| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Algebra.Heyting.Free.Expr
Documentation
Heyting algebra expression.
Note: this type doesn't have Heyting instance,
as its Eq and Ord are structural.
Constructors
| Var a | |
| Bottom | |
| Top | |
| (Expr a) :/\: (Expr a) infixr 6 | |
| (Expr a) :\/: (Expr a) infixr 5 | |
| (Expr a) :=>: (Expr a) infixr 4 |
Instances
| Foldable Expr Source # | |||||
Defined in Algebra.Heyting.Free.Expr Methods fold :: Monoid m => Expr m -> m foldMap :: Monoid m => (a -> m) -> Expr a -> m foldMap' :: Monoid m => (a -> m) -> Expr a -> m foldr :: (a -> b -> b) -> b -> Expr a -> b foldr' :: (a -> b -> b) -> b -> Expr a -> b foldl :: (b -> a -> b) -> b -> Expr a -> b foldl' :: (b -> a -> b) -> b -> Expr a -> b foldr1 :: (a -> a -> a) -> Expr a -> a foldl1 :: (a -> a -> a) -> Expr a -> a elem :: Eq a => a -> Expr a -> Bool maximum :: Ord a => Expr a -> a | |||||
| Traversable Expr Source # | |||||
| Applicative Expr Source # | |||||
| Functor Expr Source # | |||||
| Monad Expr Source # | |||||
| Generic1 Expr Source # | |||||
Defined in Algebra.Heyting.Free.Expr Associated Types
| |||||
| Data a => Data (Expr a) Source # | |||||
Defined in Algebra.Heyting.Free.Expr Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Expr a -> c (Expr a) gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Expr a) dataTypeOf :: Expr a -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Expr a)) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Expr a)) gmapT :: (forall b. Data b => b -> b) -> Expr a -> Expr a gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Expr a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Expr a -> r gmapQ :: (forall d. Data d => d -> u) -> Expr a -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Expr a -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Expr a -> m (Expr a) gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Expr a -> m (Expr a) gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Expr a -> m (Expr a) | |||||
| Generic (Expr a) Source # | |||||
Defined in Algebra.Heyting.Free.Expr Associated Types
| |||||
| Show a => Show (Expr a) Source # | |||||
| Eq a => Eq (Expr a) Source # | |||||
| Ord a => Ord (Expr a) Source # | |||||
| type Rep1 Expr Source # | |||||
Defined in Algebra.Heyting.Free.Expr type Rep1 Expr = D1 ('MetaData "Expr" "Algebra.Heyting.Free.Expr" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) ((C1 ('MetaCons "Var" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1) :+: (C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))) :+: (C1 ('MetaCons ":/\\:" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr)) :+: (C1 ('MetaCons ":\\/:" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr)) :+: C1 ('MetaCons ":=>:" ('InfixI 'RightAssociative 4) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Expr))))) | |||||
| type Rep (Expr a) Source # | |||||
Defined in Algebra.Heyting.Free.Expr type Rep (Expr a) = D1 ('MetaData "Expr" "Algebra.Heyting.Free.Expr" "lattices-2.2.1.1-J46lACPEOTBKo73SIhecCd" 'False) ((C1 ('MetaCons "Var" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: (C1 ('MetaCons "Bottom" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Top" 'PrefixI 'False) (U1 :: Type -> Type))) :+: (C1 ('MetaCons ":/\\:" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a))) :+: (C1 ('MetaCons ":\\/:" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a))) :+: C1 ('MetaCons ":=>:" ('InfixI 'RightAssociative 4) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Expr a)))))) | |||||
proofSearch :: Ord a => Expr a -> Bool Source #
Decide whether x :: is provable.Expr a
Note: this doesn't construct a proof term, but merely returns a Bool.