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Language	Haskell2010

Data.MonadicStreamFunction.InternalCore

Contents

Definitions
Monadic computations and MSFs
Feedback loops
Execution/simulation

Description

Monadic Stream Functions are synchronized stream functions with side effects.

MSFs are defined by a function unMSF :: MSF m a b -> a -> m (b, MSF m a b) that executes one step of a simulation, and produces an output in a monadic context, and a continuation to be used for future steps.

MSFs are a generalisation of the implementation mechanism used by Yampa, Wormholes and other FRP and reactive implementations.

This modules defines only the minimal core. Hopefully, other functions can be defined in terms of the functions in this module without accessing the MSF constuctor.

Synopsis

data MSF m a b = MSF {
- unMSF :: a -> m (b, MSF m a b)
}
morphGS :: Monad m2 => (forall c. (a1 -> m1 (b1, c)) -> a2 -> m2 (b2, c)) -> MSF m1 a1 b1 -> MSF m2 a2 b2
feedback :: Monad m => c -> MSF m (a, c) (b, c) -> MSF m a b
embed :: Monad m => MSF m a b -> [a] -> m [b]
reactimate :: Monad m => MSF m () () -> m ()

Definitions

data MSF m a b Source #

Stepwise, side-effectful MSFs without implicit knowledge of time.

MSFs should be applied to streams or executed indefinitely or until they terminate. See reactimate and reactimateB for details. In general, calling the value constructor MSF or the function unMSF is discouraged.

Constructors

MSF
Fields unMSF :: a -> m (b, MSF m a b)

Instances

Monad m => Arrow (MSF m) Source #	`Arrow` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Core Methods arr :: (b -> c) -> MSF m b c # first :: MSF m b c -> MSF m (b, d) (c, d) # second :: MSF m b c -> MSF m (d, b) (d, c) # (***) :: MSF m b c -> MSF m b' c' -> MSF m (b, b') (c, c') # (&&&) :: MSF m b c -> MSF m b c' -> MSF m b (c, c') #
(Monad m, MonadPlus m) => ArrowZero (MSF m) Source #	Instance of `ArrowZero` for Monadic Stream Functions (`MSF`). The monad must be an instance of `MonadPlus`.
Instance details Defined in Data.MonadicStreamFunction.Instances.ArrowPlus Methods zeroArrow :: MSF m b c #
(Monad m, MonadPlus m) => ArrowPlus (MSF m) Source #	Instance of `ArrowPlus` for Monadic Stream Functions (`MSF`). The monad must be an instance of `MonadPlus`.
Instance details Defined in Data.MonadicStreamFunction.Instances.ArrowPlus Methods (<+>) :: MSF m b c -> MSF m b c -> MSF m b c #
Monad m => ArrowChoice (MSF m) Source #	`ArrowChoice` instance for MSFs.
Instance details Defined in Data.MonadicStreamFunction.Instances.ArrowChoice Methods left :: MSF m b c -> MSF m (Either b d) (Either c d) # right :: MSF m b c -> MSF m (Either d b) (Either d c) # (+++) :: MSF m b c -> MSF m b' c' -> MSF m (Either b b') (Either c c') # (\|\|\|) :: MSF m b d -> MSF m c d -> MSF m (Either b c) d #
MonadFix m => ArrowLoop (MSF m) Source #	`ArrowLoop` instance for MSFs. The monad must be an instance of `MonadFix`.
Instance details Defined in Data.MonadicStreamFunction.Instances.ArrowLoop Methods loop :: MSF m (b, d) (c, d) -> MSF m b c #
Monad m => Category (MSF m :: Type -> Type -> Type) Source #	Instance definition for `Category`. Defines `id` and `.`.
Instance details Defined in Data.MonadicStreamFunction.InternalCore Methods id :: MSF m a a # (.) :: MSF m b c -> MSF m a b -> MSF m a c #
Monad m => Functor (MSF m a) Source #	`Functor` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Core Methods fmap :: (a0 -> b) -> MSF m a a0 -> MSF m a b # (<$) :: a0 -> MSF m a b -> MSF m a a0 #
(Functor m, Monad m) => Applicative (MSF m a) Source #	`Applicative` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Core Methods pure :: a0 -> MSF m a a0 # (<>) :: MSF m a (a0 -> b) -> MSF m a a0 -> MSF m a b # liftA2 :: (a0 -> b -> c) -> MSF m a a0 -> MSF m a b -> MSF m a c # (>) :: MSF m a a0 -> MSF m a b -> MSF m a b # (<*) :: MSF m a a0 -> MSF m a b -> MSF m a a0 #
(Functor m, Monad m, MonadPlus m) => Alternative (MSF m a) Source #
Instance details Defined in Data.MonadicStreamFunction.Instances.ArrowPlus Methods empty :: MSF m a a0 # (<\|>) :: MSF m a a0 -> MSF m a a0 -> MSF m a a0 # some :: MSF m a a0 -> MSF m a [a0] # many :: MSF m a a0 -> MSF m a [a0] #
(Monad m, Floating b) => Floating (MSF m a b) Source #	`Floating` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Instances.Num Methods pi :: MSF m a b # exp :: MSF m a b -> MSF m a b # log :: MSF m a b -> MSF m a b # sqrt :: MSF m a b -> MSF m a b # (**) :: MSF m a b -> MSF m a b -> MSF m a b # logBase :: MSF m a b -> MSF m a b -> MSF m a b # sin :: MSF m a b -> MSF m a b # cos :: MSF m a b -> MSF m a b # tan :: MSF m a b -> MSF m a b # asin :: MSF m a b -> MSF m a b # acos :: MSF m a b -> MSF m a b # atan :: MSF m a b -> MSF m a b # sinh :: MSF m a b -> MSF m a b # cosh :: MSF m a b -> MSF m a b # tanh :: MSF m a b -> MSF m a b # asinh :: MSF m a b -> MSF m a b # acosh :: MSF m a b -> MSF m a b # atanh :: MSF m a b -> MSF m a b # log1p :: MSF m a b -> MSF m a b # expm1 :: MSF m a b -> MSF m a b # log1pexp :: MSF m a b -> MSF m a b # log1mexp :: MSF m a b -> MSF m a b #
(Monad m, Fractional b) => Fractional (MSF m a b) Source #	`Fractional` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Instances.Num Methods (/) :: MSF m a b -> MSF m a b -> MSF m a b # recip :: MSF m a b -> MSF m a b # fromRational :: Rational -> MSF m a b #
(Monad m, Num b) => Num (MSF m a b) Source #	`Num` instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Instances.Num Methods (+) :: MSF m a b -> MSF m a b -> MSF m a b # (-) :: MSF m a b -> MSF m a b -> MSF m a b # (*) :: MSF m a b -> MSF m a b -> MSF m a b # negate :: MSF m a b -> MSF m a b # abs :: MSF m a b -> MSF m a b # signum :: MSF m a b -> MSF m a b # fromInteger :: Integer -> MSF m a b #
(Monad m, VectorSpace v) => VectorSpace (MSF m a v) Source #	Vector-space instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Instances.VectorSpace Methods (^/) :: MSF m a v -> Groundfield (MSF m a v) -> MSF m a v Source #
(Monad m, RModule v) => RModule (MSF m a v) Source #	R-module instance for `MSF`s.
Instance details Defined in Data.MonadicStreamFunction.Instances.VectorSpace Associated Types type Groundring (MSF m a v) :: Type Source # Methods zeroVector :: MSF m a v Source # (^) :: Groundring (MSF m a v) -> MSF m a v -> MSF m a v Source # (^) :: MSF m a v -> Groundring (MSF m a v) -> MSF m a v Source # negateVector :: MSF m a v -> MSF m a v Source # (^+^) :: MSF m a v -> MSF m a v -> MSF m a v Source # (^-^) :: MSF m a v -> MSF m a v -> MSF m a v Source #
type Groundring (MSF m a v) Source #
Instance details Defined in Data.MonadicStreamFunction.Instances.VectorSpace type Groundring (MSF m a v) = Groundring v

Monadic computations and `MSF`s

morphGS Source #

Arguments

:: Monad m2
=> (forall c. (a1 -> m1 (b1, c)) -> a2 -> m2 (b2, c))	The natural transformation. `mi`, `ai` and `bi` for `i = 1, 2` can be chosen freely, but `c` must be universally quantified
-> MSF m1 a1 b1
-> MSF m2 a2 b2

Generic lifting of a morphism to the level of MSFs.

Natural transformation to the level of MSFs.

Mathematical background: The type a -> m (b, c) is a functor in c, and MSF m a b is its greatest fixpoint, i.e. it is isomorphic to the type a -> m (b, MSF m a b), by definition. The types m, a and b are parameters of the functor. Taking a fixpoint is functorial itself, meaning that a morphism (a natural transformation) of two such functors gives a morphism (an ordinary function) of their fixpoints.

This is in a sense the most general "abstract" lifting function, i.e. the most general one that only changes input, output and side effect types, and doesn't influence control flow. Other handling functions like exception handling or ListT broadcasting necessarily change control flow.

Feedback loops

feedback :: Monad m => c -> MSF m (a, c) (b, c) -> MSF m a b Source #

Well-formed looped connection of an output component as a future input.

Execution/simulation

embed :: Monad m => MSF m a b -> [a] -> m [b] Source #

Apply a monadic stream function to a list.

Because the result is in a monad, it may be necessary to traverse the whole list to evaluate the value in the results to WHNF. For example, if the monad is the maybe monad, this may not produce anything if the MSF produces Nothing at any point, so the output stream cannot consumed progressively.

To explore the output progressively, use liftMSF and '(>>>)'', together with some action that consumes/actuates on the output.

This is called runSF in Liu, Cheng, Hudak, "Causal Commutative Arrows and Their Optimization"

reactimate :: Monad m => MSF m () () -> m () Source #

Run an MSF indefinitely passing a unit-carrying input stream.

Definitions

Monadic computations and MSFs

Feedback loops

Execution/simulation

Monadic computations and `MSF`s