{-# LANGUAGE DeriveDataTypeable  #-}
{-# LANGUAGE DeriveFoldable      #-}
{-# LANGUAGE DeriveFunctor       #-}
{-# LANGUAGE DeriveGeneric       #-}
{-# LANGUAGE DeriveTraversable   #-}
{-# LANGUAGE FlexibleContexts    #-}
{-# LANGUAGE Safe                #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeOperators       #-}
----------------------------------------------------------------------------
-- |
-- Module      :  Algebra.Lattice.Dropped
-- Copyright   :  (C) 2010-2015 Maximilian Bolingbroke, 2015-2019 Oleg Grenrus
-- License     :  BSD-3-Clause (see the file LICENSE)
--
-- Maintainer  :  Oleg Grenrus <oleg.grenrus@iki.fi>
--
----------------------------------------------------------------------------
module Algebra.Lattice.Dropped (
    Dropped(..)
  , retractDropped
  , foldDropped
  ) where

import Algebra.Lattice
import Algebra.PartialOrd

import Control.DeepSeq       (NFData (..))
import Control.Monad         (ap)
import Data.Data             (Data, Typeable)
import Data.Hashable         (Hashable (..))
import Data.Universe.Class   (Finite (..), Universe (..))
import Data.Universe.Helpers (Natural, Tagged, retag)
import GHC.Generics          (Generic, Generic1)

import qualified Test.QuickCheck as QC

--
-- Dropped
--

-- | Graft a distinct top onto an otherwise unbounded lattice.
-- As a bonus, the top will be an absorbing element for the join.
data Dropped a = Drop a
               | Top
  deriving ( Dropped a -> Dropped a -> Bool
(Dropped a -> Dropped a -> Bool)
-> (Dropped a -> Dropped a -> Bool) -> Eq (Dropped a)
forall a. Eq a => Dropped a -> Dropped a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall a. Eq a => Dropped a -> Dropped a -> Bool
== :: Dropped a -> Dropped a -> Bool
$c/= :: forall a. Eq a => Dropped a -> Dropped a -> Bool
/= :: Dropped a -> Dropped a -> Bool
Eq, Eq (Dropped a)
Eq (Dropped a) =>
(Dropped a -> Dropped a -> Ordering)
-> (Dropped a -> Dropped a -> Bool)
-> (Dropped a -> Dropped a -> Bool)
-> (Dropped a -> Dropped a -> Bool)
-> (Dropped a -> Dropped a -> Bool)
-> (Dropped a -> Dropped a -> Dropped a)
-> (Dropped a -> Dropped a -> Dropped a)
-> Ord (Dropped a)
Dropped a -> Dropped a -> Bool
Dropped a -> Dropped a -> Ordering
Dropped a -> Dropped a -> Dropped 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 (Dropped a)
forall a. Ord a => Dropped a -> Dropped a -> Bool
forall a. Ord a => Dropped a -> Dropped a -> Ordering
forall a. Ord a => Dropped a -> Dropped a -> Dropped a
$ccompare :: forall a. Ord a => Dropped a -> Dropped a -> Ordering
compare :: Dropped a -> Dropped a -> Ordering
$c< :: forall a. Ord a => Dropped a -> Dropped a -> Bool
< :: Dropped a -> Dropped a -> Bool
$c<= :: forall a. Ord a => Dropped a -> Dropped a -> Bool
<= :: Dropped a -> Dropped a -> Bool
$c> :: forall a. Ord a => Dropped a -> Dropped a -> Bool
> :: Dropped a -> Dropped a -> Bool
$c>= :: forall a. Ord a => Dropped a -> Dropped a -> Bool
>= :: Dropped a -> Dropped a -> Bool
$cmax :: forall a. Ord a => Dropped a -> Dropped a -> Dropped a
max :: Dropped a -> Dropped a -> Dropped a
$cmin :: forall a. Ord a => Dropped a -> Dropped a -> Dropped a
min :: Dropped a -> Dropped a -> Dropped a
Ord, Int -> Dropped a -> ShowS
[Dropped a] -> ShowS
Dropped a -> String
(Int -> Dropped a -> ShowS)
-> (Dropped a -> String)
-> ([Dropped a] -> ShowS)
-> Show (Dropped a)
forall a. Show a => Int -> Dropped a -> ShowS
forall a. Show a => [Dropped a] -> ShowS
forall a. Show a => Dropped a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> Dropped a -> ShowS
showsPrec :: Int -> Dropped a -> ShowS
$cshow :: forall a. Show a => Dropped a -> String
show :: Dropped a -> String
$cshowList :: forall a. Show a => [Dropped a] -> ShowS
showList :: [Dropped a] -> ShowS
Show, ReadPrec [Dropped a]
ReadPrec (Dropped a)
Int -> ReadS (Dropped a)
ReadS [Dropped a]
(Int -> ReadS (Dropped a))
-> ReadS [Dropped a]
-> ReadPrec (Dropped a)
-> ReadPrec [Dropped a]
-> Read (Dropped a)
forall a. Read a => ReadPrec [Dropped a]
forall a. Read a => ReadPrec (Dropped a)
forall a. Read a => Int -> ReadS (Dropped a)
forall a. Read a => ReadS [Dropped a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
$creadsPrec :: forall a. Read a => Int -> ReadS (Dropped a)
readsPrec :: Int -> ReadS (Dropped a)
$creadList :: forall a. Read a => ReadS [Dropped a]
readList :: ReadS [Dropped a]
$creadPrec :: forall a. Read a => ReadPrec (Dropped a)
readPrec :: ReadPrec (Dropped a)
$creadListPrec :: forall a. Read a => ReadPrec [Dropped a]
readListPrec :: ReadPrec [Dropped a]
Read, Typeable (Dropped a)
Typeable (Dropped a) =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> Dropped a -> c (Dropped a))
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Dropped a))
-> (Dropped a -> Constr)
-> (Dropped a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (Dropped a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c (Dropped a)))
-> ((forall b. Data b => b -> b) -> Dropped a -> Dropped a)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Dropped a -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Dropped a -> r)
-> (forall u. (forall d. Data d => d -> u) -> Dropped a -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Dropped a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a))
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a))
-> Data (Dropped a)
Dropped a -> Constr
Dropped a -> DataType
(forall b. Data b => b -> b) -> Dropped a -> Dropped a
forall a. Data a => Typeable (Dropped a)
forall a. Data a => Dropped a -> Constr
forall a. Data a => Dropped a -> DataType
forall a.
Data a =>
(forall b. Data b => b -> b) -> Dropped a -> Dropped a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Dropped a -> u
forall a u.
Data a =>
(forall d. Data d => d -> u) -> Dropped a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
forall a r r'.
Data a =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Dropped a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Dropped a -> c (Dropped a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Dropped a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (Dropped a))
forall a.
Typeable a =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
    (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
    (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> a -> m a)
-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> Dropped a -> u
forall u. (forall d. Data d => d -> u) -> Dropped a -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Dropped a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Dropped a -> c (Dropped a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (Dropped a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (Dropped a))
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Dropped a -> c (Dropped a)
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Dropped a -> c (Dropped a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Dropped a)
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Dropped a)
$ctoConstr :: forall a. Data a => Dropped a -> Constr
toConstr :: Dropped a -> Constr
$cdataTypeOf :: forall a. Data a => Dropped a -> DataType
dataTypeOf :: Dropped a -> DataType
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (Dropped a))
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (Dropped a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (Dropped a))
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (Dropped a))
$cgmapT :: forall a.
Data a =>
(forall b. Data b => b -> b) -> Dropped a -> Dropped a
gmapT :: (forall b. Data b => b -> b) -> Dropped a -> Dropped a
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Dropped a -> r
$cgmapQ :: forall a u.
Data a =>
(forall d. Data d => d -> u) -> Dropped a -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Dropped a -> [u]
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> Dropped a -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Dropped a -> u
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Dropped a -> m (Dropped a)
Data, Typeable, (forall x. Dropped a -> Rep (Dropped a) x)
-> (forall x. Rep (Dropped a) x -> Dropped a)
-> Generic (Dropped a)
forall x. Rep (Dropped a) x -> Dropped a
forall x. Dropped a -> Rep (Dropped a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (Dropped a) x -> Dropped a
forall a x. Dropped a -> Rep (Dropped a) x
$cfrom :: forall a x. Dropped a -> Rep (Dropped a) x
from :: forall x. Dropped a -> Rep (Dropped a) x
$cto :: forall a x. Rep (Dropped a) x -> Dropped a
to :: forall x. Rep (Dropped a) x -> Dropped a
Generic, (forall a b. (a -> b) -> Dropped a -> Dropped b)
-> (forall a b. a -> Dropped b -> Dropped a) -> Functor Dropped
forall a b. a -> Dropped b -> Dropped a
forall a b. (a -> b) -> Dropped a -> Dropped 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) -> Dropped a -> Dropped b
fmap :: forall a b. (a -> b) -> Dropped a -> Dropped b
$c<$ :: forall a b. a -> Dropped b -> Dropped a
<$ :: forall a b. a -> Dropped b -> Dropped a
Functor, (forall m. Monoid m => Dropped m -> m)
-> (forall m a. Monoid m => (a -> m) -> Dropped a -> m)
-> (forall m a. Monoid m => (a -> m) -> Dropped a -> m)
-> (forall a b. (a -> b -> b) -> b -> Dropped a -> b)
-> (forall a b. (a -> b -> b) -> b -> Dropped a -> b)
-> (forall b a. (b -> a -> b) -> b -> Dropped a -> b)
-> (forall b a. (b -> a -> b) -> b -> Dropped a -> b)
-> (forall a. (a -> a -> a) -> Dropped a -> a)
-> (forall a. (a -> a -> a) -> Dropped a -> a)
-> (forall a. Dropped a -> [a])
-> (forall a. Dropped a -> Bool)
-> (forall a. Dropped a -> Int)
-> (forall a. Eq a => a -> Dropped a -> Bool)
-> (forall a. Ord a => Dropped a -> a)
-> (forall a. Ord a => Dropped a -> a)
-> (forall a. Num a => Dropped a -> a)
-> (forall a. Num a => Dropped a -> a)
-> Foldable Dropped
forall a. Eq a => a -> Dropped a -> Bool
forall a. Num a => Dropped a -> a
forall a. Ord a => Dropped a -> a
forall m. Monoid m => Dropped m -> m
forall a. Dropped a -> Bool
forall a. Dropped a -> Int
forall a. Dropped a -> [a]
forall a. (a -> a -> a) -> Dropped a -> a
forall m a. Monoid m => (a -> m) -> Dropped a -> m
forall b a. (b -> a -> b) -> b -> Dropped a -> b
forall a b. (a -> b -> b) -> b -> Dropped 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 => Dropped m -> m
fold :: forall m. Monoid m => Dropped m -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> Dropped a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> Dropped a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> Dropped a -> m
foldMap' :: forall m a. Monoid m => (a -> m) -> Dropped a -> m
$cfoldr :: forall a b. (a -> b -> b) -> b -> Dropped a -> b
foldr :: forall a b. (a -> b -> b) -> b -> Dropped a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> Dropped a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> Dropped a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> Dropped a -> b
foldl :: forall b a. (b -> a -> b) -> b -> Dropped a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> Dropped a -> b
foldl' :: forall b a. (b -> a -> b) -> b -> Dropped a -> b
$cfoldr1 :: forall a. (a -> a -> a) -> Dropped a -> a
foldr1 :: forall a. (a -> a -> a) -> Dropped a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> Dropped a -> a
foldl1 :: forall a. (a -> a -> a) -> Dropped a -> a
$ctoList :: forall a. Dropped a -> [a]
toList :: forall a. Dropped a -> [a]
$cnull :: forall a. Dropped a -> Bool
null :: forall a. Dropped a -> Bool
$clength :: forall a. Dropped a -> Int
length :: forall a. Dropped a -> Int
$celem :: forall a. Eq a => a -> Dropped a -> Bool
elem :: forall a. Eq a => a -> Dropped a -> Bool
$cmaximum :: forall a. Ord a => Dropped a -> a
maximum :: forall a. Ord a => Dropped a -> a
$cminimum :: forall a. Ord a => Dropped a -> a
minimum :: forall a. Ord a => Dropped a -> a
$csum :: forall a. Num a => Dropped a -> a
sum :: forall a. Num a => Dropped a -> a
$cproduct :: forall a. Num a => Dropped a -> a
product :: forall a. Num a => Dropped a -> a
Foldable, Functor Dropped
Foldable Dropped
(Functor Dropped, Foldable Dropped) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> Dropped a -> f (Dropped b))
-> (forall (f :: * -> *) a.
    Applicative f =>
    Dropped (f a) -> f (Dropped a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> Dropped a -> m (Dropped b))
-> (forall (m :: * -> *) a.
    Monad m =>
    Dropped (m a) -> m (Dropped a))
-> Traversable Dropped
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 => Dropped (m a) -> m (Dropped a)
forall (f :: * -> *) a.
Applicative f =>
Dropped (f a) -> f (Dropped a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Dropped a -> m (Dropped b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Dropped a -> f (Dropped b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Dropped a -> f (Dropped b)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Dropped a -> f (Dropped b)
$csequenceA :: forall (f :: * -> *) a.
Applicative f =>
Dropped (f a) -> f (Dropped a)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
Dropped (f a) -> f (Dropped a)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Dropped a -> m (Dropped b)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Dropped a -> m (Dropped b)
$csequence :: forall (m :: * -> *) a. Monad m => Dropped (m a) -> m (Dropped a)
sequence :: forall (m :: * -> *) a. Monad m => Dropped (m a) -> m (Dropped a)
Traversable
           , (forall a. Dropped a -> Rep1 Dropped a)
-> (forall a. Rep1 Dropped a -> Dropped a) -> Generic1 Dropped
forall a. Rep1 Dropped a -> Dropped a
forall a. Dropped a -> Rep1 Dropped a
forall k (f :: k -> *).
(forall (a :: k). f a -> Rep1 f a)
-> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
$cfrom1 :: forall a. Dropped a -> Rep1 Dropped a
from1 :: forall a. Dropped a -> Rep1 Dropped a
$cto1 :: forall a. Rep1 Dropped a -> Dropped a
to1 :: forall a. Rep1 Dropped a -> Dropped a
Generic1
           )

instance Applicative Dropped where
  pure :: forall a. a -> Dropped a
pure = a -> Dropped a
forall a. a -> Dropped a
forall (m :: * -> *) a. Monad m => a -> m a
return
  <*> :: forall a b. Dropped (a -> b) -> Dropped a -> Dropped b
(<*>) = Dropped (a -> b) -> Dropped a -> Dropped b
forall (m :: * -> *) a b. Monad m => m (a -> b) -> m a -> m b
ap

instance Monad Dropped where
  return :: forall a. a -> Dropped a
return        = a -> Dropped a
forall a. a -> Dropped a
Drop
  Dropped a
Top >>= :: forall a b. Dropped a -> (a -> Dropped b) -> Dropped b
>>= a -> Dropped b
_     = Dropped b
forall a. Dropped a
Top
  Drop a
x >>= a -> Dropped b
f  = a -> Dropped b
f a
x

instance NFData a => NFData (Dropped a) where
  rnf :: Dropped a -> ()
rnf Dropped a
Top      = ()
  rnf (Drop a
a) = a -> ()
forall a. NFData a => a -> ()
rnf a
a

instance Hashable a => Hashable (Dropped a)

instance PartialOrd a => PartialOrd (Dropped a) where
  leq :: Dropped a -> Dropped a -> Bool
leq Dropped a
_ Dropped a
Top = Bool
True
  leq Dropped a
Top Dropped a
_ = Bool
False
  leq (Drop a
x) (Drop a
y) = a -> a -> Bool
forall a. PartialOrd a => a -> a -> Bool
leq a
x a
y
  comparable :: Dropped a -> Dropped a -> Bool
comparable Dropped a
Top Dropped a
_ = Bool
True
  comparable Dropped a
_ Dropped a
Top = Bool
True
  comparable (Drop a
x) (Drop a
y) = a -> a -> Bool
forall a. PartialOrd a => a -> a -> Bool
comparable a
x a
y

instance Lattice a => Lattice (Dropped a) where
    Dropped a
Top    \/ :: Dropped a -> Dropped a -> Dropped a
\/ Dropped a
_      = Dropped a
forall a. Dropped a
Top
    Dropped a
_      \/ Dropped a
Top    = Dropped a
forall a. Dropped a
Top
    Drop a
x \/ Drop a
y = a -> Dropped a
forall a. a -> Dropped a
Drop (a
x a -> a -> a
forall a. Lattice a => a -> a -> a
\/ a
y)

    Dropped a
Top    /\ :: Dropped a -> Dropped a -> Dropped a
/\ Dropped a
drop_y = Dropped a
drop_y
    Dropped a
drop_x /\ Dropped a
Top    = Dropped a
drop_x
    Drop a
x /\ Drop a
y = a -> Dropped a
forall a. a -> Dropped a
Drop (a
x a -> a -> a
forall a. Lattice a => a -> a -> a
/\ a
y)

instance BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Dropped a) where
    bottom :: Dropped a
bottom = a -> Dropped a
forall a. a -> Dropped a
Drop a
forall a. BoundedJoinSemiLattice a => a
bottom

instance Lattice a => BoundedMeetSemiLattice (Dropped a) where
    top :: Dropped a
top = Dropped a
forall a. Dropped a
Top

-- | Interpret @'Dropped' a@ using the 'BoundedMeetSemiLattice' of @a@.
retractDropped :: BoundedMeetSemiLattice a => Dropped a -> a
retractDropped :: forall a. BoundedMeetSemiLattice a => Dropped a -> a
retractDropped = a -> (a -> a) -> Dropped a -> a
forall b a. b -> (a -> b) -> Dropped a -> b
foldDropped a
forall a. BoundedMeetSemiLattice a => a
top a -> a
forall a. a -> a
id

-- | Similar to @'maybe'@, but for @'Dropped'@ type.
foldDropped :: b -> (a -> b) -> Dropped a -> b
foldDropped :: forall b a. b -> (a -> b) -> Dropped a -> b
foldDropped b
_ a -> b
f (Drop a
x) = a -> b
f a
x
foldDropped b
y a -> b
_ Dropped a
Top      = b
y

instance Universe a => Universe (Dropped a) where
    universe :: [Dropped a]
universe = Dropped a
forall a. Dropped a
Top Dropped a -> [Dropped a] -> [Dropped a]
forall a. a -> [a] -> [a]
: (a -> Dropped a) -> [a] -> [Dropped a]
forall a b. (a -> b) -> [a] -> [b]
map a -> Dropped a
forall a. a -> Dropped a
Drop [a]
forall a. Universe a => [a]
universe
instance Finite a => Finite (Dropped a) where
    universeF :: [Dropped a]
universeF = Dropped a
forall a. Dropped a
Top Dropped a -> [Dropped a] -> [Dropped a]
forall a. a -> [a] -> [a]
: (a -> Dropped a) -> [a] -> [Dropped a]
forall a b. (a -> b) -> [a] -> [b]
map a -> Dropped a
forall a. a -> Dropped a
Drop [a]
forall a. Finite a => [a]
universeF
    cardinality :: Tagged (Dropped a) Natural
cardinality = (Natural -> Natural)
-> Tagged (Dropped a) Natural -> Tagged (Dropped a) Natural
forall a b.
(a -> b) -> Tagged (Dropped a) a -> Tagged (Dropped a) b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Natural -> Natural
forall a. Enum a => a -> a
succ (Tagged a Natural -> Tagged (Dropped a) Natural
forall {k1} {k2} (s :: k1) b (t :: k2). Tagged s b -> Tagged t b
retag (Tagged a Natural
forall a. Finite a => Tagged a Natural
cardinality :: Tagged a Natural))

instance QC.Arbitrary a => QC.Arbitrary (Dropped a) where
    arbitrary :: Gen (Dropped a)
arbitrary = [(Int, Gen (Dropped a))] -> Gen (Dropped a)
forall a. HasCallStack => [(Int, Gen a)] -> Gen a
QC.frequency
        [ (Int
1, Dropped a -> Gen (Dropped a)
forall a. a -> Gen a
forall (f :: * -> *) a. Applicative f => a -> f a
pure Dropped a
forall a. Dropped a
Top)
        , (Int
9, a -> Dropped a
forall a. a -> Dropped a
Drop (a -> Dropped a) -> Gen a -> Gen (Dropped a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen a
forall a. Arbitrary a => Gen a
QC.arbitrary)
        ]

    shrink :: Dropped a -> [Dropped a]
shrink Dropped a
Top      = []
    shrink (Drop a
x) = Dropped a
forall a. Dropped a
Top Dropped a -> [Dropped a] -> [Dropped a]
forall a. a -> [a] -> [a]
: (a -> Dropped a) -> [a] -> [Dropped a]
forall a b. (a -> b) -> [a] -> [b]
map a -> Dropped a
forall a. a -> Dropped a
Drop (a -> [a]
forall a. Arbitrary a => a -> [a]
QC.shrink a
x)

instance QC.CoArbitrary a => QC.CoArbitrary (Dropped a) where
    coarbitrary :: forall b. Dropped a -> Gen b -> Gen b
coarbitrary Dropped a
Top      = Int -> Gen b -> Gen b
forall n a. Integral n => n -> Gen a -> Gen a
QC.variant (Int
0 :: Int)
    coarbitrary (Drop a
x) = Int -> Gen b -> Gen b
forall n a. Integral n => n -> Gen a -> Gen a
QC.variant (Int
1 :: Int) (Gen b -> Gen b) -> (Gen b -> Gen b) -> Gen b -> Gen b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Gen b -> Gen b
forall b. a -> Gen b -> Gen b
forall a b. CoArbitrary a => a -> Gen b -> Gen b
QC.coarbitrary a
x

instance QC.Function a => QC.Function (Dropped a) where
    function :: forall b. (Dropped a -> b) -> Dropped a :-> b
function = (Dropped a -> Maybe a)
-> (Maybe a -> Dropped a) -> (Dropped a -> b) -> Dropped a :-> b
forall b a c.
Function b =>
(a -> b) -> (b -> a) -> (a -> c) -> a :-> c
QC.functionMap Dropped a -> Maybe a
forall {a}. Dropped a -> Maybe a
fromDropped Maybe a -> Dropped a
forall {a}. Maybe a -> Dropped a
toDropped where
        fromDropped :: Dropped a -> Maybe a
fromDropped = Maybe a -> (a -> Maybe a) -> Dropped a -> Maybe a
forall b a. b -> (a -> b) -> Dropped a -> b
foldDropped Maybe a
forall a. Maybe a
Nothing a -> Maybe a
forall a. a -> Maybe a
Just
        toDropped :: Maybe a -> Dropped a
toDropped   = Dropped a -> (a -> Dropped a) -> Maybe a -> Dropped a
forall b a. b -> (a -> b) -> Maybe a -> b
maybe Dropped a
forall a. Dropped a
Top a -> Dropped a
forall a. a -> Dropped a
Drop