> {-# OPTIONS_HADDOCK show-extensions #-}
>
> module LTK.Decide.Definite
> (
> isDef
> , isDefM
> , isRDef
> , isRDefM
>
> , isTDef
> , isTDefM
> , isTRDef
> , isTRDefM
> ) where
> import qualified Data.Set as Set
> import LTK.FSA
> import LTK.Algebra
> import LTK.Tiers (project)
>
>
> isDef :: (Ord n, Ord e) => FSA n e -> Bool
> isDef :: FSA n e -> Bool
isDef = SynMon n e -> Bool
forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isDefM (SynMon n e -> Bool) -> (FSA n e -> SynMon n e) -> FSA n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FSA n e -> SynMon n e
forall e n.
(Ord e, Ord n) =>
FSA n e -> FSA ([Maybe n], [Symbol e]) e
syntacticMonoid
>
> isDefM :: (Ord n, Ord e) => SynMon n e -> Bool
> isDefM :: SynMon n e -> Bool
isDefM SynMon n e
s = (Set (State ([Maybe n], [Symbol e])) -> Bool)
-> [Set (State ([Maybe n], [Symbol e]))] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ((Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
1) (Int -> Bool)
-> (Set (State ([Maybe n], [Symbol e])) -> Int)
-> Set (State ([Maybe n], [Symbol e]))
-> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Set (State ([Maybe n], [Symbol e])) -> Int
forall a. Set a -> Int
Set.size) ([Set (State ([Maybe n], [Symbol e]))] -> Bool)
-> (Set (State ([Maybe n], [Symbol e]))
-> [Set (State ([Maybe n], [Symbol e]))])
-> Set (State ([Maybe n], [Symbol e]))
-> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (State ([Maybe n], [Symbol e])
-> Set (State ([Maybe n], [Symbol e])))
-> [State ([Maybe n], [Symbol e])]
-> [Set (State ([Maybe n], [Symbol e]))]
forall a b. (a -> b) -> [a] -> [b]
map (SynMon n e
-> State ([Maybe n], [Symbol e])
-> Set (State ([Maybe n], [Symbol e]))
forall n e.
(Ord n, Ord e) =>
FSA (n, [Symbol e]) e
-> State (n, [Symbol e]) -> Set (State (n, [Symbol e]))
primitiveIdealL SynMon n e
s)
> ([State ([Maybe n], [Symbol e])]
-> [Set (State ([Maybe n], [Symbol e]))])
-> (Set (State ([Maybe n], [Symbol e]))
-> [State ([Maybe n], [Symbol e])])
-> Set (State ([Maybe n], [Symbol e]))
-> [Set (State ([Maybe n], [Symbol e]))]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Set (State ([Maybe n], [Symbol e]))
-> [State ([Maybe n], [Symbol e])]
forall a. Set a -> [a]
Set.toList (Set (State ([Maybe n], [Symbol e])) -> Bool)
-> Set (State ([Maybe n], [Symbol e])) -> Bool
forall a b. (a -> b) -> a -> b
$ SynMon n e -> Set (State ([Maybe n], [Symbol e]))
forall n e. (Ord n, Ord e) => FSA (n, [Symbol e]) e -> Set (T n e)
idempotents SynMon n e
s
>
>
> isRDef :: (Ord n, Ord e) => FSA n e -> Bool
> isRDef :: FSA n e -> Bool
isRDef = SynMon n e -> Bool
forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isRDefM (SynMon n e -> Bool) -> (FSA n e -> SynMon n e) -> FSA n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FSA n e -> SynMon n e
forall e n.
(Ord e, Ord n) =>
FSA n e -> FSA ([Maybe n], [Symbol e]) e
syntacticMonoid
>
> isRDefM :: (Ord n, Ord e) => SynMon n e -> Bool
> isRDefM :: SynMon n e -> Bool
isRDefM SynMon n e
s = (Set (State ([Maybe n], [Symbol e])) -> Bool)
-> [Set (State ([Maybe n], [Symbol e]))] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ((Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
1) (Int -> Bool)
-> (Set (State ([Maybe n], [Symbol e])) -> Int)
-> Set (State ([Maybe n], [Symbol e]))
-> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Set (State ([Maybe n], [Symbol e])) -> Int
forall a. Set a -> Int
Set.size) ([Set (State ([Maybe n], [Symbol e]))] -> Bool)
-> (Set (State ([Maybe n], [Symbol e]))
-> [Set (State ([Maybe n], [Symbol e]))])
-> Set (State ([Maybe n], [Symbol e]))
-> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (State ([Maybe n], [Symbol e])
-> Set (State ([Maybe n], [Symbol e])))
-> [State ([Maybe n], [Symbol e])]
-> [Set (State ([Maybe n], [Symbol e]))]
forall a b. (a -> b) -> [a] -> [b]
map (SynMon n e
-> State ([Maybe n], [Symbol e])
-> Set (State ([Maybe n], [Symbol e]))
forall n e. (Ord n, Ord e) => FSA n e -> State n -> Set (State n)
primitiveIdealR SynMon n e
s)
> ([State ([Maybe n], [Symbol e])]
-> [Set (State ([Maybe n], [Symbol e]))])
-> (Set (State ([Maybe n], [Symbol e]))
-> [State ([Maybe n], [Symbol e])])
-> Set (State ([Maybe n], [Symbol e]))
-> [Set (State ([Maybe n], [Symbol e]))]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Set (State ([Maybe n], [Symbol e]))
-> [State ([Maybe n], [Symbol e])]
forall a. Set a -> [a]
Set.toList (Set (State ([Maybe n], [Symbol e])) -> Bool)
-> Set (State ([Maybe n], [Symbol e])) -> Bool
forall a b. (a -> b) -> a -> b
$ SynMon n e -> Set (State ([Maybe n], [Symbol e]))
forall n e. (Ord n, Ord e) => FSA (n, [Symbol e]) e -> Set (T n e)
idempotents SynMon n e
s
>
> isTDef :: (Ord n, Ord e) => FSA n e -> Bool
> isTDef :: FSA n e -> Bool
isTDef = FSA n e -> Bool
forall n e. (Ord n, Ord e) => FSA n e -> Bool
isDef (FSA n e -> Bool) -> (FSA n e -> FSA n e) -> FSA n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FSA n e -> FSA n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project
>
> isTDefM :: (Ord n, Ord e) => SynMon n e -> Bool
> isTDefM :: SynMon n e -> Bool
isTDefM = SynMon n e -> Bool
forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isDefM (SynMon n e -> Bool)
-> (SynMon n e -> SynMon n e) -> SynMon n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. SynMon n e -> SynMon n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project
>
> isTRDef :: (Ord n, Ord e) => FSA n e -> Bool
> isTRDef :: FSA n e -> Bool
isTRDef = FSA n e -> Bool
forall n e. (Ord n, Ord e) => FSA n e -> Bool
isRDef (FSA n e -> Bool) -> (FSA n e -> FSA n e) -> FSA n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FSA n e -> FSA n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project
>
> isTRDefM :: (Ord n, Ord e) => SynMon n e -> Bool
> isTRDefM :: SynMon n e -> Bool
isTRDefM = SynMon n e -> Bool
forall n e. (Ord n, Ord e) => SynMon n e -> Bool
isRDefM (SynMon n e -> Bool)
-> (SynMon n e -> SynMon n e) -> SynMon n e -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. SynMon n e -> SynMon n e
forall n e. (Ord n, Ord e) => FSA n e -> FSA n e
project