{-# LANGUAGE CPP #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveTraversable #-}
module Distribution.SPDX.Extra.Internal
(LatticeSyntax(..), dual, freeVars, equivalent, preorder, satisfiable) where
import Control.Applicative
import Control.Monad
import Control.Monad.Trans.State.Strict
import Data.Data
import Data.Foldable
import Data.Traversable
import Prelude hiding (all, or)
import qualified Data.Map.Strict as Map
data LatticeSyntax a = LVar a
| LBound Bool
| LJoin (LatticeSyntax a) (LatticeSyntax a)
| LMeet (LatticeSyntax a) (LatticeSyntax a)
deriving (LatticeSyntax a -> LatticeSyntax a -> Bool
(LatticeSyntax a -> LatticeSyntax a -> Bool)
-> (LatticeSyntax a -> LatticeSyntax a -> Bool)
-> Eq (LatticeSyntax a)
forall a. Eq a => LatticeSyntax a -> LatticeSyntax a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c/= :: forall a. Eq a => LatticeSyntax a -> LatticeSyntax a -> Bool
== :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c== :: forall a. Eq a => LatticeSyntax a -> LatticeSyntax a -> Bool
Eq, Eq (LatticeSyntax a)
Eq (LatticeSyntax a)
-> (LatticeSyntax a -> LatticeSyntax a -> Ordering)
-> (LatticeSyntax a -> LatticeSyntax a -> Bool)
-> (LatticeSyntax a -> LatticeSyntax a -> Bool)
-> (LatticeSyntax a -> LatticeSyntax a -> Bool)
-> (LatticeSyntax a -> LatticeSyntax a -> Bool)
-> (LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a)
-> (LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a)
-> Ord (LatticeSyntax a)
LatticeSyntax a -> LatticeSyntax a -> Bool
LatticeSyntax a -> LatticeSyntax a -> Ordering
LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax 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 (LatticeSyntax a)
forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Ordering
forall a.
Ord a =>
LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
min :: LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
$cmin :: forall a.
Ord a =>
LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
max :: LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
$cmax :: forall a.
Ord a =>
LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
>= :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c>= :: forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
> :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c> :: forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
<= :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c<= :: forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
< :: LatticeSyntax a -> LatticeSyntax a -> Bool
$c< :: forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
compare :: LatticeSyntax a -> LatticeSyntax a -> Ordering
$ccompare :: forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (LatticeSyntax a)
Ord, ReadPrec [LatticeSyntax a]
ReadPrec (LatticeSyntax a)
Int -> ReadS (LatticeSyntax a)
ReadS [LatticeSyntax a]
(Int -> ReadS (LatticeSyntax a))
-> ReadS [LatticeSyntax a]
-> ReadPrec (LatticeSyntax a)
-> ReadPrec [LatticeSyntax a]
-> Read (LatticeSyntax a)
forall a. Read a => ReadPrec [LatticeSyntax a]
forall a. Read a => ReadPrec (LatticeSyntax a)
forall a. Read a => Int -> ReadS (LatticeSyntax a)
forall a. Read a => ReadS [LatticeSyntax a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
readListPrec :: ReadPrec [LatticeSyntax a]
$creadListPrec :: forall a. Read a => ReadPrec [LatticeSyntax a]
readPrec :: ReadPrec (LatticeSyntax a)
$creadPrec :: forall a. Read a => ReadPrec (LatticeSyntax a)
readList :: ReadS [LatticeSyntax a]
$creadList :: forall a. Read a => ReadS [LatticeSyntax a]
readsPrec :: Int -> ReadS (LatticeSyntax a)
$creadsPrec :: forall a. Read a => Int -> ReadS (LatticeSyntax a)
Read, Int -> LatticeSyntax a -> ShowS
[LatticeSyntax a] -> ShowS
LatticeSyntax a -> String
(Int -> LatticeSyntax a -> ShowS)
-> (LatticeSyntax a -> String)
-> ([LatticeSyntax a] -> ShowS)
-> Show (LatticeSyntax a)
forall a. Show a => Int -> LatticeSyntax a -> ShowS
forall a. Show a => [LatticeSyntax a] -> ShowS
forall a. Show a => LatticeSyntax a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [LatticeSyntax a] -> ShowS
$cshowList :: forall a. Show a => [LatticeSyntax a] -> ShowS
show :: LatticeSyntax a -> String
$cshow :: forall a. Show a => LatticeSyntax a -> String
showsPrec :: Int -> LatticeSyntax a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> LatticeSyntax a -> ShowS
Show, a -> LatticeSyntax b -> LatticeSyntax a
(a -> b) -> LatticeSyntax a -> LatticeSyntax b
(forall a b. (a -> b) -> LatticeSyntax a -> LatticeSyntax b)
-> (forall a b. a -> LatticeSyntax b -> LatticeSyntax a)
-> Functor LatticeSyntax
forall a b. a -> LatticeSyntax b -> LatticeSyntax a
forall a b. (a -> b) -> LatticeSyntax a -> LatticeSyntax b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: a -> LatticeSyntax b -> LatticeSyntax a
$c<$ :: forall a b. a -> LatticeSyntax b -> LatticeSyntax a
fmap :: (a -> b) -> LatticeSyntax a -> LatticeSyntax b
$cfmap :: forall a b. (a -> b) -> LatticeSyntax a -> LatticeSyntax b
Functor, LatticeSyntax a -> Bool
(a -> m) -> LatticeSyntax a -> m
(a -> b -> b) -> b -> LatticeSyntax a -> b
(forall m. Monoid m => LatticeSyntax m -> m)
-> (forall m a. Monoid m => (a -> m) -> LatticeSyntax a -> m)
-> (forall m a. Monoid m => (a -> m) -> LatticeSyntax a -> m)
-> (forall a b. (a -> b -> b) -> b -> LatticeSyntax a -> b)
-> (forall a b. (a -> b -> b) -> b -> LatticeSyntax a -> b)
-> (forall b a. (b -> a -> b) -> b -> LatticeSyntax a -> b)
-> (forall b a. (b -> a -> b) -> b -> LatticeSyntax a -> b)
-> (forall a. (a -> a -> a) -> LatticeSyntax a -> a)
-> (forall a. (a -> a -> a) -> LatticeSyntax a -> a)
-> (forall a. LatticeSyntax a -> [a])
-> (forall a. LatticeSyntax a -> Bool)
-> (forall a. LatticeSyntax a -> Int)
-> (forall a. Eq a => a -> LatticeSyntax a -> Bool)
-> (forall a. Ord a => LatticeSyntax a -> a)
-> (forall a. Ord a => LatticeSyntax a -> a)
-> (forall a. Num a => LatticeSyntax a -> a)
-> (forall a. Num a => LatticeSyntax a -> a)
-> Foldable LatticeSyntax
forall a. Eq a => a -> LatticeSyntax a -> Bool
forall a. Num a => LatticeSyntax a -> a
forall a. Ord a => LatticeSyntax a -> a
forall m. Monoid m => LatticeSyntax m -> m
forall a. LatticeSyntax a -> Bool
forall a. LatticeSyntax a -> Int
forall a. LatticeSyntax a -> [a]
forall a. (a -> a -> a) -> LatticeSyntax a -> a
forall m a. Monoid m => (a -> m) -> LatticeSyntax a -> m
forall b a. (b -> a -> b) -> b -> LatticeSyntax a -> b
forall a b. (a -> b -> b) -> b -> LatticeSyntax 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
product :: LatticeSyntax a -> a
$cproduct :: forall a. Num a => LatticeSyntax a -> a
sum :: LatticeSyntax a -> a
$csum :: forall a. Num a => LatticeSyntax a -> a
minimum :: LatticeSyntax a -> a
$cminimum :: forall a. Ord a => LatticeSyntax a -> a
maximum :: LatticeSyntax a -> a
$cmaximum :: forall a. Ord a => LatticeSyntax a -> a
elem :: a -> LatticeSyntax a -> Bool
$celem :: forall a. Eq a => a -> LatticeSyntax a -> Bool
length :: LatticeSyntax a -> Int
$clength :: forall a. LatticeSyntax a -> Int
null :: LatticeSyntax a -> Bool
$cnull :: forall a. LatticeSyntax a -> Bool
toList :: LatticeSyntax a -> [a]
$ctoList :: forall a. LatticeSyntax a -> [a]
foldl1 :: (a -> a -> a) -> LatticeSyntax a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> LatticeSyntax a -> a
foldr1 :: (a -> a -> a) -> LatticeSyntax a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> LatticeSyntax a -> a
foldl' :: (b -> a -> b) -> b -> LatticeSyntax a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> LatticeSyntax a -> b
foldl :: (b -> a -> b) -> b -> LatticeSyntax a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> LatticeSyntax a -> b
foldr' :: (a -> b -> b) -> b -> LatticeSyntax a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> LatticeSyntax a -> b
foldr :: (a -> b -> b) -> b -> LatticeSyntax a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> LatticeSyntax a -> b
foldMap' :: (a -> m) -> LatticeSyntax a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> LatticeSyntax a -> m
foldMap :: (a -> m) -> LatticeSyntax a -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> LatticeSyntax a -> m
fold :: LatticeSyntax m -> m
$cfold :: forall m. Monoid m => LatticeSyntax m -> m
Foldable, Functor LatticeSyntax
Foldable LatticeSyntax
Functor LatticeSyntax
-> Foldable LatticeSyntax
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LatticeSyntax a -> f (LatticeSyntax b))
-> (forall (f :: * -> *) a.
Applicative f =>
LatticeSyntax (f a) -> f (LatticeSyntax a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LatticeSyntax a -> m (LatticeSyntax b))
-> (forall (m :: * -> *) a.
Monad m =>
LatticeSyntax (m a) -> m (LatticeSyntax a))
-> Traversable LatticeSyntax
(a -> f b) -> LatticeSyntax a -> f (LatticeSyntax b)
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 =>
LatticeSyntax (m a) -> m (LatticeSyntax a)
forall (f :: * -> *) a.
Applicative f =>
LatticeSyntax (f a) -> f (LatticeSyntax a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LatticeSyntax a -> m (LatticeSyntax b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LatticeSyntax a -> f (LatticeSyntax b)
sequence :: LatticeSyntax (m a) -> m (LatticeSyntax a)
$csequence :: forall (m :: * -> *) a.
Monad m =>
LatticeSyntax (m a) -> m (LatticeSyntax a)
mapM :: (a -> m b) -> LatticeSyntax a -> m (LatticeSyntax b)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LatticeSyntax a -> m (LatticeSyntax b)
sequenceA :: LatticeSyntax (f a) -> f (LatticeSyntax a)
$csequenceA :: forall (f :: * -> *) a.
Applicative f =>
LatticeSyntax (f a) -> f (LatticeSyntax a)
traverse :: (a -> f b) -> LatticeSyntax a -> f (LatticeSyntax b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LatticeSyntax a -> f (LatticeSyntax b)
$cp2Traversable :: Foldable LatticeSyntax
$cp1Traversable :: Functor LatticeSyntax
Traversable, Typeable, Typeable (LatticeSyntax a)
DataType
Constr
Typeable (LatticeSyntax a)
-> (forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a))
-> (forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a))
-> (LatticeSyntax a -> Constr)
-> (LatticeSyntax a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (LatticeSyntax a)))
-> ((forall b. Data b => b -> b)
-> LatticeSyntax a -> LatticeSyntax a)
-> (forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r)
-> (forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r)
-> (forall u.
(forall d. Data d => d -> u) -> LatticeSyntax a -> [u])
-> (forall u.
Int -> (forall d. Data d => d -> u) -> LatticeSyntax a -> u)
-> (forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a))
-> (forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a))
-> (forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a))
-> Data (LatticeSyntax a)
LatticeSyntax a -> DataType
LatticeSyntax a -> Constr
(forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a))
(forall b. Data b => b -> b) -> LatticeSyntax a -> LatticeSyntax a
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a)
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a)
forall a. Data a => Typeable (LatticeSyntax a)
forall a. Data a => LatticeSyntax a -> DataType
forall a. Data a => LatticeSyntax a -> Constr
forall a.
Data a =>
(forall b. Data b => b -> b) -> LatticeSyntax a -> LatticeSyntax a
forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> LatticeSyntax a -> u
forall a u.
Data a =>
(forall d. Data d => d -> u) -> LatticeSyntax a -> [u]
forall a r r'.
Data a =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
forall a r r'.
Data a =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a)
forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a)
forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a))
forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (LatticeSyntax 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) -> LatticeSyntax a -> u
forall u. (forall d. Data d => d -> u) -> LatticeSyntax a -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a)
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a)
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a))
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (LatticeSyntax a))
$cLMeet :: Constr
$cLJoin :: Constr
$cLBound :: Constr
$cLVar :: Constr
$tLatticeSyntax :: DataType
gmapMo :: (forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
$cgmapMo :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
gmapMp :: (forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
$cgmapMp :: forall a (m :: * -> *).
(Data a, MonadPlus m) =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
gmapM :: (forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
$cgmapM :: forall a (m :: * -> *).
(Data a, Monad m) =>
(forall d. Data d => d -> m d)
-> LatticeSyntax a -> m (LatticeSyntax a)
gmapQi :: Int -> (forall d. Data d => d -> u) -> LatticeSyntax a -> u
$cgmapQi :: forall a u.
Data a =>
Int -> (forall d. Data d => d -> u) -> LatticeSyntax a -> u
gmapQ :: (forall d. Data d => d -> u) -> LatticeSyntax a -> [u]
$cgmapQ :: forall a u.
Data a =>
(forall d. Data d => d -> u) -> LatticeSyntax a -> [u]
gmapQr :: (r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
$cgmapQr :: forall a r r'.
Data a =>
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
gmapQl :: (r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
$cgmapQl :: forall a r r'.
Data a =>
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> LatticeSyntax a -> r
gmapT :: (forall b. Data b => b -> b) -> LatticeSyntax a -> LatticeSyntax a
$cgmapT :: forall a.
Data a =>
(forall b. Data b => b -> b) -> LatticeSyntax a -> LatticeSyntax a
dataCast2 :: (forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (LatticeSyntax a))
$cdataCast2 :: forall a (t :: * -> * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c (LatticeSyntax a))
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a))
$cdataCast1 :: forall a (t :: * -> *) (c :: * -> *).
(Data a, Typeable t) =>
(forall d. Data d => c (t d)) -> Maybe (c (LatticeSyntax a))
dataTypeOf :: LatticeSyntax a -> DataType
$cdataTypeOf :: forall a. Data a => LatticeSyntax a -> DataType
toConstr :: LatticeSyntax a -> Constr
$ctoConstr :: forall a. Data a => LatticeSyntax a -> Constr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a)
$cgunfold :: forall a (c :: * -> *).
Data a =>
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (LatticeSyntax a)
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a)
$cgfoldl :: forall a (c :: * -> *).
Data a =>
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LatticeSyntax a -> c (LatticeSyntax a)
$cp1Data :: forall a. Data a => Typeable (LatticeSyntax a)
Data)
instance Applicative LatticeSyntax where
pure :: a -> LatticeSyntax a
pure = a -> LatticeSyntax a
forall (m :: * -> *) a. Monad m => a -> m a
return
<*> :: LatticeSyntax (a -> b) -> LatticeSyntax a -> LatticeSyntax b
(<*>) = LatticeSyntax (a -> b) -> LatticeSyntax a -> LatticeSyntax b
forall (m :: * -> *) a b. Monad m => m (a -> b) -> m a -> m b
ap
instance Monad LatticeSyntax where
return :: a -> LatticeSyntax a
return = a -> LatticeSyntax a
forall a. a -> LatticeSyntax a
LVar
LVar a
x >>= :: LatticeSyntax a -> (a -> LatticeSyntax b) -> LatticeSyntax b
>>= a -> LatticeSyntax b
f = a -> LatticeSyntax b
f a
x
LBound Bool
b >>= a -> LatticeSyntax b
_ = Bool -> LatticeSyntax b
forall a. Bool -> LatticeSyntax a
LBound Bool
b
LJoin LatticeSyntax a
a LatticeSyntax a
b >>= a -> LatticeSyntax b
f = LatticeSyntax b -> LatticeSyntax b -> LatticeSyntax b
forall a. LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
LJoin (LatticeSyntax a
a LatticeSyntax a -> (a -> LatticeSyntax b) -> LatticeSyntax b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> LatticeSyntax b
f) (LatticeSyntax a
b LatticeSyntax a -> (a -> LatticeSyntax b) -> LatticeSyntax b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> LatticeSyntax b
f)
LMeet LatticeSyntax a
a LatticeSyntax a
b >>= a -> LatticeSyntax b
f = LatticeSyntax b -> LatticeSyntax b -> LatticeSyntax b
forall a. LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
LMeet (LatticeSyntax a
a LatticeSyntax a -> (a -> LatticeSyntax b) -> LatticeSyntax b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> LatticeSyntax b
f) (LatticeSyntax a
b LatticeSyntax a -> (a -> LatticeSyntax b) -> LatticeSyntax b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> LatticeSyntax b
f)
freeVars :: LatticeSyntax a -> [a]
freeVars :: LatticeSyntax a -> [a]
freeVars = LatticeSyntax a -> [a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList
dual :: LatticeSyntax a -> LatticeSyntax a
dual :: LatticeSyntax a -> LatticeSyntax a
dual (LVar a
v) = a -> LatticeSyntax a
forall a. a -> LatticeSyntax a
LVar a
v
dual (LBound Bool
t) = Bool -> LatticeSyntax a
forall a. Bool -> LatticeSyntax a
LBound (Bool -> LatticeSyntax a) -> Bool -> LatticeSyntax a
forall a b. (a -> b) -> a -> b
$ Bool -> Bool
not Bool
t
dual (LJoin LatticeSyntax a
a LatticeSyntax a
b) = LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
LMeet (LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a
dual LatticeSyntax a
a) (LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a
dual LatticeSyntax a
b)
dual (LMeet LatticeSyntax a
a LatticeSyntax a
b) = LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
LJoin (LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a
dual LatticeSyntax a
a) (LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a
dual LatticeSyntax a
b)
equivalent :: Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
equivalent :: LatticeSyntax a -> LatticeSyntax a -> Bool
equivalent LatticeSyntax a
a LatticeSyntax a
b = ((Bool, Bool) -> Bool) -> [(Bool, Bool)] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ((Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
(==)) ([(Bool, Bool)] -> Bool)
-> (Eval a (Bool, Bool) -> [(Bool, Bool)])
-> Eval a (Bool, Bool)
-> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Eval a (Bool, Bool) -> [(Bool, Bool)]
forall v a. Eval v a -> [a]
runEval (Eval a (Bool, Bool) -> Bool) -> Eval a (Bool, Bool) -> Bool
forall a b. (a -> b) -> a -> b
$ Eval a (Bool, Bool)
p
where p :: Eval a (Bool, Bool)
p = (,) (Bool -> Bool -> (Bool, Bool))
-> Eval a Bool -> Eval a (Bool -> (Bool, Bool))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> LatticeSyntax a -> Eval a Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax a
a Eval a (Bool -> (Bool, Bool)) -> Eval a Bool -> Eval a (Bool, Bool)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> LatticeSyntax a -> Eval a Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax a
b
preorder :: Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
preorder :: LatticeSyntax a -> LatticeSyntax a -> Bool
preorder LatticeSyntax a
a LatticeSyntax a
b = (LatticeSyntax a
a LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
forall a. LatticeSyntax a -> LatticeSyntax a -> LatticeSyntax a
`LJoin` LatticeSyntax a
b) LatticeSyntax a -> LatticeSyntax a -> Bool
forall a. Ord a => LatticeSyntax a -> LatticeSyntax a -> Bool
`equivalent` LatticeSyntax a
b
satisfiable :: Ord a => LatticeSyntax a -> Bool
satisfiable :: LatticeSyntax a -> Bool
satisfiable = [Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
or ([Bool] -> Bool)
-> (LatticeSyntax a -> [Bool]) -> LatticeSyntax a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Eval a Bool -> [Bool]
forall v a. Eval v a -> [a]
runEval (Eval a Bool -> [Bool])
-> (LatticeSyntax a -> Eval a Bool) -> LatticeSyntax a -> [Bool]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. LatticeSyntax a -> Eval a Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice
newtype Eval v a = Eval { Eval v a -> StateT (Map v Bool) [] a
unEval :: StateT (Map.Map v Bool) [] a }
instance Functor (Eval v) where
fmap :: (a -> b) -> Eval v a -> Eval v b
fmap = (a -> b) -> Eval v a -> Eval v b
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM
instance Applicative (Eval v) where
pure :: a -> Eval v a
pure = a -> Eval v a
forall (m :: * -> *) a. Monad m => a -> m a
return
<*> :: Eval v (a -> b) -> Eval v a -> Eval v b
(<*>) = Eval v (a -> b) -> Eval v a -> Eval v b
forall (m :: * -> *) a b. Monad m => m (a -> b) -> m a -> m b
ap
instance Alternative (Eval v) where
empty :: Eval v a
empty = Eval v a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
<|> :: Eval v a -> Eval v a -> Eval v a
(<|>) = Eval v a -> Eval v a -> Eval v a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
mplus
instance Monad (Eval v) where
return :: a -> Eval v a
return = StateT (Map v Bool) [] a -> Eval v a
forall v a. StateT (Map v Bool) [] a -> Eval v a
Eval (StateT (Map v Bool) [] a -> Eval v a)
-> (a -> StateT (Map v Bool) [] a) -> a -> Eval v a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> StateT (Map v Bool) [] a
forall (m :: * -> *) a. Monad m => a -> m a
return
Eval StateT (Map v Bool) [] a
m >>= :: Eval v a -> (a -> Eval v b) -> Eval v b
>>= a -> Eval v b
k = StateT (Map v Bool) [] b -> Eval v b
forall v a. StateT (Map v Bool) [] a -> Eval v a
Eval (StateT (Map v Bool) [] b -> Eval v b)
-> StateT (Map v Bool) [] b -> Eval v b
forall a b. (a -> b) -> a -> b
$ StateT (Map v Bool) [] a
m StateT (Map v Bool) [] a
-> (a -> StateT (Map v Bool) [] b) -> StateT (Map v Bool) [] b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= Eval v b -> StateT (Map v Bool) [] b
forall v a. Eval v a -> StateT (Map v Bool) [] a
unEval (Eval v b -> StateT (Map v Bool) [] b)
-> (a -> Eval v b) -> a -> StateT (Map v Bool) [] b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Eval v b
k
instance MonadPlus (Eval v) where
mzero :: Eval v a
mzero = StateT (Map v Bool) [] a -> Eval v a
forall v a. StateT (Map v Bool) [] a -> Eval v a
Eval StateT (Map v Bool) [] a
forall (m :: * -> *) a. MonadPlus m => m a
mzero
Eval StateT (Map v Bool) [] a
a mplus :: Eval v a -> Eval v a -> Eval v a
`mplus` Eval StateT (Map v Bool) [] a
b = StateT (Map v Bool) [] a -> Eval v a
forall v a. StateT (Map v Bool) [] a -> Eval v a
Eval (StateT (Map v Bool) [] a -> Eval v a)
-> StateT (Map v Bool) [] a -> Eval v a
forall a b. (a -> b) -> a -> b
$ StateT (Map v Bool) [] a
a StateT (Map v Bool) [] a
-> StateT (Map v Bool) [] a -> StateT (Map v Bool) [] a
forall (m :: * -> *) a. MonadPlus m => m a -> m a -> m a
`mplus` StateT (Map v Bool) [] a
b
runEval :: Eval v a -> [a]
runEval :: Eval v a -> [a]
runEval Eval v a
act = StateT (Map v Bool) [] a -> Map v Bool -> [a]
forall (m :: * -> *) s a. Monad m => StateT s m a -> s -> m a
evalStateT (Eval v a -> StateT (Map v Bool) [] a
forall v a. Eval v a -> StateT (Map v Bool) [] a
unEval Eval v a
act) Map v Bool
forall k a. Map k a
Map.empty
evalLattice :: Ord v => LatticeSyntax v -> Eval v Bool
evalLattice :: LatticeSyntax v -> Eval v Bool
evalLattice (LVar v
v) = v -> Eval v Bool
forall v. Ord v => v -> Eval v Bool
guess v
v
evalLattice (LBound Bool
b) = Bool -> Eval v Bool
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
b
evalLattice (LJoin LatticeSyntax v
a LatticeSyntax v
b) = LatticeSyntax v -> Eval v Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax v
a Eval v Bool -> Eval v Bool -> Eval v Bool
forall (m :: * -> *). Monad m => m Bool -> m Bool -> m Bool
||^ LatticeSyntax v -> Eval v Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax v
b
evalLattice (LMeet LatticeSyntax v
a LatticeSyntax v
b) = LatticeSyntax v -> Eval v Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax v
a Eval v Bool -> Eval v Bool -> Eval v Bool
forall (m :: * -> *). Monad m => m Bool -> m Bool -> m Bool
&&^ LatticeSyntax v -> Eval v Bool
forall v. Ord v => LatticeSyntax v -> Eval v Bool
evalLattice LatticeSyntax v
b
guess :: Ord v => v -> Eval v Bool
guess :: v -> Eval v Bool
guess v
v = StateT (Map v Bool) [] Bool -> Eval v Bool
forall v a. StateT (Map v Bool) [] a -> Eval v a
Eval (StateT (Map v Bool) [] Bool -> Eval v Bool)
-> StateT (Map v Bool) [] Bool -> Eval v Bool
forall a b. (a -> b) -> a -> b
$ do
Map v Bool
st <- StateT (Map v Bool) [] (Map v Bool)
forall (m :: * -> *) s. Monad m => StateT s m s
get
let remember :: Bool -> StateT (Map v Bool) m Bool
remember Bool
b = Map v Bool -> StateT (Map v Bool) m ()
forall (m :: * -> *) s. Monad m => s -> StateT s m ()
put (v -> Bool -> Map v Bool -> Map v Bool
forall k a. Ord k => k -> a -> Map k a -> Map k a
Map.insert v
v Bool
b Map v Bool
st) StateT (Map v Bool) m ()
-> StateT (Map v Bool) m Bool -> StateT (Map v Bool) m Bool
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> Bool -> StateT (Map v Bool) m Bool
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
b
case v -> Map v Bool -> Maybe Bool
forall k a. Ord k => k -> Map k a -> Maybe a
Map.lookup v
v Map v Bool
st of
Just Bool
b -> Bool -> StateT (Map v Bool) [] Bool
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
b
Maybe Bool
Nothing -> Bool -> StateT (Map v Bool) [] Bool
forall (m :: * -> *). Monad m => Bool -> StateT (Map v Bool) m Bool
remember Bool
True StateT (Map v Bool) [] Bool
-> StateT (Map v Bool) [] Bool -> StateT (Map v Bool) [] Bool
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> Bool -> StateT (Map v Bool) [] Bool
forall (m :: * -> *). Monad m => Bool -> StateT (Map v Bool) m Bool
remember Bool
False
ifM :: Monad m => m Bool -> m a -> m a -> m a
ifM :: m Bool -> m a -> m a -> m a
ifM m Bool
b m a
t m a
f = do Bool
b' <- m Bool
b; if Bool
b' then m a
t else m a
f
(||^) :: Monad m => m Bool -> m Bool -> m Bool
||^ :: m Bool -> m Bool -> m Bool
(||^) m Bool
a m Bool
b = m Bool -> m Bool -> m Bool -> m Bool
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM m Bool
a (Bool -> m Bool
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
True) m Bool
b
(&&^) :: Monad m => m Bool -> m Bool -> m Bool
&&^ :: m Bool -> m Bool -> m Bool
(&&^) m Bool
a m Bool
b = m Bool -> m Bool -> m Bool -> m Bool
forall (m :: * -> *) a. Monad m => m Bool -> m a -> m a -> m a
ifM m Bool
a m Bool
b (Bool -> m Bool
forall (m :: * -> *) a. Monad m => a -> m a
return Bool
False)