module Internal.Signal ( -- * Signals Signal (osfSwitch, ssfSwitch), -- * Switching switch, polySwitch, -- * Signal functions SignalFun (OSF, SSF), unOSF, unSSF, sfApp, (:->), PolySignalFun (PolySignalFun), PolyOSF (PolyOSF), PolySSF (PolySSF), polyOSF, polySSF, unPolyOSF, unPolySSF, -- * Signal shapes Of, -- * Sampling Sampler (sample, samplerMap), Samplee (dSample, sSample), (<#>), (#>), (<#), -- * Connectors Consumer (Consumer), consume, Producer (Producer), produce ) where -- Control import Control.Applicative as Applicative -- for documentation only import Control.Monad.ST as ST -- for documentation only -- Internal import {-# SOURCE #-} Internal.Signal.Discrete as DSignal import {-# SOURCE #-} Internal.Signal.Segmented as SSignal -- FRP.Grapefruit import FRP.Grapefruit.Circuit as Circuit -- Fixities infixl 4 <#> infixl 4 #> infixl 4 <# -- * Signals -- |The class of all signal types. class Signal signal where osfSwitch :: SSignal era (PolyOSF signal val) -> signal era val ssfSwitch :: SSignal era (PolySSF signal val shape) -> (signal era val -> SignalFun era shape) -- * Switching {-| This function generates a signal whose behavior switches between that of different other signals over time. Since the result type @'SignalFun' era shape@ is isomorphic to an n-ary function type, we can see @switch@ as a function which takes a first argument, called the function signal, and /n/ further arguments, called the argument signals, and yields a signal, called the result signal. The result signal is composed of different sections. There is one section for each segment of the function signal. Such a section is formed as follows: For each argument signal, the part which corresponds to the time intervall of the functions signal’s segment is cut out of the argument signal. The value of the function signal is applied to the resulting /n/ signal parts. The result of this application is the desired section of the result signal. The signal functions which are applied to the parts of the argument signals use an universally quantified era parameter. This ensures that the results of these functions do not depend on signals from the outside but only on the parts of the argument signals. This is important since operations on signals require that their argument and result signals are of the same era. The usage of universial quantification in the type of @switch@ corresponds to the usage of rank 2 polymorphism in the type of 'runST'. -} switch :: SSignal era (forall era'. SignalFun era' shape) -> SignalFun era shape switch = polySwitch . fmap PolySignalFun polySwitch :: SSignal era (PolySignalFun shape) -> SignalFun era shape polySwitch funSignal@(SSignal (PolySignalFun init) _) = fun' where fun' = case init of OSF _ -> OSF $ osfSwitch (fmap polyOSF funSignal) SSF _ -> SSF $ ssfSwitch (fmap polySSF funSignal) -- * Signal functions -- FIXME: Hyperlink to :-> and document the data constructors seperately as soon as this works. {-| A signal function is a function which maps a certain number of signals to one signal whereby all argument signals and the result signal have the same era. The @era@ parameter of @SignalFun@ denotes the era of all argument signals and the result signal. The @shape@ parameter is a phantom parameter which specifies the number of argument signals as well as the types of the argument signals and the result signal without their era parameters. It has the following form: @ /signal_1/ `'Of'` /val_1/ :-> ... :-> /signal_n/ `'Of'` /val_n/ :-> /signal'/ `'Of'` /val'/ @ The data constructors 'OSF' and 'SSF' construct signal functions of zero and non-zero arity, respectively. (The @O@ stands for “zero” and the @S@ stands for “successor”.) A signal function is typically formed by an expression like @ 'SSF' $ \/signal_1/ -> ... 'SSF' $ \/signal_n/ -> 'OSF' $ /signal'/ @ where @/signal'/@ is an expression that might use @/signal_1/@ to @/signal_n/@. Signal functions are usually applied like this: @ 'unOSF' $ /signalFun/ `'sfApp'` /signal_1/ `'sfApp'` ... `'sfApp'` /signal_n/ @ -} data SignalFun era shape where OSF :: (Signal signal) => signal era val -> SignalFun era (signal `Of` val) SSF :: (Signal signal) => (signal era val -> SignalFun era shape) -> SignalFun era (signal `Of` val :-> shape) -- |Converts a nullary signal function into its corresponding signal. unOSF :: SignalFun era (signal `Of` val) -> signal era val unOSF (OSF signal) = signal -- |Converts a signal function of non-zero arity into a true function. unSSF :: SignalFun era (signal `Of` val :-> shape) -> (signal era val -> SignalFun era shape) unSSF (SSF fun) = fun infixl 4 `sfApp` {-| Applies a signal function to a signal. @sfApp@ is equivalent to 'unSSF'. -} sfApp :: SignalFun era (signal `Of` val :-> shape) -> signal era val -> SignalFun era shape sfApp = unSSF infixr 1 :-> {-| The @:->@ operator is used to form signal function shapes for 'SignalFun'. The shape @/argShape/ :-> /resultShape/@ stands for functions which map signals of shape @/argShape/@ to signal functions of shape @/resultShape/@. -} data argShape :-> resultShape newtype PolySignalFun shape = PolySignalFun (forall era. SignalFun era shape) newtype PolyOSF signal val = PolyOSF (forall era. signal era val) newtype PolySSF signal val shape = PolySSF (forall era. signal era val -> SignalFun era shape) polyOSF :: PolySignalFun (signal `Of` val) -> PolyOSF signal val polyOSF (PolySignalFun signalFun) = PolyOSF (unOSF signalFun) polySSF :: PolySignalFun (signal `Of` val :-> shape) -> PolySSF signal val shape polySSF (PolySignalFun signalFun) = PolySSF (unSSF signalFun) unPolyOSF :: PolyOSF signal val -> signal era val unPolyOSF (PolyOSF signal) = signal unPolySSF :: PolySSF signal val shape -> signal era val -> SignalFun era shape unPolySSF (PolySSF fun) = fun -- * Signal shapes -- FIXME: Make :-> a hyperlink when this works. {-| @Of@ is used to form signal shapes. Signal shapes are used as phantom types and denote a signal type except its era parameter. A signal shape @/signal/ `Of` /val/@ stands for a signal of type @/signal/ /era/ /val/@ where the era parameter is provided by an external source. Signal shapes are used as signal function shapes of nullary functions and as argument shapes for @:->@. In this case, the era parameter is the era parameter of 'SignalFun'. Signal shapes are also used in records as defined by the module @FRP.Grapefruit.Record@ of package grapefruit-records. -} data (signal :: * -> * -> *) `Of` val -- * Sampling {-| The class of all signals which can be seen as discrete sequences of values. Such signals can be used to sample signals of class 'Samplee'. -} class Sampler sampler where sample :: (Samplee samplee) => sampler era (val -> val') -> samplee era val -> sampler era val' -- for internal use only samplerMap :: (val -> val') -> (sampler era val -> sampler era val') -- Samplee could also be called “dense signal”. {-| The class of all signals which assign a value to each time of their era. Such signals can be sampled by signals of class 'Sampler'. -} class Samplee samplee where -- for internal use only dSample :: DSignal era (val -> val') -> samplee era val -> DSignal era val' -- for internal use only sSample :: SSignal era (val -> val') -> samplee era val -> SSignal era val' {-| Sampling of signals. A signal @/sampler/ <#> /samplee/@ has a value at each time where @/sampler/@ has a value. The value of @/sampler/ <#> /samplee/@ is formed by applying the value of @/sampler/@ to the value, @/samplee/@ has at this time. This function has similarities with '<*>'. -} (<#>) :: (Sampler sampler, Samplee samplee) => sampler era (val -> val') -> samplee era val -> sampler era val' (<#>) = sample {-| Sampling of signals where the values of the sampler are ignored. The following equation holds: @ /sampler/ #> /samplee/ = id '<$' /sampler/ '<#>' /samplee/ @ This function has similarities with '*>'. -} (#>) :: (Sampler sampler, Samplee samplee) => sampler era dummy -> samplee era val -> sampler era val (#>) = (<#>) . samplerMap (const (\ val -> val)) {-| Sampling of signals where the values of the samplee are ignored. The following equation holds: @ /sampler/ <# /samplee/ = const '<$>' /sampler/ '<#>' /samplee/ @ This function has similarities with '<*'. -} (<#) :: (Sampler sampler, Samplee samplee) => sampler era val -> samplee era dummy -> sampler era val (<#) = (<#>) . samplerMap const -- * Connectors -- |A consumer says what to do with a given signal. newtype Consumer signal val = Consumer (forall era. Circuit era (signal era val) ()) -- ^A consumer, represented by a circuit that consumes a signal. -- |Yields a circuit which consumes a signal. consume :: Consumer signal val -> Circuit era (signal era val) () consume (Consumer circuit) = circuit -- |A producer says how to produce a certain signal. newtype Producer signal val = Producer (forall era. Circuit era () (signal era val)) -- ^A producer, represented by a circuit that produces a signal. -- |Yields a circuit which produces a signal. produce :: Producer signal val -> Circuit era () (signal era val) produce (Producer circuit) = circuit