Safe Haskell	Safe-Inferred
Language	Haskell2010

Language.Expression

Description

Implements higher-ranked equivalents of Functor, Monad, Foldable and Traversable.

Synopsis

class HFunctor (h :: (u -> *) -> u -> *) where
- hmap :: (forall b. t b -> t' b) -> h t a -> h t' a
class HPointed h where
- hpure :: t a -> h t a
class HBind h where
- (^>>=) :: h t a -> (forall b. t b -> h t' b) -> h t' a
class (HFunctor h, HPointed h, HBind h) => HMonad h
hliftM :: (HPointed h, HBind h) => (forall b. t b -> t' b) -> h t a -> h t' a
hjoin :: HBind h => h (h t) a -> h t a
class HFunctor h => HTraversable h where
- htraverse :: Applicative f => (forall b. t b -> f (t' b)) -> h t a -> f (h t' a)
- hsequence :: Applicative f => h (Compose f t) a -> f (h t a)
hfoldMapMonoid :: (HTraversable h, Monoid m) => (forall b. t b -> m) -> h t a -> m
hbindTraverse :: (HTraversable h, HMonad h, Applicative f) => (forall b. t b -> f (h t' b)) -> h t a -> f (h t' a)
class HBifunctor (h :: (k -> *) -> (k -> *) -> k -> *) where
- hbimap :: (forall b. s b -> s' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a
- hfirst :: (forall b. s b -> s' b) -> h s t a -> h s' t a
- hsecond :: (forall b. t b -> t' b) -> h s t a -> h s t' a
class HBifunctor h => HBitraversable h where
- hbitraverse :: Applicative f => (forall b. s b -> f (s' b)) -> (forall b. t b -> f (t' b)) -> h s t a -> f (h s' t' a)
hbifoldMapMonoid :: (Monoid m, HBitraversable h) => (forall b. s b -> m) -> (forall b. t b -> m) -> h s t a -> m
class HDuofunctor (h :: ((u -> *) -> u -> *) -> (u -> *) -> u -> *) where
- hduomap :: (forall g g' b. (forall c. g c -> g' c) -> s g b -> s' g' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a
hduomapFirst :: HDuofunctor h => (forall g g' b. (forall c. g c -> g' c) -> s g b -> s' g' b) -> h s t a -> h s' t a
hduomapFirst' :: (HDuofunctor h, HFunctor s) => (forall g b. s g b -> s' g b) -> h s t a -> h s' t a
hduomapSecond :: (HDuofunctor h, HFunctor s) => (forall b. t b -> t' b) -> h s t a -> h s t' a
class HDuofunctor h => HDuotraversable h where
- hduotraverse :: Applicative f => (forall g g' b. (forall c. g c -> f (g' c)) -> s g b -> f (s' g' b)) -> (forall b. t b -> f (t' b)) -> h s t a -> f (h s' t' a)
hduotraverseFirst :: (HDuotraversable h, Applicative f) => (forall g g' b. (forall c. g c -> f (g' c)) -> s g b -> f (s' g' b)) -> h s t a -> f (h s' t a)
hduotraverseFirst' :: (HDuotraversable h, HTraversable s, Monad f) => (forall g b. s g b -> f (s' g b)) -> h s t a -> f (h s' t a)
hduotraverseSecond :: (HDuotraversable h, HTraversable s, Applicative f) => (forall b. t b -> f (t' b)) -> h s t a -> f (h s t' a)
class HFoldableAt k h where
- hfoldMap :: (forall b. t b -> k b) -> h t a -> k a
implHfoldMap :: HFunctor h => (h k a -> k a) -> (forall b. t b -> k b) -> h t a -> k a
implHfoldMapCompose :: (HTraversable h, Monad m) => (h k a -> m (k a)) -> (forall b. t b -> Compose m k b) -> h t a -> Compose m k a
hfold :: HFoldableAt t h => h t a -> t a
hfoldA :: (HFoldableAt (Compose f t) h, Applicative f) => h t a -> f (t a)
hfoldMapA :: (HFoldableAt (Compose f k) h, Applicative f) => (forall b. t b -> f (k b)) -> h t a -> f (k a)
hfoldTraverse :: (HFoldableAt k h, HTraversable h, Applicative f) => (forall b. t b -> f (k b)) -> h t a -> f (k a)
class HBifoldableAt k h where
- hbifoldMap :: (forall b. f b -> k b) -> (forall b. g b -> k b) -> h f g a -> k a
hbifold :: HBifoldableAt k h => h k k a -> k a
class HDuofoldableAt k h where
- hduofoldMap :: HTraversable s => (forall g b. (forall c. g c -> k c) -> s g b -> k b) -> (forall b. t b -> k b) -> h s t a -> k a
implHduofoldMap :: (HDuofunctor h, HFunctor s) => ((forall g b. (forall c. g c -> k c) -> s g b -> k b) -> h s k a -> k a) -> (forall g b. (forall c. g c -> k c) -> s g b -> k b) -> (forall b. t b -> k b) -> h s t a -> k a
implHduofoldMapCompose :: (HDuotraversable h, HTraversable s, Monad m) => ((forall g b. (forall c. g c -> m (k c)) -> s g b -> m (k b)) -> h s k a -> m (k a)) -> (forall g b. (forall c. g c -> Compose m k c) -> s g b -> Compose m k b) -> (forall b. t b -> Compose m k b) -> h s t a -> Compose m k a
data HFree h t a
- = HPure (t a)
- | HWrap (h (HFree h t) a)

Documentation

class HFunctor (h :: (u -> *) -> u -> *) where Source #

Higher-ranked analogue of Functor.

Minimal complete definition

Nothing

Methods

hmap :: (forall b. t b -> t' b) -> h t a -> h t' a Source #

Higher-ranked analogue of fmap. Has a default implementation in terms of htraverse for HTraversable h.

default hmap :: HTraversable h => (forall b. t b -> t' b) -> h t a -> h t' a Source #

Instances

Instances details

HFunctor (Reverse :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Reverse t a -> Reverse t' a Source #
HFunctor (Sum f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Sum f t a -> Sum f t' a Source #
HFunctor (Product f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Product f t a -> Product f t' a Source #
HFunctor h => HFunctor (HFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> HFree h t a -> HFree h t' a Source #
HFunctor (BV g :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> BV g t a -> BV g t' a Source #
HDuofunctor h => HFunctor (SFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> SFree h t a -> SFree h t' a Source #
Functor f => HFunctor (Compose f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Compose f t a -> Compose f t' a Source #
HFunctor h => HFunctor (Scope g h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Scope g h t a -> Scope g h t' a Source #
HFunctor h => HFunctor (Scoped h f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> Scoped h f t a -> Scoped h f t' a Source #
HFunctor (GeneralOp op :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.GeneralOp Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> GeneralOp op t a -> GeneralOp op t' a Source #
HFunctor SimpleOp Source #
Instance details Defined in Language.Expression.Example Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> SimpleOp t a -> SimpleOp t' a Source #
HFunctor LogicOp Source #
Instance details Defined in Language.Expression.Prop Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> LogicOp t a -> LogicOp t' a Source #
HFunctor (ExceptT e :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> ExceptT e t a -> ExceptT e t' a Source #
HFunctor (ReaderT r :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> ReaderT r t a -> ReaderT r t' a Source #
HFunctor (StateT s :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> StateT s t a -> StateT s t' a Source #
HFunctor (StateT s :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> StateT s t a -> StateT s t' a Source #
HFunctor (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> WriterT w t a -> WriterT w t' a Source #
HFunctor (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> WriterT w t a -> WriterT w t' a Source #
(HFunctor op, HFunctor (OpChoice ops)) => HFunctor (OpChoice (op ': ops) :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> OpChoice (op ': ops) t a -> OpChoice (op ': ops) t' a Source #
HFunctor (OpChoice ('[] :: [(Type -> Type) -> Type -> Type])) Source #
Instance details Defined in Language.Expression.Choice Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> OpChoice '[] t a -> OpChoice '[] t' a Source #
HFunctor (OpChoice ops) => HFunctor (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods hmap :: forall t t' (a :: u). (forall (b :: u). t b -> t' b) -> HFree' ops t a -> HFree' ops t' a Source #

class HPointed h where Source #

Half of the higher-ranked analogue of Monad.

Methods

hpure :: t a -> h t a Source #

Higher-ranked analogue of pure or return.

Instances

Instances details

HPointed (Reverse :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k0). t a -> Reverse t a Source #
HPointed (Sum f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k0). t a -> Sum f t a Source #
HPointed (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k0). t a -> HFree h t a Source #
HPointed (BV g :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hpure :: forall t (a :: k0). t a -> BV g t a Source #
HPointed (SFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hpure :: forall t (a :: k0). t a -> SFree h t a Source #
Applicative f => HPointed (Compose f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k0). t a -> Compose f t a Source #
HPointed h => HPointed (Scope g h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hpure :: forall t (a :: k0). t a -> Scope g h t a Source #
HPointed (ReaderT r :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k). t a -> ReaderT r t a Source #
HPointed (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods hpure :: forall t (a :: k). t a -> HFree' ops t a Source #

class HBind h where Source #

Half of the higher-ranked analogue of Monad.

Methods

(^>>=) :: h t a -> (forall b. t b -> h t' b) -> h t' a infixr 1 Source #

Higher-ranked analogue of >>=.

Instances

Instances details

HBind (Reverse :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). Reverse t a -> (forall (b :: k0). t b -> Reverse t' b) -> Reverse t' a Source #
HBind (Sum f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). Sum f t a -> (forall (b :: k0). t b -> Sum f t' b) -> Sum f t' a Source #
HFunctor h => HBind (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). HFree h t a -> (forall (b :: k0). t b -> HFree h t' b) -> HFree h t' a Source #
HBind (BV g :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). BV g t a -> (forall (b :: k0). t b -> BV g t' b) -> BV g t' a Source #
HDuofunctor h => HBind (SFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). SFree h t a -> (forall (b :: k0). t b -> SFree h t' b) -> SFree h t' a Source #
Monad f => HBind (Compose f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). Compose f t a -> (forall (b :: k0). t b -> Compose f t' b) -> Compose f t' a Source #
HBind (ReaderT r :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k) (t' :: k -> Type). ReaderT r t a -> (forall (b :: k). t b -> ReaderT r t' b) -> ReaderT r t' a Source #
HFunctor (OpChoice ops) => HBind (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods (^>>=) :: forall t (a :: k) (t' :: k -> Type). HFree' ops t a -> (forall (b :: k). t b -> HFree' ops t' b) -> HFree' ops t' a Source #

class (HFunctor h, HPointed h, HBind h) => HMonad h Source #

Higher-ranked analogue of Monad.

NB there's no such thing as HApplicative for a reason. Consider f :: h t a -> h t' a -> h (Product t t') a, i.e. the higher-ranked analogue of liftA2 (,) :: f a -> f b -> f (a, b). Unfortunately f can't exist, because Product pairs up values of the same type, and in our constructions, h potentially contains values of many types; a just happens to be the one at the top level. There's no guarantee that the two structures will have the same types inside to pair together.

Instances

Instances details

HMonad (Reverse :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression
HMonad (Sum f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression
HFunctor h => HMonad (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression
HMonad (BV g :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope
HDuofunctor h => HMonad (SFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope
HMonad (ReaderT r :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression
HFunctor (OpChoice ops) => HMonad (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice

hliftM :: (HPointed h, HBind h) => (forall b. t b -> t' b) -> h t a -> h t' a Source #

Implements hmap from just an HPointed and HBind instance. Can be used to implement HFunctor for your HMonads that aren't HTraversable.

hjoin :: HBind h => h (h t) a -> h t a Source #

Higher-ranked analogue of join.

class HFunctor h => HTraversable h where Source #

Higher-ranked analogue of Traversable.

Minimal complete definition

htraverse | hsequence

Methods

htraverse :: Applicative f => (forall b. t b -> f (t' b)) -> h t a -> f (h t' a) Source #

Higher-ranked analogue of traverse.

hsequence :: Applicative f => h (Compose f t) a -> f (h t a) Source #

Higher-ranked analogue of sequenceA.

Instances

Instances details

HTraversable (Reverse :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> Reverse t a -> f (Reverse t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => Reverse (Compose f t) a -> f (Reverse t a) Source #
HTraversable (Sum f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f0 t t' (a :: u0). Applicative f0 => (forall (b :: u0). t b -> f0 (t' b)) -> Sum f t a -> f0 (Sum f t' a) Source # hsequence :: forall f0 (t :: u0 -> Type) (a :: u0). Applicative f0 => Sum f (Compose f0 t) a -> f0 (Sum f t a) Source #
HTraversable (Product f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f0 t t' (a :: u0). Applicative f0 => (forall (b :: u0). t b -> f0 (t' b)) -> Product f t a -> f0 (Product f t' a) Source # hsequence :: forall f0 (t :: u0 -> Type) (a :: u0). Applicative f0 => Product f (Compose f0 t) a -> f0 (Product f t a) Source #
HTraversable h => HTraversable (HFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> HFree h t a -> f (HFree h t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => HFree h (Compose f t) a -> f (HFree h t a) Source #
HTraversable (BV g :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> BV g t a -> f (BV g t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => BV g (Compose f t) a -> f (BV g t a) Source #
HDuotraversable h => HTraversable (SFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> SFree h t a -> f (SFree h t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => SFree h (Compose f t) a -> f (SFree h t a) Source #
Traversable f => HTraversable (Compose f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f0 t t' (a :: u0). Applicative f0 => (forall (b :: u0). t b -> f0 (t' b)) -> Compose f t a -> f0 (Compose f t' a) Source # hsequence :: forall f0 (t :: u0 -> Type) (a :: u0). Applicative f0 => Compose f (Compose f0 t) a -> f0 (Compose f t a) Source #
HTraversable h => HTraversable (Scope g h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> Scope g h t a -> f (Scope g h t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => Scope g h (Compose f t) a -> f (Scope g h t a) Source #
HTraversable h => HTraversable (Scoped h f :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods htraverse :: forall f0 t t' (a :: u0). Applicative f0 => (forall (b :: u0). t b -> f0 (t' b)) -> Scoped h f t a -> f0 (Scoped h f t' a) Source # hsequence :: forall f0 (t :: u0 -> Type) (a :: u0). Applicative f0 => Scoped h f (Compose f0 t) a -> f0 (Scoped h f t a) Source #
HTraversable (GeneralOp op :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.GeneralOp Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> GeneralOp op t a -> f (GeneralOp op t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => GeneralOp op (Compose f t) a -> f (GeneralOp op t a) Source #
HTraversable SimpleOp Source #
Instance details Defined in Language.Expression.Example Methods htraverse :: forall f t t' (a :: u). Applicative f => (forall (b :: u). t b -> f (t' b)) -> SimpleOp t a -> f (SimpleOp t' a) Source # hsequence :: forall f (t :: u -> Type) (a :: u). Applicative f => SimpleOp (Compose f t) a -> f (SimpleOp t a) Source #
HTraversable LogicOp Source #
Instance details Defined in Language.Expression.Prop Methods htraverse :: forall f t t' (a :: u). Applicative f => (forall (b :: u). t b -> f (t' b)) -> LogicOp t a -> f (LogicOp t' a) Source # hsequence :: forall f (t :: u -> Type) (a :: u). Applicative f => LogicOp (Compose f t) a -> f (LogicOp t a) Source #
(HTraversable op, HTraversable (OpChoice ops)) => HTraversable (OpChoice (op ': ops) :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods htraverse :: forall f t t' (a :: u). Applicative f => (forall (b :: u). t b -> f (t' b)) -> OpChoice (op ': ops) t a -> f (OpChoice (op ': ops) t' a) Source # hsequence :: forall f (t :: u -> Type) (a :: u). Applicative f => OpChoice (op ': ops) (Compose f t) a -> f (OpChoice (op ': ops) t a) Source #
HTraversable (OpChoice ('[] :: [(Type -> Type) -> Type -> Type])) Source #
Instance details Defined in Language.Expression.Choice Methods htraverse :: forall f t t' (a :: u). Applicative f => (forall (b :: u). t b -> f (t' b)) -> OpChoice '[] t a -> f (OpChoice '[] t' a) Source # hsequence :: forall f (t :: u -> Type) (a :: u). Applicative f => OpChoice '[] (Compose f t) a -> f (OpChoice '[] t a) Source #
HTraversable (OpChoice ops) => HTraversable (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods htraverse :: forall f t t' (a :: u). Applicative f => (forall (b :: u). t b -> f (t' b)) -> HFree' ops t a -> f (HFree' ops t' a) Source # hsequence :: forall f (t :: u -> Type) (a :: u). Applicative f => HFree' ops (Compose f t) a -> f (HFree' ops t a) Source #

hfoldMapMonoid :: (HTraversable h, Monoid m) => (forall b. t b -> m) -> h t a -> m Source #

An HTraversable instance lets you do something similar to foldMap. For a more flexible operation, see hfoldMap.

hbindTraverse :: (HTraversable h, HMonad h, Applicative f) => (forall b. t b -> f (h t' b)) -> h t a -> f (h t' a) Source #

class HBifunctor (h :: (k -> *) -> (k -> *) -> k -> *) where Source #

Higher-ranked analogue of Bifunctor.

Minimal complete definition

Nothing

Methods

hbimap :: (forall b. s b -> s' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a Source #

Higher-ranked analogue of bimap.

default hbimap :: HBitraversable h => (forall b. s b -> s' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a Source #

hfirst :: (forall b. s b -> s' b) -> h s t a -> h s' t a Source #

hsecond :: (forall b. t b -> t' b) -> h s t a -> h s t' a Source #

Instances

Instances details

HBifunctor (Sum :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hbimap :: forall s s' t t' (a :: k0). (forall (b :: k0). s b -> s' b) -> (forall (b :: k0). t b -> t' b) -> Sum s t a -> Sum s' t' a Source # hfirst :: forall s s' (t :: k0 -> Type) (a :: k0). (forall (b :: k0). s b -> s' b) -> Sum s t a -> Sum s' t a Source # hsecond :: forall t t' (s :: k0 -> Type) (a :: k0). (forall (b :: k0). t b -> t' b) -> Sum s t a -> Sum s t' a Source #
HBifunctor (Product :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hbimap :: forall s s' t t' (a :: k0). (forall (b :: k0). s b -> s' b) -> (forall (b :: k0). t b -> t' b) -> Product s t a -> Product s' t' a Source # hfirst :: forall s s' (t :: k0 -> Type) (a :: k0). (forall (b :: k0). s b -> s' b) -> Product s t a -> Product s' t a Source # hsecond :: forall t t' (s :: k0 -> Type) (a :: k0). (forall (b :: k0). t b -> t' b) -> Product s t a -> Product s t' a Source #
HBifunctor (BV :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbimap :: forall s s' t t' (a :: k0). (forall (b :: k0). s b -> s' b) -> (forall (b :: k0). t b -> t' b) -> BV s t a -> BV s' t' a Source # hfirst :: forall s s' (t :: k0 -> Type) (a :: k0). (forall (b :: k0). s b -> s' b) -> BV s t a -> BV s' t a Source # hsecond :: forall t t' (s :: k0 -> Type) (a :: k0). (forall (b :: k0). t b -> t' b) -> BV s t a -> BV s t' a Source #
HFunctor h => HBifunctor (Scoped h :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbimap :: forall s s' t t' (a :: k0). (forall (b :: k0). s b -> s' b) -> (forall (b :: k0). t b -> t' b) -> Scoped h s t a -> Scoped h s' t' a Source # hfirst :: forall s s' (t :: k0 -> Type) (a :: k0). (forall (b :: k0). s b -> s' b) -> Scoped h s t a -> Scoped h s' t a Source # hsecond :: forall t t' (s :: k0 -> Type) (a :: k0). (forall (b :: k0). t b -> t' b) -> Scoped h s t a -> Scoped h s t' a Source #

class HBifunctor h => HBitraversable h where Source #

Methods

hbitraverse :: Applicative f => (forall b. s b -> f (s' b)) -> (forall b. t b -> f (t' b)) -> h s t a -> f (h s' t' a) Source #

Instances

Instances details

HBitraversable (Sum :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hbitraverse :: forall f s s' t t' (a :: k0). Applicative f => (forall (b :: k0). s b -> f (s' b)) -> (forall (b :: k0). t b -> f (t' b)) -> Sum s t a -> f (Sum s' t' a) Source #
HBitraversable (Product :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hbitraverse :: forall f s s' t t' (a :: k0). Applicative f => (forall (b :: k0). s b -> f (s' b)) -> (forall (b :: k0). t b -> f (t' b)) -> Product s t a -> f (Product s' t' a) Source #
HBitraversable (BV :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbitraverse :: forall f s s' t t' (a :: k0). Applicative f => (forall (b :: k0). s b -> f (s' b)) -> (forall (b :: k0). t b -> f (t' b)) -> BV s t a -> f (BV s' t' a) Source #
HTraversable h => HBitraversable (Scoped h :: (k -> Type) -> (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbitraverse :: forall f s s' t t' (a :: k0). Applicative f => (forall (b :: k0). s b -> f (s' b)) -> (forall (b :: k0). t b -> f (t' b)) -> Scoped h s t a -> f (Scoped h s' t' a) Source #

hbifoldMapMonoid :: (Monoid m, HBitraversable h) => (forall b. s b -> m) -> (forall b. t b -> m) -> h s t a -> m Source #

class HDuofunctor (h :: ((u -> *) -> u -> *) -> (u -> *) -> u -> *) where Source #

Minimal complete definition

Nothing

Methods

hduomap :: (forall g g' b. (forall c. g c -> g' c) -> s g b -> s' g' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a Source #

default hduomap :: HDuotraversable h => (forall g g' b. (forall c. g c -> g' c) -> s g b -> s' g' b) -> (forall b. t b -> t' b) -> h s t a -> h s' t' a Source #

Instances

Instances details

HDuofunctor (HFree :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hduomap :: forall s s' t t' (a :: u0). (forall (g :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g c -> g' c) -> s g b -> s' g' b) -> (forall (b :: u0). t b -> t' b) -> HFree s t a -> HFree s' t' a Source #
HDuofunctor (Scope g :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hduomap :: forall s s' t t' (a :: u0). (forall (g0 :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g0 c -> g' c) -> s g0 b -> s' g' b) -> (forall (b :: u0). t b -> t' b) -> Scope g s t a -> Scope g s' t' a Source #

hduomapFirst :: HDuofunctor h => (forall g g' b. (forall c. g c -> g' c) -> s g b -> s' g' b) -> h s t a -> h s' t a Source #

hduomapFirst' :: (HDuofunctor h, HFunctor s) => (forall g b. s g b -> s' g b) -> h s t a -> h s' t a Source #

hduomapSecond :: (HDuofunctor h, HFunctor s) => (forall b. t b -> t' b) -> h s t a -> h s t' a Source #

class HDuofunctor h => HDuotraversable h where Source #

Methods

hduotraverse :: Applicative f => (forall g g' b. (forall c. g c -> f (g' c)) -> s g b -> f (s' g' b)) -> (forall b. t b -> f (t' b)) -> h s t a -> f (h s' t' a) Source #

Instances

Instances details

HDuotraversable (HFree :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hduotraverse :: forall f s s' t t' (a :: u0). Applicative f => (forall (g :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g c -> f (g' c)) -> s g b -> f (s' g' b)) -> (forall (b :: u0). t b -> f (t' b)) -> HFree s t a -> f (HFree s' t' a) Source #
HDuotraversable (Scope g :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hduotraverse :: forall f s s' t t' (a :: u0). Applicative f => (forall (g0 :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g0 c -> f (g' c)) -> s g0 b -> f (s' g' b)) -> (forall (b :: u0). t b -> f (t' b)) -> Scope g s t a -> f (Scope g s' t' a) Source #

hduotraverseFirst :: (HDuotraversable h, Applicative f) => (forall g g' b. (forall c. g c -> f (g' c)) -> s g b -> f (s' g' b)) -> h s t a -> f (h s' t a) Source #

hduotraverseFirst' :: (HDuotraversable h, HTraversable s, Monad f) => (forall g b. s g b -> f (s' g b)) -> h s t a -> f (h s' t a) Source #

hduotraverseSecond :: (HDuotraversable h, HTraversable s, Applicative f) => (forall b. t b -> f (t' b)) -> h s t a -> f (h s t' a) Source #

class HFoldableAt k h where Source #

This is a more flexible, higher-ranked version of Foldable. While Foldable only allows you to fold into a Monoid, HFoldable allows you to fold into some arbitrary type constructor k. This means that the instance can take advantage of additional structure inside k and h, to combine internal results in different ways, rather than just the mappend available to foldMap.

Notice that if you have

instance (Monoid m) => HFoldableAt (Const m) h

then hfoldMap behaves very much like regular foldMap.

Methods

hfoldMap :: (forall b. t b -> k b) -> h t a -> k a Source #

Instances

Instances details

HFoldableAt (k2 :: k1 -> Type) (Reverse :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> Reverse t a -> k2 a Source #
HFoldableAt (k2 :: k1 -> Type) (Sum k2 :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> Sum k2 t a -> k2 a Source #
HFoldableAt k2 h => HFoldableAt (k2 :: k1 -> Type) (HFree h :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> HFree h t a -> k2 a Source #
(HDuotraversable h, HDuofoldableAt k2 h) => HFoldableAt (k2 :: k1 -> Type) (SFree h :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> SFree h t a -> k2 a Source #
EvalOpAt k2 op => HFoldableAt (k2 :: k1 -> Type) (GeneralOp op :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression.GeneralOp Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> GeneralOp op t a -> k2 a Source #
HFoldableAt Identity SimpleOp Source #
Instance details Defined in Language.Expression.Example Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> Identity b) -> SimpleOp t a -> Identity a Source #
HFoldableAt Identity LogicOp Source #
Instance details Defined in Language.Expression.Prop Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> Identity b) -> LogicOp t a -> Identity a Source #
HFoldableAt SBV SimpleOp Source #
Instance details Defined in Language.Expression.Example Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> SBV b) -> SimpleOp t a -> SBV a Source #
HFoldableAt SBV LogicOp Source #
Instance details Defined in Language.Expression.Prop Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> SBV b) -> LogicOp t a -> SBV a Source #
(HFoldableAt k op, HFoldableAt k (OpChoice ops)) => HFoldableAt (k :: Type -> Type) (OpChoice (op ': ops) :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods hfoldMap :: forall t (a :: k0). (forall (b :: k0). t b -> k b) -> OpChoice (op ': ops) t a -> k a Source #
HFoldableAt (k :: Type -> Type) (OpChoice ('[] :: [(Type -> Type) -> Type -> Type])) Source #
Instance details Defined in Language.Expression.Choice Methods hfoldMap :: forall t (a :: k0). (forall (b :: k0). t b -> k b) -> OpChoice '[] t a -> k a Source #
(HFoldableAt k (OpChoice ops), HFunctor (OpChoice ops)) => HFoldableAt (k :: Type -> Type) (HFree' ops :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression.Choice Methods hfoldMap :: forall t (a :: k0). (forall (b :: k0). t b -> k b) -> HFree' ops t a -> k a Source #
Alternative k => HFoldableAt (k :: Type -> Type) (Product k :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k0). (forall (b :: k0). t b -> k b) -> Product k t a -> k a Source #
(Alternative g, Foldable f) => HFoldableAt (g :: Type -> Type) (Compose f :: (Type -> Type) -> Type -> Type) Source #	e.g. `(Monoid m, Foldable f) => HFoldableAt (Const m) (Compose f)`
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> g b) -> Compose f t a -> g a Source #

implHfoldMap :: HFunctor h => (h k a -> k a) -> (forall b. t b -> k b) -> h t a -> k a Source #

For HFunctors, provides an implementation of hfoldMap in terms of a simple hfold-like function.

implHfoldMapCompose :: (HTraversable h, Monad m) => (h k a -> m (k a)) -> (forall b. t b -> Compose m k b) -> h t a -> Compose m k a Source #

A helper function for implementing instances with the general form Monad m => HFoldableAt (Compose m t) h. I.e. folding that requires a monadic context of some kind.

hfold :: HFoldableAt t h => h t a -> t a Source #

Higher-ranked equivalent of fold.

hfoldA :: (HFoldableAt (Compose f t) h, Applicative f) => h t a -> f (t a) Source #

Fold in an applicative context.

hfoldMapA :: (HFoldableAt (Compose f k) h, Applicative f) => (forall b. t b -> f (k b)) -> h t a -> f (k a) Source #

Fold in an applicative context.

hfoldTraverse :: (HFoldableAt k h, HTraversable h, Applicative f) => (forall b. t b -> f (k b)) -> h t a -> f (k a) Source #

hfoldTraverse is to hfoldMap as htraverse is to hmap.

class HBifoldableAt k h where Source #

Methods

hbifoldMap :: (forall b. f b -> k b) -> (forall b. g b -> k b) -> h f g a -> k a Source #

Instances

Instances details

HBifoldableAt (k2 :: k1 -> Type) (Sum :: (k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hbifoldMap :: forall f g (a :: k). (forall (b :: k). f b -> k2 b) -> (forall (b :: k). g b -> k2 b) -> Sum f g a -> k2 a Source #
HBifoldableAt (k2 :: k1 -> Type) (BV :: (k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbifoldMap :: forall f g (a :: k). (forall (b :: k). f b -> k2 b) -> (forall (b :: k). g b -> k2 b) -> BV f g a -> k2 a Source #
(HFunctor h, HFoldableAt k2 h) => HBifoldableAt (k2 :: k1 -> Type) (Scoped h :: (k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hbifoldMap :: forall f g (a :: k). (forall (b :: k). f b -> k2 b) -> (forall (b :: k). g b -> k2 b) -> Scoped h f g a -> k2 a Source #
Alternative k => HBifoldableAt (k :: Type -> Type) (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Language.Expression Methods hbifoldMap :: forall f g (a :: k0). (forall (b :: k0). f b -> k b) -> (forall (b :: k0). g b -> k b) -> Product f g a -> k a Source #

hbifold :: HBifoldableAt k h => h k k a -> k a Source #

class HDuofoldableAt k h where Source #

Methods

hduofoldMap :: HTraversable s => (forall g b. (forall c. g c -> k c) -> s g b -> k b) -> (forall b. t b -> k b) -> h s t a -> k a Source #

Instances

Instances details

HDuofoldableAt (k2 :: k1 -> Type) (HFree :: ((k1 -> Type) -> k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hduofoldMap :: forall s t (a :: k). HTraversable s => (forall (g :: k -> Type) (b :: k). (forall (c :: k). g c -> k2 c) -> s g b -> k2 b) -> (forall (b :: k). t b -> k2 b) -> HFree s t a -> k2 a Source #
HDuofoldableAt (k2 :: k1 -> Type) (Scope k2 :: ((k1 -> Type) -> k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression.Scope Methods hduofoldMap :: forall s t (a :: k). HTraversable s => (forall (g :: k -> Type) (b :: k). (forall (c :: k). g c -> k2 c) -> s g b -> k2 b) -> (forall (b :: k). t b -> k2 b) -> Scope k2 s t a -> k2 a Source #

implHduofoldMap :: (HDuofunctor h, HFunctor s) => ((forall g b. (forall c. g c -> k c) -> s g b -> k b) -> h s k a -> k a) -> (forall g b. (forall c. g c -> k c) -> s g b -> k b) -> (forall b. t b -> k b) -> h s t a -> k a Source #

implHduofoldMapCompose :: (HDuotraversable h, HTraversable s, Monad m) => ((forall g b. (forall c. g c -> m (k c)) -> s g b -> m (k b)) -> h s k a -> m (k a)) -> (forall g b. (forall c. g c -> Compose m k c) -> s g b -> Compose m k b) -> (forall b. t b -> Compose m k b) -> h s t a -> Compose m k a Source #

data HFree h t a Source #

HFree h is a higher-ranked free monad over the higher-ranked functor h. That means that given HFunctor h, we get HMonad (HFree h) for free.

Constructors

HPure (t a)
HWrap (h (HFree h t) a)

Instances

Instances details

HDuofoldableAt (k2 :: k1 -> Type) (HFree :: ((k1 -> Type) -> k1 -> Type) -> (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hduofoldMap :: forall s t (a :: k). HTraversable s => (forall (g :: k -> Type) (b :: k). (forall (c :: k). g c -> k2 c) -> s g b -> k2 b) -> (forall (b :: k). t b -> k2 b) -> HFree s t a -> k2 a Source #
HFoldableAt k2 h => HFoldableAt (k2 :: k1 -> Type) (HFree h :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Language.Expression Methods hfoldMap :: forall t (a :: k). (forall (b :: k). t b -> k2 b) -> HFree h t a -> k2 a Source #
Pretty2 op => Pretty2 (HFree op :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression.Pretty Methods pretty2 :: forall (t :: k0 -> Type) (a :: k1). Pretty1 t => HFree op t a -> String Source # prettys2Prec :: forall (t :: k0 -> Type) (a :: k1). Pretty1 t => Int -> HFree op t a -> ShowS Source #
HDuotraversable (HFree :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hduotraverse :: forall f s s' t t' (a :: u0). Applicative f => (forall (g :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g c -> f (g' c)) -> s g b -> f (s' g' b)) -> (forall (b :: u0). t b -> f (t' b)) -> HFree s t a -> f (HFree s' t' a) Source #
HDuofunctor (HFree :: ((u -> Type) -> u -> Type) -> (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hduomap :: forall s s' t t' (a :: u0). (forall (g :: u0 -> Type) (g' :: u0 -> Type) (b :: u0). (forall (c :: u0). g c -> g' c) -> s g b -> s' g' b) -> (forall (b :: u0). t b -> t' b) -> HFree s t a -> HFree s' t' a Source #
HTraversable h => HTraversable (HFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods htraverse :: forall f t t' (a :: u0). Applicative f => (forall (b :: u0). t b -> f (t' b)) -> HFree h t a -> f (HFree h t' a) Source # hsequence :: forall f (t :: u0 -> Type) (a :: u0). Applicative f => HFree h (Compose f t) a -> f (HFree h t a) Source #
HFunctor h => HMonad (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression
HFunctor h => HBind (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods (^>>=) :: forall t (a :: k0) (t' :: k0 -> Type). HFree h t a -> (forall (b :: k0). t b -> HFree h t' b) -> HFree h t' a Source #
HPointed (HFree h :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Language.Expression Methods hpure :: forall t (a :: k0). t a -> HFree h t a Source #
HFunctor h => HFunctor (HFree h :: (u -> Type) -> u -> Type) Source #
Instance details Defined in Language.Expression Methods hmap :: forall t t' (a :: u0). (forall (b :: u0). t b -> t' b) -> HFree h t a -> HFree h t' a Source #
Num (WhileExpr l AlgReal) Source #
Instance details Defined in Language.While.Syntax Methods (+) :: WhileExpr l AlgReal -> WhileExpr l AlgReal -> WhileExpr l AlgReal # (-) :: WhileExpr l AlgReal -> WhileExpr l AlgReal -> WhileExpr l AlgReal # (*) :: WhileExpr l AlgReal -> WhileExpr l AlgReal -> WhileExpr l AlgReal # negate :: WhileExpr l AlgReal -> WhileExpr l AlgReal # abs :: WhileExpr l AlgReal -> WhileExpr l AlgReal # signum :: WhileExpr l AlgReal -> WhileExpr l AlgReal # fromInteger :: Integer -> WhileExpr l AlgReal #
IsString s => IsString (WhileExpr s AlgReal) Source #
Instance details Defined in Language.While.Syntax Methods fromString :: String -> WhileExpr s AlgReal #