Safe Haskell	None
Language	GHC2021

Control.Monad.Indexed

Contents

Indexed monad hierarchy
- Deriving-via combinators
Index monad combinators
- Product of indexed gadgets
- Lift non-indexed gadgets to indexed
Additional technical definitions

Description

This module defines the main indexed monad hierarchy and some standard indexed monad combinators. This is meant to look familiar to Haskell programmers. Notice how there is no indexed functor class as, thanks to quantified constraints, this role is played by the Prelude's Functor class. Notice also how some traditional classes like MonadPlus and Alternative are synonyms thanks to the Additive type class.

Synopsis

class (forall (i :: k) (j :: k). Functor (f i j), forall (i :: k). Applicative (f i i)) => Applicative (f :: k -> k -> Type -> Type) where
- pure :: forall a (i :: k). a -> f i i a
- (<*>) :: forall (i :: k) (j :: k) a b (k1 :: k). f i j (a -> b) -> f j k1 a -> f i k1 b
- liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> f i j a -> f j k1 b -> f i k1 c
- (*>) :: forall (i :: k) (j :: k) a (k1 :: k) b. f i j a -> f j k1 b -> f i k1 b
- (<*) :: forall (i :: k) (j :: k) a (k1 :: k) b. f i j a -> f j k1 b -> f i k1 a
class (Applicative m, forall (i :: k). Monad (m i i)) => Monad (m :: k -> k -> Type -> Type) where
- (>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. m i j a -> (a -> m j k1 b) -> m i k1 b
type Alternative (m :: k -> k -> Type -> Type) = (Applicative m, forall (r :: k) (r' :: k) a. Additive (m r r' a))
type MonadPlus (m :: k -> k -> Type -> Type) = (Monad m, forall (r :: k) (r' :: k) a. Additive (m r r' a))
guard :: forall {k} m (i :: k). Alternative m => Bool -> m i i ()
class Fail (m :: k -> k1 -> k2 -> Type) where
- fail :: forall (i :: k) (j :: k1) (a :: k2). String -> m i j a
type MonadFail (m :: k -> k -> Type -> Type) = (Monad m, Fail m)
guardF :: forall {k} m (i :: k). (Applicative m, Fail m) => Bool -> String -> m i i ()
newtype FromIndexed (m :: k -> k1 -> k2 -> Type) (i :: k) (j :: k1) (a :: k2) = FromIndexed (m i j a)
data ((f :: k -> k1 -> k2 -> Type) :*: (g :: k -> k1 -> k2 -> Type)) (i :: k) (j :: k1) (a :: k2) = (:*:) (f i j a) (g i j a)
fst_star :: forall {k1} {k2} {k3} f (g :: k1 -> k2 -> k3 -> Type) (i :: k1) (j :: k2) (a :: k3). (f :*: g) i j a -> f i j a
snd_star :: forall {k1} {k2} {k3} (f :: k1 -> k2 -> k3 -> Type) g (i :: k1) (j :: k2) (a :: k3). (f :*: g) i j a -> g i j a
newtype IgnoreIndices (m :: k -> Type) (i :: k1) (j :: k2) (a :: k) = IgnoreIndices {
- unIgnoreIndices :: m a
}
(>>) :: forall {k1} m (i :: k1) (j :: k1) (k2 :: k1) a. Applicative m => m i j () -> m j k2 a -> m i k2 a

Indexed monad hierarchy

class (forall (i :: k) (j :: k). Functor (f i j), forall (i :: k). Applicative (f i i)) => Applicative (f :: k -> k -> Type -> Type) where Source #

Minimal complete definition

pure

Methods

pure :: forall a (i :: k). a -> f i i a Source #

(<*>) :: forall (i :: k) (j :: k) a b (k1 :: k). f i j (a -> b) -> f j k1 a -> f i k1 b infixl 4 Source #

default (<*>) :: forall (i :: k) (j :: k) a b (k1 :: k). Monad f => f i j (a -> b) -> f j k1 a -> f i k1 b Source #

liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> f i j a -> f j k1 b -> f i k1 c Source #

(*>) :: forall (i :: k) (j :: k) a (k1 :: k) b. f i j a -> f j k1 b -> f i k1 b infixl 4 Source #

(<*) :: forall (i :: k) (j :: k) a (k1 :: k) b. f i j a -> f j k1 b -> f i k1 a infixl 4 Source #

Instances

Instances details

Comonad w => Applicative (ContW w :: Type -> Type -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed.Cont Methods pure :: a -> ContW w i i a Source # (<>) :: ContW w i j (a -> b) -> ContW w j k1 a -> ContW w i k1 b Source # liftA2 :: (a -> b -> c) -> ContW w i j a -> ContW w j k1 b -> ContW w i k1 c Source # (>) :: ContW w i j a -> ContW w j k1 b -> ContW w i k1 b Source # (<*) :: ContW w i j a -> ContW w j k1 b -> ContW w i k1 a Source #
Comonad w => Applicative (Cont2W w :: Type -> Type -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed.Cont2 Methods pure :: a -> Cont2W w i i a Source # (<>) :: Cont2W w i j (a -> b) -> Cont2W w j k1 a -> Cont2W w i k1 b Source # liftA2 :: (a -> b -> c) -> Cont2W w i j a -> Cont2W w j k1 b -> Cont2W w i k1 c Source # (>) :: Cont2W w i j a -> Cont2W w j k1 b -> Cont2W w i k1 b Source # (<*) :: Cont2W w i j a -> Cont2W w j k1 b -> Cont2W w i k1 a Source #
Applicative f => Applicative (IgnoreIndices f :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: forall a (i :: k). a -> IgnoreIndices f i i a Source # (<>) :: forall (i :: k) (j :: k) a b (k1 :: k). IgnoreIndices f i j (a -> b) -> IgnoreIndices f j k1 a -> IgnoreIndices f i k1 b Source # liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 c Source # (>) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 b Source # (<*) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 a Source #
(Applicative f, Applicative g) => Applicative (f :*: g :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: forall a (i :: k). a -> (f :: g) i i a Source # (<>) :: forall (i :: k) (j :: k) a b (k1 :: k). (f :: g) i j (a -> b) -> (f :: g) j k1 a -> (f :: g) i k1 b Source # liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 c Source # (>) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 b Source # (<) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 a Source #

class (Applicative m, forall (i :: k). Monad (m i i)) => Monad (m :: k -> k -> Type -> Type) where Source #

Methods

(>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. m i j a -> (a -> m j k1 b) -> m i k1 b Source #

Instances

Instances details

Comonad w => Monad (ContW w :: Type -> Type -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed.Cont Methods (>>=) :: ContW w i j a -> (a -> ContW w j k1 b) -> ContW w i k1 b Source #
Comonad w => Monad (Cont2W w :: Type -> Type -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed.Cont2 Methods (>>=) :: Cont2W w i j a -> (a -> Cont2W w j k1 b) -> Cont2W w i k1 b Source #
Monad m => Monad (IgnoreIndices m :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices m i j a -> (a -> IgnoreIndices m j k1 b) -> IgnoreIndices m i k1 b Source #
(Monad f, Monad g) => Monad (f :*: g :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (a -> (f :: g) j k1 b) -> (f :*: g) i k1 b Source #

type Alternative (m :: k -> k -> Type -> Type) = (Applicative m, forall (r :: k) (r' :: k) a. Additive (m r r' a)) Source #

type MonadPlus (m :: k -> k -> Type -> Type) = (Monad m, forall (r :: k) (r' :: k) a. Additive (m r r' a)) Source #

guard :: forall {k} m (i :: k). Alternative m => Bool -> m i i () Source #

class Fail (m :: k -> k1 -> k2 -> Type) where Source #

This class is mainly used for the qualified `do`-notation, as described in the documentation for MonadFail. Occasionally used to fail with an error message in monads which support it, see for instance guardF below.

Methods

fail :: forall (i :: k) (j :: k1) (a :: k2). String -> m i j a Source #

Instances

Instances details

MonadFail m => Fail (IgnoreIndices m :: k1 -> k2 -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods fail :: forall (i :: k1) (j :: k2) a. String -> IgnoreIndices m i j a Source #
(Fail f, Fail g) => Fail (f :*: g :: k1 -> k2 -> k3 -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods fail :: forall (i :: k1) (j :: k2) (a :: k3). String -> (f :*: g) i j a Source #

type MonadFail (m :: k -> k -> Type -> Type) = (Monad m, Fail m) Source #

guardF :: forall {k} m (i :: k). (Applicative m, Fail m) => Bool -> String -> m i i () Source #

Deriving-via combinators

newtype FromIndexed (m :: k -> k1 -> k2 -> Type) (i :: k) (j :: k1) (a :: k2) Source #

A deriving via combinator

Constructors

FromIndexed (m i j a)

Instances

Instances details

(Alternative m, i ~ j) => Alternative (FromIndexed m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods empty :: FromIndexed m i j a # (<\|>) :: FromIndexed m i j a -> FromIndexed m i j a -> FromIndexed m i j a # some :: FromIndexed m i j a -> FromIndexed m i j [a] # many :: FromIndexed m i j a -> FromIndexed m i j [a] #
(Applicative m, i ~ j) => Applicative (FromIndexed m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: a -> FromIndexed m i j a # (<>) :: FromIndexed m i j (a -> b) -> FromIndexed m i j a -> FromIndexed m i j b # liftA2 :: (a -> b -> c) -> FromIndexed m i j a -> FromIndexed m i j b -> FromIndexed m i j c # (>) :: FromIndexed m i j a -> FromIndexed m i j b -> FromIndexed m i j b # (<*) :: FromIndexed m i j a -> FromIndexed m i j b -> FromIndexed m i j a #
Functor (m i j) => Functor (FromIndexed m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods fmap :: (a -> b) -> FromIndexed m i j a -> FromIndexed m i j b # (<$) :: a -> FromIndexed m i j b -> FromIndexed m i j a #
(Monad m, i ~ j) => Monad (FromIndexed m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: FromIndexed m i j a -> (a -> FromIndexed m i j b) -> FromIndexed m i j b # (>>) :: FromIndexed m i j a -> FromIndexed m i j b -> FromIndexed m i j b # return :: a -> FromIndexed m i j a #
(MonadPlus m, i ~ j) => MonadPlus (FromIndexed m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods mzero :: FromIndexed m i j a # mplus :: FromIndexed m i j a -> FromIndexed m i j a -> FromIndexed m i j a #

Index monad combinators

Product of indexed gadgets

data ((f :: k -> k1 -> k2 -> Type) :*: (g :: k -> k1 -> k2 -> Type)) (i :: k) (j :: k1) (a :: k2) Source #

Constructors

(:*:) (f i j a) (g i j a)

Instances

Instances details

(Fail f, Fail g) => Fail (f :*: g :: k1 -> k2 -> k3 -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods fail :: forall (i :: k1) (j :: k2) (a :: k3). String -> (f :*: g) i j a Source #
(Applicative f, Applicative g) => Applicative (f :*: g :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: forall a (i :: k). a -> (f :: g) i i a Source # (<>) :: forall (i :: k) (j :: k) a b (k1 :: k). (f :: g) i j (a -> b) -> (f :: g) j k1 a -> (f :: g) i k1 b Source # liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 c Source # (>) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 b Source # (<) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (f :: g) j k1 b -> (f :: g) i k1 a Source #
(Monad f, Monad g) => Monad (f :*: g :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. (f :: g) i j a -> (a -> (f :: g) j k1 b) -> (f :*: g) i k1 b Source #
(Shifty f, Shifty g) => Shifty (f :*: g) Source #
Instance details Defined in Control.Monad.Indexed.Cont2 Methods shift :: ((a -> r' -> r') -> r -> (f :: g) r k k) -> (f :: g) r r' a Source #
(Stacked f, Stacked g) => Stacked (f :*: g) Source #
Instance details Defined in Control.Monad.Indexed.Cont2 Methods shift_ :: ((r' -> r') -> r -> (f :: g) r r'' r'') -> (f :: g) r r' () Source #
(Alternative (f i j), Alternative (g i j)) => Alternative ((f :*: g) i j) Source #
Instance details Defined in Control.Monad.Indexed Methods empty :: (f :: g) i j a # (<\|>) :: (f :: g) i j a -> (f :: g) i j a -> (f :: g) i j a # some :: (f :: g) i j a -> (f :: g) i j [a] # many :: (f :: g) i j a -> (f :: g) i j [a] #
(Applicative (f i j), Applicative (g i j)) => Applicative ((f :*: g) i j) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: a -> (f :: g) i j a # (<>) :: (f :: g) i j (a -> b) -> (f :: g) i j a -> (f :: g) i j b # liftA2 :: (a -> b -> c) -> (f :: g) i j a -> (f :: g) i j b -> (f :: g) i j c # (>) :: (f :: g) i j a -> (f :: g) i j b -> (f :: g) i j b # (<) :: (f :: g) i j a -> (f :: g) i j b -> (f :: g) i j a #
(Functor (f i j), Functor (g i j)) => Functor ((f :*: g) i j) Source #
Instance details Defined in Control.Monad.Indexed Methods fmap :: (a -> b) -> (f :: g) i j a -> (f :: g) i j b # (<$) :: a -> (f :: g) i j b -> (f :: g) i j a #
(Monad (f i j), Monad (g i j)) => Monad ((f :*: g) i j) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: (f :: g) i j a -> (a -> (f :: g) i j b) -> (f :: g) i j b # (>>) :: (f :: g) i j a -> (f :: g) i j b -> (f :: g) i j b # return :: a -> (f :*: g) i j a #
(MonadPlus (f i j), MonadPlus (g i j)) => MonadPlus ((f :*: g) i j) Source #
Instance details Defined in Control.Monad.Indexed Methods mzero :: (f :: g) i j a # mplus :: (f :: g) i j a -> (f :: g) i j a -> (f :: g) i j a #
(Additive (f r r' a), Additive (g r r' a)) => Additive ((f :*: g) r r' a) Source #
Instance details Defined in Control.Monad.Indexed Methods empty :: (f :: g) r r' a Source # (<\|>) :: (f :: g) r r' a -> (f :: g) r r' a -> (f :: g) r r' a Source #

fst_star :: forall {k1} {k2} {k3} f (g :: k1 -> k2 -> k3 -> Type) (i :: k1) (j :: k2) (a :: k3). (f :*: g) i j a -> f i j a Source #

snd_star :: forall {k1} {k2} {k3} (f :: k1 -> k2 -> k3 -> Type) g (i :: k1) (j :: k2) (a :: k3). (f :*: g) i j a -> g i j a Source #

Lift non-indexed gadgets to indexed

newtype IgnoreIndices (m :: k -> Type) (i :: k1) (j :: k2) (a :: k) Source #

Constructors

IgnoreIndices
Fields unIgnoreIndices :: m a

Instances

Instances details

MonadFail m => Fail (IgnoreIndices m :: k1 -> k2 -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods fail :: forall (i :: k1) (j :: k2) a. String -> IgnoreIndices m i j a Source #
Applicative f => Applicative (IgnoreIndices f :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: forall a (i :: k). a -> IgnoreIndices f i i a Source # (<>) :: forall (i :: k) (j :: k) a b (k1 :: k). IgnoreIndices f i j (a -> b) -> IgnoreIndices f j k1 a -> IgnoreIndices f i k1 b Source # liftA2 :: forall a b c (i :: k) (j :: k) (k1 :: k). (a -> b -> c) -> IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 c Source # (>) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 b Source # (<*) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices f i j a -> IgnoreIndices f j k1 b -> IgnoreIndices f i k1 a Source #
Monad m => Monad (IgnoreIndices m :: k -> k -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: forall (i :: k) (j :: k) a (k1 :: k) b. IgnoreIndices m i j a -> (a -> IgnoreIndices m j k1 b) -> IgnoreIndices m i k1 b Source #
Applicative m => Stacked (IgnoreIndices m :: Type -> Type -> Type -> Type) Source #
Instance details Defined in Control.Monad.Indexed.Cont2 Methods shift_ :: ((r' -> r') -> r -> IgnoreIndices m r r'' r'') -> IgnoreIndices m r r' () Source #
Alternative m => Alternative (IgnoreIndices m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods empty :: IgnoreIndices m i j a # (<\|>) :: IgnoreIndices m i j a -> IgnoreIndices m i j a -> IgnoreIndices m i j a # some :: IgnoreIndices m i j a -> IgnoreIndices m i j [a] # many :: IgnoreIndices m i j a -> IgnoreIndices m i j [a] #
Applicative m => Applicative (IgnoreIndices m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods pure :: a -> IgnoreIndices m i j a # (<>) :: IgnoreIndices m i j (a -> b) -> IgnoreIndices m i j a -> IgnoreIndices m i j b # liftA2 :: (a -> b -> c) -> IgnoreIndices m i j a -> IgnoreIndices m i j b -> IgnoreIndices m i j c # (>) :: IgnoreIndices m i j a -> IgnoreIndices m i j b -> IgnoreIndices m i j b # (<*) :: IgnoreIndices m i j a -> IgnoreIndices m i j b -> IgnoreIndices m i j a #
Functor m => Functor (IgnoreIndices m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods fmap :: (a -> b) -> IgnoreIndices m i j a -> IgnoreIndices m i j b # (<$) :: a -> IgnoreIndices m i j b -> IgnoreIndices m i j a #
Monad m => Monad (IgnoreIndices m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods (>>=) :: IgnoreIndices m i j a -> (a -> IgnoreIndices m i j b) -> IgnoreIndices m i j b # (>>) :: IgnoreIndices m i j a -> IgnoreIndices m i j b -> IgnoreIndices m i j b # return :: a -> IgnoreIndices m i j a #
MonadPlus m => MonadPlus (IgnoreIndices m i j) Source #
Instance details Defined in Control.Monad.Indexed Methods mzero :: IgnoreIndices m i j a # mplus :: IgnoreIndices m i j a -> IgnoreIndices m i j a -> IgnoreIndices m i j a #
Alternative m => Additive (IgnoreIndices m r r' a) Source #
Instance details Defined in Control.Monad.Indexed Methods empty :: IgnoreIndices m r r' a Source # (<\|>) :: IgnoreIndices m r r' a -> IgnoreIndices m r r' a -> IgnoreIndices m r r' a Source #

Additional technical definitions

(>>) :: forall {k1} m (i :: k1) (j :: k1) (k2 :: k1) a. Applicative m => m i j () -> m j k2 a -> m i k2 a Source #

Synonym of *> used for QualifiedDo notation.