtMostTwo b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> AtMostTwo a -> f (AtMostTwo b)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> AtMostTwo a -> f (AtMostTwo b)
$csequenceA :: forall (f :: * -> *) a.
Applicative f =>
AtMostTwo (f a) -> f (AtMostTwo a)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
AtMostTwo (f a) -> f (AtMostTwo a)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> AtMostTwo a -> m (AtMostTwo b)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> AtMostTwo a -> m (AtMostTwo b)
$csequence :: forall (m :: * -> *) a.
Monad m =>
AtMostTwo (m a) -> m (AtMostTwo a)
sequence :: forall (m :: * -> *) a.
Monad m =>
AtMostTwo (m a) -> m (AtMostTwo a)
Traversable)

instance Show1 AtMostTwo where
  liftShowsPrec :: forall a.
(Int -> a -> ShowS)
-> ([a] -> ShowS) -> Int -> AtMostTwo a -> ShowS
liftShowsPrec Int -> a -> ShowS
sp [a] -> ShowS
_ Int
d = \case
    AtMostTwo a
Zero ->
      \String
s -> String
s String -> ShowS
forall a. Semigroup a => a -> a -> a
<> String
"Zero"
    One a
x ->
      (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
forall a. (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
showsUnaryWith Int -> a -> ShowS
sp String
"One" Int
d a
x
    Two a
x a
y ->
      (Int -> a -> ShowS)
-> (Int -> a -> ShowS) -> String -> Int -> a -> a -> ShowS
forall a b.
(Int -> a -> ShowS)
-> (Int -> b -> ShowS) -> String -> Int -> a -> b -> ShowS
showsBinaryWith Int -> a -> ShowS
sp Int -> a -> ShowS
sp String
"Two" Int
d a
x a
y

instance Eq1   AtMostTwo where
  liftEq :: forall a b. (a -> b -> Bool) -> AtMostTwo a -> AtMostTwo b -> Bool
liftEq a -> b -> Bool
_ AtMostTwo a
Zero      AtMostTwo b
Zero        = Bool
True
  liftEq a -> b -> Bool
f (One a
x)   (One b
x')    = a -> b -> Bool
f a
x b
x'
  liftEq a -> b -> Bool
f (Two a
x a
y) (Two b
x' b
y') = a -> b -> Bool
f a
x b
x' Bool -> Bool -> Bool
&& a -> b -> Bool
f a
y b
y'
  liftEq a -> b -> Bool
_ AtMostTwo a
_         AtMostTwo b
_           = Bool
False

instance Ord1  AtMostTwo where
  liftCompare :: forall a b.
(a -> b -> Ordering) -> AtMostTwo a -> AtMostTwo b -> Ordering
liftCompare a -> b -> Ordering
_ AtMostTwo a
Zero      AtMostTwo b
Zero        = Ordering
EQ
  liftCompare a -> b -> Ordering
_ AtMostTwo a
Zero      AtMostTwo b
_           = Ordering
LT

  liftCompare a -> b -> Ordering
_ (One a
_)   AtMostTwo b
Zero        = Ordering
GT
  liftCompare a -> b -> Ordering
f (One a
x)   (One b
x')    = a -> b -> Ordering
f a
x b
x'
  liftCompare a -> b -> Ordering
_ (One a
_)   (Two b
_ b
_)   = Ordering
LT

  liftCompare a -> b -> Ordering
f (Two a
x a
y) (Two b
x' b
y') = a -> b -> Ordering
f a
x b
x' Ordering -> Ordering -> Ordering
forall a. Semigroup a => a -> a -> a
<> a -> b -> Ordering
f a
y b
y'
  liftCompare a -> b -> Ordering
_ AtMostTwo a
_         AtMostTwo b
_           = Ordering
GT