> {-# OPTIONS_HADDOCK show-extensions #-}
>
> module LTK.Decide.Acom (isAcom, isAcomM, comTest) where
> import Data.Set (Set)
> import qualified Data.Set as Set
> import LTK.Decide.SF (isSFM)
> import LTK.FSA
> import LTK.Algebra
> type S n e = (n, [Symbol e])
>
>
> isAcom :: (Ord n, Ord e) => FSA n e -> Bool
> isAcom :: forall n e. (Ord n, Ord e) => FSA n e -> Bool
isAcom = forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isAcomM forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall e n.
(Ord e, Ord n) =>
FSA n e -> FSA ([Maybe n], [Symbol e]) e
syntacticMonoid
>
> isAcomM :: (Ord n, Ord e) => SynMon n e -> Bool
> isAcomM :: forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isAcomM = forall a. (a -> Bool) -> (a -> Bool) -> a -> Bool
both forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isSFM (\SynMon n e
m -> forall n e.
(Ord n, Ord e) =>
SynMon n e -> Set (State (S [Maybe n] e)) -> Bool
comTest SynMon n e
m (forall e n. (Ord e, Ord n) => FSA n e -> Set (State n)
states SynMon n e
m))
>
> comTest :: (Ord n, Ord e) =>
> SynMon n e -> Set (State (S [Maybe n] e)) -> Bool
> comTest :: forall n e.
(Ord n, Ord e) =>
SynMon n e -> Set (State (S [Maybe n] e)) -> Bool
comTest SynMon n e
m Set (State (S [Maybe n] e))
qs
> | forall a. Set a -> Int
Set.size (forall n e. FSA n e -> Set (State n)
initials SynMon n e
m) forall a. Eq a => a -> a -> Bool
/= Int
1 = forall a. Set a -> Bool
Set.null (forall n e. FSA n e -> Set (State n)
initials SynMon n e
m)
> | Bool
otherwise = forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ([Symbol e], [Symbol e]) -> Bool
commutes forall a b. (a -> b) -> a -> b
$ forall a. Set a -> [a]
Set.toList Set ([Symbol e], [Symbol e])
p
> where p :: Set ([Symbol e], [Symbol e])
p = forall a. Ord a => Set a -> Set (a, a)
pairs forall a b. (a -> b) -> a -> b
$ forall (s :: * -> *) b1 b a.
(Collapsible s, Container (s b1) b) =>
(a -> b) -> s a -> s b1
tmap (forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall n. State n -> n
nodeLabel) Set (State (S [Maybe n] e))
qs
> i :: State (S [Maybe n] e)
i = forall a. Set a -> a
Set.findMin forall a b. (a -> b) -> a -> b
$ forall n e. FSA n e -> Set (State n)
initials SynMon n e
m
> commutes :: ([Symbol e], [Symbol e]) -> Bool
commutes ([Symbol e], [Symbol e])
x = forall n e.
(Ord n, Ord e) =>
FSA n e -> [Symbol e] -> State n -> Set (State n)
follow SynMon n e
m (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry forall a. [a] -> [a] -> [a]
(++) ([Symbol e], [Symbol e])
x) State (S [Maybe n] e)
i
> forall a. Eq a => a -> a -> Bool
== forall n e.
(Ord n, Ord e) =>
FSA n e -> [Symbol e] -> State n -> Set (State n)
follow SynMon n e
m (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry (forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a. [a] -> [a] -> [a]
(++)) ([Symbol e], [Symbol e])
x) State (S [Maybe n] e)
i
> pairs :: Ord a => Set a -> Set (a, a)
> pairs :: forall a. Ord a => Set a -> Set (a, a)
pairs Set a
xs = forall (c :: * -> *) a b.
Collapsible c =>
(a -> b -> b) -> b -> c a -> b
collapse (forall c a. Container c a => c -> c -> c
union forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall {a}. a -> Set (a, a)
f) forall c a. Container c a => c
empty Set a
xs
> where f :: a -> Set (a, a)
f a
x = forall a b. (a -> b) -> Set a -> Set b
Set.mapMonotonic ((,) a
x) Set a
xs