Sirea

Simply Reactive! Declarative orchestration in Haskell using the Reactive Demand Programming (RDP) model.

an RDP application is a complex symphony of signals and declarative effects orchestrated in space and time

RDP is stateless logic on a stateful grid

Everybody knows "side-effects aren't compositional". But that statement is only true in general. There are useful subsets of side-effects that have nice properties - e.g. idempotence, commutativity, monotonicity. For a small subset of effects, one can achieve equational reasoning and refactoring on par with the very best pure, law abiding programming models. I call these declarative effects. Any pure functional programming advocate also knows effects are rarely essential, i.e. that sufficient cleverness will find a wonderfully pure solution most problems. How much more could be achieved with just a little cleverness and a few, highly constrained, declarative effects?

Reactive Demand Programming was developed as an answer to that question.

In RDP, the only effect is observing of the active set of demands by a resource. Those demands are typically queries or control signals. RDP's effect model was inspired from a symmetric observer effect in physics and psychology: one cannot observe a system without influencing its behavior. Since observation implies influence, it is possible to observe for the sole purpose of influence. Thus, only one concept is needed for query and control.

Demands are represented as long-lived signals. Signal processing is local, modular, and composable. Treating the signals as a set is essential for RDP's spatial idempotence and commutativity.

The answer: Anything worth doing can be done with declarative effects. (Or, rather: Anything worth being can become with declarative effects.) This includes state, video, music, sensor networks, control systems, user interface. All can be adequately observed and influenced via the RDP paradigm. It does take new idioms and abstractions (especially new state models) to effectively adapt and utilize external resources.

What is Reactive Demand Programming?

Most programmers, even those who rarely venture beyond imperative abstractions, are familiar with at least one declarative dataflow concept: the spreadsheet. RDP might be framed as a natural way to extend spreadsheets with functions and effects:

• Every cell is described by a function. Access to a cell always requires a parameter.
• Cells carrying simple values are represented as functions that ignore their parameters.
• A cell's function may be evaluated continuously and concurrently with many parameters.
• Some "special" cells represent externals such as mouse, keyboard, database, display.
• Special cells can observe the full, concurrent set of parameters to influence values.
• Functions may be used as parameters or results. (Cell names can be used as functions.)

The spreadsheet analogy does suggest the question: how does one display a cell whose value is a function?

Wonderful answers to that question have been developed in other projects, such as naked objects, and tangible values. A simplistic answer would be to just query the cell with a value Print and display whatever is returned (numbers, text, SVG, etc.). Alternatively, one might use a visitor pattern: pass a canvas-abstraction to the cell, then allow the cell to print itself (potentially even print some interactive widgets). RDP will express these abstractions more easily and effectively than the paradigms for which they were initially developed.

However, I mean to emphasize the reactive and dataflow aspect of spreadsheets.

RDP, like a spreadsheet, enables dataflow. But RDP is a bidirectional dataflow model. In addition to receiving values, every downstream client is also pushing values upstream: parameters. Those values are used in many ways: as database queries, as control signals, to publish data, or to register services. The bidirectional flow makes RDP far more expressive, modular, extensible, and composable than traditional spreadsheets.

The cost of supporting bidirectional dataflow and effects on externals is RDP must abandon the illusion of "instantaneous" dataflow. Dataflow takes time, especially when it involves a requests on external resources. Time is essential to dampen and understand any feedback properties. RDP uses explicit, logical latency to support safe, consistent propagation and processing of values. It can take time for a change upstream to affect a downstream client, or for a change in a client to affect an upstream service. But it will be a very predictable amount of time.

An RDP-based spreadsheet would be a wonderful application of RDP: for teaching RDP, for live programming, and as a potential killer application in its own right. However, it must wait until Sirea is further along.

RDP does not use a spreadsheet nomenclature. But there are names for corresponding elements in RDP:

• Time-varying parameters and responses are formally modeled as signals.
• The effectful "functions" of RDP are called behaviors.
• The "special" cells are said to access resources.

Using its bidirectional dataflows and dynamic behaviors, RDP can represent multi-agent systems, ad-hoc workflows, OO patterns, frameworks, overlay networks. In combination with external state resources, RDP is a complete paradigm for general purpose programming.

It may help to read some of RDP's background and motivations:

• a comment that helped some people: a journey towards RDP
• the mailing list reactive-demand@googlegroups.com
• the author's blog

Sirea Status

Sirea is now in an alpha state. All the primitive behaviors (everything in Sirea.Behavior) have been implemented, plus partitions and a few trivial resources (clock, printing to console). Demand monitors are coming soon.

Haskell Packages

Several packages are planned for Sirea. This toplevel directory is sirea-core.

• sirea-core (80%) primitive behaviors, demand monitor, resources, utilities, startup and shutdown.
• sirea-filesys (1%) simplistic reading and writing of filesystem, with reactive updates
• sirea-glfw (1%) keyboard, mouse, joystick, GL window; experimental GL API in RDP/Sirea
• sirea-jackaudio (0%) experimental stateless sound API in RDP/Sirea; JACK backend
• sirea-state (0%) term rewriting, state transition system, tuple space, history
• sirea-stable (0%) a stateless stable model based on weighted constraint logic
• sirea-wx (0%) experimental immediate-mode GUI API with external state; wxHaskell backend
• sirea-wapp (0%) live web apps; pages as loading agents; serve mixed client/server dynamic RDP behaviors
• sirea-plugins (0%) live loading and constraint-based linking of plugins, leveraging Data.Typeable and
• sirea-live (0%) a blank-slate application to run a live soup of plugins

Once I start settling on APIs for GL, sound, GUI, web-services, etc. I plan to divide APIs into parts - one part for plugin header (a typable data type) and another part for the plugin implementations. For now, I expect to keep most of these together in one GIT project.

Specific Features

Reactive Demand Programming offers many wonderful, high level features that make Sirea a pleasure to use. RDP also offers interesting state models that would not have been envisioned for imperative systems. These are discussed in later sections. Here, I'll aim for a short list of Sirea specific features.

• Type Driven Resource Locators. Users of Sirea have almost zero overhead for connecting to arbitrary resources and using them. Resources and threads are named by types. Data.Typeable and typeOf are leveraged for initialization, sharing, and resource management. Any IO boiler plate is easily shifted to a few typeclasses in adapter libraries. The plugins module will take this feature further, replacing Haskell's name-based import system with a type-driven import model.

• Orthogonal Persistence. Reactive Demand Programming necessarily models state as an external resource. Sirea takes full advantage of this, by making all state resources persistent (excepting those that are semantically volatile, such as short windowed history).

• Live Programming. Live programming has been done in many languages, including Haskell. However, it has generally been ad-hoc, requiring a highly constrained programming style. Reactive Demand Programming offers a sound foundation for live programming, including dependency management and state. Sirea will support live programming through a blank slate application combined with runtime compilation and reloading of plugins. You will be able to start your Sirea/Haskell application before writing it. This has potential beyond RDP, to become a primary way to develop Haskell applications.

• Multi-Agent Systems. If an RDP behavior is specified primarily for its effects, it is easy to consider it an agent for a multi-agent system. Sirea favors this idea for the higher level application behaviors: the initial SireaApp is an agent; the module Sirea.AgentResource allows unique agents to be modeled as resources via a typeclass; the live programming model will be agent-based, allowing multiple plugins to each contribute resources.

• Performance. Sirea is designed to perform competitively and predictably. This includes solutions for update ordering problems, batching of updates between threads, minimal use of caches, speculative evaluation and resource acquisition, bounded buffers to control memory and ensure fairness, a few simple optimizations, and behaviors for data parallelism. Sirea is suitable for soft real-time applications.

• Batteries Included. Sirea is intended to be a complete application framework, a valid option for industry work. Convenience functions, documentation, and utility behaviors are included. Planned packages will cover many common resources - user input, graphics, filesystem, web services. Ultimately, Sirea should be a serious, mature application framework - the first of its kind for truly declarative programming.

Weaknesses

The weaknesses of Sirea RDP belong more to Sirea than to RDP.

• Developers must use a point-free style for RDP behaviors in Sirea. This a very rewarding style once you become familiar with it, and the full power of Haskell functions is still available (via bfmap, beval). But newcomers often find point-free intimidating.

• RDP is designed for object capability model systems, using dynamic behaviors as runtime composable capabilities. Sirea, however, is designed to be convenient in Haskell, and supports ambient, typeful access to resources. (Object capability model is great, but the module, FFI, and linking systems really must be designed for it.)

• Sirea is sensitive to the OS clock. Sirea and RDP can tolerate a few milliseconds drift, but ideally need robust, monotonic, well synchronized clocks. It is best to use Sirea in conjunction with a time services for the OS.

• Sirea attempts to recognize and logically deactivate for the duration of a suspended state (e.g. when the laptop sleeps), but the current implementation seems to have a high heap overhead when recovering. I'm working on this one.

• Performance of dynamic behaviors is poor - i.e. expensive install and maintain; difficult to optimize and anticipate. RDP is designed with an assumption of having very few, relatively stable 'layers' of dynamic behavior, e.g. for staged metaprogramming. Sirea can handle that much. More will probably take a dedicated RDP language or EDSL that can perform partial evaluations, tracing, or other cross-layer optimizations.

Reactive Demand Programming (in Sirea)

The Reactive Demand Programming (RDP) view divides the world into three kinds of things: resources, behaviors, and signals.

• Resources might broadly be classed into sensors, actuators, state, and services. Specific examples include keyboard, mouse, joystick, webcam, microphone, monitor, speaker, filesystem, databases, network, printers. By nature, resources are external to RDP, but may be accessed by RDP behaviors. Resources cannot be created in RDP: there is no equivalent to OOP new. However, resources may be dynamically discovered at runtime, and clever manipulations of stateful resources (such as a filesystem) can model creation in terms of discovery (e.g. by computing a unique filename).

• Behaviors describe computation-rich data plumbing between resources. Some behaviors will represent access to a resource, providing a capability to observe or influence it. But the majority of behaviors in an RDP application are often simple data plumbing and pure transforms (cf. Sirea.Behavior). RDP behaviors cannot accumulate state; all state is kept in external resources. A simple, linear behavior might gain a joystick signal from GLFW, transform that signal into controls for a robotic arm, bcross over to a partition representing the robot resource, then push the signal to the robotic arm. (getJoyData >>> bfmap joyToRobotArmCtrl >>> bcross >>> controlArm). RDP can express many independently concurrent behaviors, e.g. using |*|. Behaviors can be dynamic, i.e. there is a behavior to evaluate behaviors (beval).

• Signals describe values as they change over time. Those values typically represent states - e.g. the position of a mouse, frames from a webcam, content for a video display. Future states are not entirely predictable, so signals must be updated over time. Propagating those updates and transforming the signals are the primary roles of behaviors. It is not possible to observe a signal's history, and consequently signals are constrained by durations of explicit, active observation. For example, a signal describing the position of a joystick is only active while a behavior is actively observing it. Behaviors cannot create or destroy signals, but can manipulate existing signals in flexible ways.

RDP programming directly concerns only the behaviors. An RDP "application" is a behavior analogous to IO () or void main(), with trivial inputs and outputs and activated entirely for declarative effects. Signals and resources are not programmable abstractions within RDP. They are not first class. However, signals and resources are useful concepts for motivating, understanding, and explaining behaviors. Also, many Sirea users - especially early adopters - will develop adapters to resources and services. Developing these adapters requires a very concrete understanding of the signal and resource models.

Signals and resources are concretely relevant for developing resource adapters and FFI.

Resources and signals are useful concepts for motivating and understanding the behaviors, but are not programming abstractions. (Signals and resources are concretely relevant if developing an adapter between Sirea and an ad-hoc resource, such as a joystick.) An RDP application in Sirea is a behavior that is installed between resources and bootstrapped by the Sirea runtime (e.g. via runSireaApp).

A few short examples of resources, behaviors, and signals:

• A mouse is a resource. A mouse might be accessed by a behavior called glfwMousePos. The glfwMousePos behavior will respond to a unit-typed input signal (representing a long-lived query, in particular the duration and time of the query) with an output signal (representing the mouse's position, updated over the lifetime of the query). The output signal can be transformed and transported by more behaviors to do something useful, such as influence state that affects a display.

• An SQL database is a resource. An SQL database might be accessed by a behavior called queryDB. The input signal might contain a SELECT * FROM foo WHERE (bar > 10) query string. The output signal would contain the query result, a list of entries from foo. Alternatively, the result might contain some error information, saying that there is no foo, or that the connection could not be established. It is possible for both the query string and the output signal to change over time, e.g. to update the demand to (bar > 12), or to receive update indicating changes due a DB update. In general, these changes are independent - i.e. it is possible that two different query strings result in the same data, and it is possible that some database changes are irrelevant to the query result.

• When RDP programmers need a signal with the constant value 3, they will use bconst 3. There is a concept of "the 3 signal" - s_always 3, which is, was, and forever will be 3. But RDP cannot create the 3 signal. RDP can only transform some existing signal into a 3, maintaining the start and stop time and partition of the existing signal. This protects duration coupling. There are many other operations on pure signals that are illegal for direct use in RDP (fold, mask, etc.), which is why RDP developers do not have direct access to signals.

RDP toes more than one line to achieve its compositional properties and declarative effects. Those lines result in several software fences that initially seem limiting to developers unfamiliar with the declarative style. Fortunately, it should not take long to learn idioms and patterns to work within these constraints.

The best way to learn RDP is probably to use it, and to implement examples a few lines at a time. I'll make an effort to provide many example as I make progress in implementing the RDP utilities. The following sections discuss signals, behaviors, and resources more deeply.

Signal Values

Note: RDP developers do not use first-class signals. RDP developers do not use second-class signals. RDP developers do not directly observe or manipulate signals. However, an understanding of signals is essential for understanding RDP. Concrete knowledge of signals and their representation is also necessary to adapt Sirea to external resources (adapters to other paradigms are almost never purely RDP code).

A Signal is a value. A signal describes another value as it changes over time. Often, the the time-varying value will represent state of an external resource. For example, if I were to continuously observe the state of the "w" key on my keyboard, it would be in an up state most of the time, and in a down state for the brief times I press the button, as when writing "down", "when", or "writing". I could represent this in a signal by mapping the position of the "w" key on a precise timeline.

    ________  _________  ____________  Up ("w" not pressed)
          t1__t2     t3__t4            Down ("w" pressed)

One might represent this discrete-varying signal in a data structure as follows:

    signal= (Up, [(t1, Down), (t2, Up), (t3, Down), (t4, Up)])
             |   ^ known updates
             ^ value for all history

Note that the states can be stored as a sequence of discrete updates, but full signal still represents a time-varying value. That is, the signal is Up until t1, then Down until t2, then Up until t3, etc.. The meaning of this representation is important. For example, the meaning suggests that the time values had better be in some strictly increasing monotonic order.

(Aside: RDP does not use events. Events very strongly favor an imperative effects model, and require excessive use of internal state 1. However, RDP has no difficulty representing short-lived states like the position of a key on the keyboard. Further, an RDP adapter to a keyboard resource may translate a stream of keyboard events into an RDP signal. Sirea will not "miss" any key states while you're observing the keyboard.)

For RDP, the above signal is incomplete. Signals have a lifespan (also called activity cycle) - a definite start time, and indefinite end time. This lifespan is not a property of the keyboard, but rather a property of the observer of the keyboard. An observer must start observing at some definite time. In Sirea, lifespan is represented by wrapping every signal value in a Maybe type, and use the Nothing value to indicate durations where no observation occurs.

        ________  _________  ____________     Just Up ("w" not pressed)
        t0    t1__t2     t3__t4        t5     Just Down ("w" pressed)
    NNNN                                 NNNN Nothing
   
    signal= (Nothing, [(t0, Just Up), (t1, Just Down), (t2, Just Up), 
                       (t3, Just Down), (t4, Just Up), (t5, Nothing)])

The use of Maybe allows sequential signals to be combined on a single update stream, and supports efficient implementation of the asynchronous sum type (x :|: y) (see below).

Note: The Nothing value used here does not represent failure. Failure must always be represented by an active signal. E.g. if I want to represent the possibility that the keyboard is inaccessible, then I'd need to use a type like Either KeyState Error for the active signal. This is necessary for RDP's duration coupling invariant, and is preferable because it allows RDP behaviors to observe failure and take appropriate action.

Representing Concrete Signals

Sirea has gone through a few implementations of signals. The current representation is essentially the same as the list described above, but slightly more compact and with an assumption that the list is of finite length or even spine-strict (such that we can safely filter false updates). Some operations will search for the end of the list. Sirea cannot directly represent infinite signals unless they are constant. This only impacts a few trivial behaviors that are time-varying but utterly predictable, such as logical clocks. Advantages of this constraint are that it is easy to reason about memory and performance in a loop, and it generalizes well to networked systems. There is also no risk of divergence when eliminating false updates.

Signals have an abstract API. The representation is rarely accessed directly.

Updating Signals

Signal updates are not observable within an RDP expression, but are accessible when developing resource adapters and FFI bindings for Sirea. Conceptually, a newly constructed RDP behavior graph has all signals initially set to an inactive state. Subsequent updates will activate resources and control the state of the RDP system. Updates are performed through LnkUp structures, which are provided in the process of compiling and constructing the behavior.

    data LnkUp a = LnkUp 
        { ln_touch :: IO ()
        , ln_update :: StableT -> T -> Sig a -> IO ()
        , ln_idle :: StableT -> IO ()
        }

The update method indicates that we're to switch to the provided signal at the given time. (The roles of stability, touch, and idle are described in a later section about implementing RDP behaviors.) In a general sense, RDP updates could be more expressive than switching the full future of a signal. (E.g. if a signal value is a set, it would be convenient to add or remove specific values from the set.) But, in interest of keeping it simple, Sirea only supports whole future updates. (Specialized behavior constructors for operating on patches might be a feasible option down the road.)

Signal updates have several nice properties in addition to those of general message passing:

• updates to a full signal are idempotent; useful for resilience on a shoddy network connection
• sequential updates are composable by "piggybacking"; useful when fast source feeds slow consumer.
• updates allow takebacks (limited by stability); optimistic concurrency, eventual consistency
• updates can target future; masks variability in latency, simplifies scheduling, avoids rework
• resource control and GC can be built into signals by controlling activity and stability

These are in addition to the many benefits associated with anticipation and speculative evaluation.

In Sirea, a behavior is compiled into a network with all signals inactive. The first signal update will activate the behavior. See more on implementing RDP behaviors in a later section.

Continuous Signals?

There are many problem domains where support for continuous-varying signals would be useful: motion, sound, animation, charting, physics, probability. Sirea currently supports only discrete-varying signals, which is quite suitable for digital information (boolean values, integers, text). However, RDP in general can support piecewise-continuous signals.

I am interested in eventually developing support for continuous signals, most likely in a transformative layer above Sirea RDP. This has at least two special requirements:

• Upon bdelay need to time-shift the signal contents.
• Instead of bsplit need some support for zero-crossings.

Viable candidates include trigonometric polynomials or plain old polynomials. These models are symbolic, can be represented as a simple vector of coefficients, are easy to serialize or utilize on a GPU, and multi-dimensional variations are feasible. Use of Haskell functions (T -> a) is also feasible, though opaque and full of semantic garbage (such as discontinuous signals).

Signals in Space and Time

Concrete signals are effective for tightly coupled values that are processed and updated together. But more structure is necessary for flexibility, efficiency, and scalability. Sirea uses three structural notations for complex signals.

1. (S p a) - represents a concrete signal (Sig a) located spatially at partition p. Unless subjected to dead code elimination, this results in a signal value being represented at partition p. Use of the p type prevents implicit communication of signals between partitions. Developers must use bcross or similar to cross partitions, which simplifies Sirea's communication model and improves its efficiency.

2. (x :&: y) - describes an asynchronous product of signals. Both elements, x and y, are active at roughly the same time, depending on differences in delay. Both have the same active durations. By modeling a product in different partitions, i.e. ((S p1 a) :&: (S p2 b)), an asynchronous product can model a distributed computation.

3. (x :|: y) - describes an asynchronous sum of signals, like a switching network. In general, the x and y are active at different times, but differences in latency on the different branches can cause brief overlap for transition from the faster to the slower. The active duration is split between x and y.

The asynchronous property is a consequence of constructs like bleft (bdelay 0.02) or bfirst (bdelay 0.01), resulting in component signals having different latencies. These are logical delays, achieved by increasing the su_state and su_stability times, and thus have no significant performance consequence. Modeling of delays is important semantically, both to dampen feedback loops and to allow signals time to propagate through a complex behavior. This is a different notion of asynchrony than is common to multi-threading, promises, actors. RDP can model the latter form of asynchrony by use of shared state communication, e.g. blackboard models, task queues. But latencies for asynchronous products and signals are statically known, making them suitable for real-time systems.

Use of bsynch will logically synchronize complex signals by logically delaying the lower-latency concrete signals. This results in signals being logically aligned. Since this is static, it works even if they are distributed across multiple partitions. Logical synchronization is very efficient, and can be more precise than state-based synchronization. Whether logically synchronous operations will be physically synchronized depends on the ability to synchronize clocks or at least estimate clock offsets.

There are two special signals, which were developed to better fit various theoretic models.

• S0 - a signal that is useless because it does not exist
• S1 - a signal that is useless because is stuck in an abstract partition

While RDP developers cannot destroy signals, they can dump them someplace irretrievable (S1). Similarly, while RDP developers cannot create signals, they can invent unused signal types in a choice (S0). Most Sirea users will stick to binl or bfst rather than mess with these types.

Behaviors

Behaviors describe computation-rich dataflow networks that manipulate signals. A behavior will be compiled and installed, establishing a concrete instance of the behavior, a concrete dataflow network. Installing a behavior has no effect other than to prepare a few unique names and caches. The initial signal is inactive. Once installed, a behavior is activated by signal update.

Some behaviors provide access to effectful resources such as sensors, actuators, or shared state. For concrete instances of those behaviors, updates to the input signal are often independent of updates to the output signal. E.g. one does not need to update a query signal for a mouse or keyboard or video camera to receive many updates to a signal representing observed values. Conversely, a stateful resource or an OK|Error signal from an actuator might be very stable despite many changes to inputs. Effects on resources are declarative, based on the set of active signals at any given time.

Different resources tend to update at different times and frequencies. Use of the complex signal types (x :&: y) and (x :|: y) enable developers to describe subnets that update at different rates. This is critical for efficiency. Developers can easily control and reason about which behavior subnets might be updated based on changes upstream. By arranging for some signals to be more stable (e.g. by utilizing an intermediate state resource) developers can protect subsystems that cannot handle rapid or short-term variations in input.

A Sirea RDP "application" is a behavior whose activation is bootstrapped by runSireaApp. The behavior has trivial signal types, and thus is activated only for its declarative effects. Otherwise, there is nothing special about the application behavior. Developers can easily pretend the application behavior is dynamically activated by an even larger behavior, or may even compose it into a larger behavior.

RDP is metacircular: it's behaviors "all the way down".

Behaviors as Dataflow Networks

Behaviors are composed as dataflows across an open system. Abstractly, those dataflows are signals. For the concrete, installed behavior, those dataflows are signal updates.

The simplest dataflow is linear and is appropriately called a "pipeline". The constructor for pipelines is >>>. This operator is from Control.Category, where (>>>) = flip (.). Composition with >>> is associative, chainable, and models dataflow from left to right. This results in code that is relatively read and document with English.

    (>>>) :: (Category b) => b x y -> b y z -> b x z
    f >>> g >>> h -- a pipeline of three behaviors

Developers may be familiar with pipelines from using command line interfaces, modern graphics processing, or other flow programming models. However, many dataflow systems are based on streams rather than signals. A signal describes one value as it varies over time. Streams are not so constrained, often representing iteration over collections or sequence of independent events. (It is not difficult to model a signal in a stream, or a stream in a signal. But it still takes state and labor. The default has a significant impact on programmer experience.) In Reactive Demand Programming, these pipelines will often represent continuous, effectful observation and influence of time-varying values. For example:

    load "myImage.svg" >>> renderJPG >>> save "myImage.jpg"

This behavior, while active, would continuously load "myImage.svg", render it to a JPG value, then save that result to "myImage.jpg". Of course, this is continuous only in the logical, abstract sense; the implementation would only fully load, render, and save when first activated and when "myImage.svg" changes. (Aside: the "when first activated" is often one time too many; an alternative would be to observe timestamps and to activate this behavior when a difference is detected.)

The notion of behaviors as dataflow "networks" is due to use of the complex signal types. Each concrete signal type (S p a) will have its own stream of signal updates. Different concrete signals may also be distributed across partitions. The signal type (S P1 x :&: S P2 y) describes a pair of concrete signals distributed across two partitions. Composition of distributed signals (x :&: y) involves composing x and y independently. This is supported by three primitive behaviors:

    bfirst   :: (BProd b) => b x x' -> b (x :&: y) (x' :&: y)
    bswap    :: (BProd b) => b (x :&: y) (y :&: x)
    bassoclp :: (BProd b) => b (x :&: (y :&: z)) ((x :&: y) :&: z)

The bfirst constructor allows operating on just the x signal, while bswap and bassoclp allow ad-hoc dataplumbing to shift any subset of (:&:) signals into the x position. Above these, several utility functions can be built, such as bsecond, bassocrp, and the (***) operator:

    bsecond  :: (BProd b) => b y y' -> b (x :&: y) (x :&: y')
    bsecond f = bswap >>> bfirst f >>> bswap

    bassocrp :: (BProd b) => b ((x :&: y) :&: z) (x :&: (y :&: z))
    bassocrp = (bfirst bswap >>> bswap) >>> bassoclp >>> (bfirst bswap >>> bswap)

    (***)    :: (BProd b) => b x x' -> b y y' -> b (x :&: y) (x' :&: y')
    f *** g = bfirst f >>> bsecond g

Reactive Demand Programming provides many useful declarative properties. Developers can consequently collapse complex constructs into simple, equivalent concepts. I don't wish to start proving theorems in this README, but developers can reason that (f1 *** g1) >>> (f2 *** g2) is equal to (f1 >>> f2) *** (g1 >>> g2) due to associativity of (>>>) and spatial commutativity.

    __f__   __g__   ______     __f__     ______   __g__   __f__
         \ /     \ /                           \ /     \ /
    bswap-X       X         =  (***)  =         X       X
    _____/ \_____/ \______     __g__     ______/ \_____/ \_____

    bfirst f >>> bsecond g  = f *** g  = bsecond g >>> bfirst f -- spatial commutativity
    f >>> (g >>> h) = (f >>> g) >>> h

    __f1__     __f2__     __f1 >>> f2__
          \   /  
    (***)  >>>  (***)  =      (***)
    __g1__/   \__g2__     __g1 >>> g2__

    (f1 *** g1) >>> (f2 *** g2) = (f1 >>> f2) *** (g1 >>> g2)
    bswap >>> bswap = id
    bfirst f1 >>> bfirst f2 = bfirst (f1 >>> f2)

These properties make it easy to understand (***) as describing concurrent composition of pipelines. These networks can be much more complex, e.g. (foo *** ((bar *** baz) *** qux)) would describe four concurrent behaviors on potentially distributed signals. Use of bswap, bassoclp, and bassocrp also allow developers to treat (***) as at least conceptually associative and commutative. Those operations are explicit because Haskell encodes the current permutation and association of signals in the type system.

To initially construct a concurrent dataflow, one will generally use the behavior bdup to duplicate a signal. Reactive Demand Programming cannot create a signal from scratch, but can duplicate a signal. Duplicating a signal will also duplicate the signal updates. (The branches won't begin to update independently until interacting with other resources.) Conversely, one can terminate a pipeline with bfst.

    bdup  :: (BProd b) => b x (x :&: x)
    bfst  :: (BProd b) => b (x :&: y) x

Duplicating signals then using them in different ways enables developers to build complex dataflow networks. Sirea has decent dead-code elimination; if you duplicate a complex signal then filter them using bfst to get what you need, Sirea will skip duplicating the signals that aren't used on both paths.

More utility behaviors are derived from bdup and bfst:

    (&&&) :: (BProd b) => b x y -> b x z -> b x (y :&: z)
    f &&& g = bdup >>> (f *** g)

    bsnd  :: (BProd b) => b (x :&: y) y
    bsnd = bswap >>> bfst

    bvoid :: (BProd b) => b x y -> b x x
    bvoid f = bdup >>> bfirst f >>> bsnd

    (|*|) :: (BProd b) => b x y -> b x z -> b x x
    f |*| g = bvoid f >>> bvoid g

Those last two constructors are especially useful: they allow behaviors to conveniently represent declarative statements, i.e. behaviors that exist only for their declarative effects. This is a close analog to the traditional imperative statements, which are executed for imperative side-effects. Declarative statements have nice properties that imperative statements do not, especially being commutative (bvoid f >>> bvoid g = bvoid g >>> bvoid f; f |*| g = g |*| f) and idempotent (bvoid f >>> bvoid f = bvoid f). Declarative statements are also associative and have identity, but those properties are common to imperative.

Sirea performs its own compilation of behaviors, which will eliminate most data plumbing and perform dead-sink eliminations. (E.g. bdup will only duplicate the specific concrete signals that are needed on both paths.)

Behaviors as Multi-Agent Systems

Many systems can be conveniently understood in terms of multiple agents operating in a shared environment. Each agent continuously observes its environment and may attempt to influence the environment or (through environmental resources and a blackboard metaphor) the other agents. Depending on the agents, behaviors may be cooperative or competitive.

In RDP, the |*| operator introduces a behavior that can only be observed through its effects on the environment. This, effectively, describes a composition of agents for a multi-agent system. Consider the following behavior:

    let buildImage = load "myImage.svg" >>> renderJPG >>> save "myImage.jpg" in
    let displayImage = load "myImage.jpg" >>> displayJPG in
    buildImage |*| displayImage

Here, developers can justifiably understand buildImage as an agent with a very specific duty. The same developer, in a different context, might understand buildImage as a pipeline. This flexibility is useful; which understanding serves best will depend on context. The same can be said of displayImage. Multi-agent systems work best when the agents do not name directly interact or name one another: this keeps agents disentangled, and provides developers much freedom to add, remove, or replace agents. However, multi-agent systems often interact indirectly through shared resources in an open system . In this case, buildImage and displayImage interact indirectly, through the filesystem.

Sirea encourages the agent view at the higher level. The Sirea.AgentResource module simplifies breaking a complex application into one agent per task. A typical SireaApp might be considered a single agent or a composite of toplevel agents.

Behavior Switching Networks

In addition to the (:&:) typed signals, Sirea supports (:|:) typed signals. Behaviors that process these signals describe switching networks, where only one subnet is active at a time based on a decision upstream (typically via bsplit). Most of the basic behaviors for (:&:) have a dual for (:|:):

    bleft    :: (BSum b) => b x x' -> b (x :|: y) (x' :|: y)
    bmirror  :: (BSum b) => b (x :|: y) (y :|: x)
    bassocls :: (BSum b) => b (x :|: (y :|: z)) ((x :|: y) :|: z)
    bmerge   :: (BSum b) => b (x :|: x) x
    binl     :: (BSum b) => b x (x :|: y)

    bright   :: (BSum b) => b y y' -> b (x :|: y) (x :|: y')
    bassocrs :: (BSum b) => b ((x :|: y) :|: z) (x :|: (y :|: z))
    (+++)    :: (BSum b) => b x x' -> b y y' -> b (x :|: y) (x' :|: y')
    (|||)    :: (BSum b) => b x z  -> b y z  -> b (x :|: y) z
    binr     :: (BSum b) => b y (x :|: y)

With product (:&:), sum (:|:), and unit (S p ()), developers can represent arbitrary data types - booleans, composition of booleans into 32-bit numbers, and so on - without relying on a second paradigm. Of course, this would be dreadfully inefficient on modern architectures (without a lot of high-level optimizations).

Developers must also support interactions between the (:&:) and (:|:) types. The two basic interactions involve factoring a signal that occurs regardless of choice (bconjoin), or distributing a signal across a choice (bdisjoin). Conjoin is quite trivial - duplicate, filter, and merge. Disjoin, however, requires a little extra attention.

    -- factor `x` from a decision
    bconjoin :: (BSum b, BProd b) => b ((x :&: y) :|: (x :&: z)) (x :&: (y :|: z))
    bconjoin = (getX &&& getYZ)
        where getX = (bfst +++ bfst) >>> bmerge
              getYZ = (bsnd +++ bsnd)

    -- distribute `x` across a decision
    bdisjoin :: (BDisjoin b, SigInP p x) => b (x :&: ((S p () :&: y) :|: z)) ((x :&: y) :|: (x :&: z))

For disjoin, the (S p ()) signal represents the decision. This is necessary because y and z may be complex signals distributed across arbitrary partitions. The SigInP p x indicates that x is fully in partition p. (Sirea avoids any implicit communication between partitions.) The implementation duplicates each concrete signal in x then masks it with the decision signal for the left, and the inverse decision signal for the right.

Between disjoin, dup, and merge, a few familiar utility functions can be defined: bWhen, bUnless, bIfThenElse.

Sadly, there is no useful dual to the multi-agent concept. The dual to bvoid (bskip :: b y x -> b x x) seems useless, except as a way to mark dead code.

Haskell Functions as Behaviors

Sirea provides easy access for applying Haskell functions and propagating Haskell values:

    bfmap  :: (BFmap b) => (x -> y) -> b (S p x) (S p y)
    bconst :: (BFmap b) => c -> b (S p x_) (S p c)
    bzap   :: (BZip b)  => b (S p (x->y) :&: S p x) (S p y)
    bsplit :: (BSplit b)=> b (S p (Either x y)) (S p x :|: S p y)
     
    bzipWith fn = bfirst (bfmap fn) >>> bzap
    bzip = bzipWith (,)
    bsplitOn fn = bfmap fn' >>> bsplit
        where fn' x = if (fn x) then Left x else Right x

These functions can support gathering and transforming data as needed to influence resources. Though, some caution is warranted: RDP is designed for real-time systems. Developers should constrain themselves to functions that are either real-time or close enough. Long-running or batch-processing functions should be modeled as an explicit process manipulating a stateful resource.

Eventually, I would like to compile behaviors for partitions outside the Haskell process, e.g. for client-side JavaScript, CG shaders, or GPGPUs. This can still be achieved, but it will take an extra layer that only partially compiles into Sirea to constrain access to opaque Haskell functions and types.

Staged Programming with Dynamic Behaviors

Useful applications can be developed by composing a static set of behaviors in myriad ways. But dynamic behaviors enable so much more: discovery of resources, open extension, service brokering, runtime upgrade, live programming, dynamic reconfiguration, staged metaprogramming, capability security patterns (grant, attenuation, revocation), and flexible adaptation to a changing environment.

A behavior that allows dynamic behaviors is beval. Evaluation in Reactive Demand Programming is a continuous act, so what beval actually does is compile and install a dataflow network at runtime. The installed behavior will change over time, dynamically, based on a signal. Ideally, beval would look like this:

    beval :: (BDynamic b) => b (S p (b x y) :&: x) y -- IDEAL

This says that behavior type b can install a time-varying instance of the same type, supply some inputs, and get some outputs. Unfortunately, this ideal model has three weaknesses: it does not indicate static latency between x and y, it does not work nicely for behavior transforms, and it may require implicit communication between partitions (if x is not in p). To cover these weaknesses, here is the actual beval behavior:

    beval :: (BDynamic b b', SigInP p x) => DT -> b (S p (b' x y) :&: x) (y :|: S p ()) -- ACTUAL

The DT value provides a static latency for the behavior, and the S p () output indicates an error, which happens if you try to evaluate a behavior that is larger than the given DT value. (I'd prefer to use dependent types for time, but those aren't trivial to model in Haskell.) The b' inner type supports behavior transformers or layers. The SigInP p x constraint ensures all the x signals are in the same partition as the behavior signal.

Dynamic behaviors can serve several of the same roles as (:|:) signals, but (:|:) is more openly composable and may sometimes offer performance advantages. No best practices are yet established for when to use sums vs. dynamic behaviors for RDP, but for a small number of commonly used, statically known choices it will probably be better to favor sums.

NOTE: Sirea uses speculative evaluation to compile and install dynamic behaviors a few seconds before they are necessary. Thus, even though beval indicates only one behavior as active, in practice multiple behaviors are installed and active, computing recent past and near future in parallel. If the dynamic behaviors are relatively stable - and assuming the CPU can keep up with the higher burden - this can reduce latencies experienced by the user.

CAUTION: Compared to first-class functions in Haskell, dynamic behaviors in Sirea are relatively expensive and lack effective cross-level optimizations. Dynamic behaviors for Sirea should be relatively stable, such that the expense of changing behaviors is amortized over time. Use dynamic behaviors where necessary for expressiveness, but use them sparingly.

Spatial Behaviors

Resources are often bound to a partitions. Broadly, the notion of an RDP "partition" might extend to remote services, tabs in a browser, or particular GPUs. Reactive Demand Programming is designed for automatic code distribution. An RDP application behavior is compiled into shards (subprogram behaviors) that are distributed across many different partitions. The shards can efficiently influence and observe resources local to that partition. RDP addresses historically legitimate fears of hosting untrusted code in three ways:

• RDP supports object capability security patterns. Capabilities enable shards to carry very fine-grained proof of authority, and they separate the concern for how the shards obtained those capabilities in the first place.
• In RDP, capabilities are dynamic behaviors, which are provided by signals, which are implicitly traceable and revocable. There is never any risk in an RDP system of authorities being "grandfathered" into the system due to lack of visibility or foresight. The cause for every grant can be traced to a particular agent or behavior. Administrators have a free license for easy takebacks. (This is augmented further by RDP's "open loop" nature: resources in RDP are external, and external resources are easy to extend system with new diagnostics, alerts, observations.)
• RDP is designed for real time systems. The space-time costs associated with any behavior or shard are statically predictable. This is important from a security perspective to control against denial-of-service or buggy code that enters infinite loops. RDP developers who need infinite loops must use external state resources, which are easy to diagnose.

Reactive Demand Programming has strong potential to abstract, install, and extend overlay networks with very little effort. This is a primary design goal of RDP.

Unfortunately, Sirea does none of these things! For convenience with Haskell's module system, Sirea uses type-driven resource access, which is effectively an ambient authority (unless types are propagated in certain ways). Sirea does not enforce real time anything (though does encourage soft real time).

Sirea's scope is limited to the Haskell process. In Sirea, the notion of a partition equates to a humble Haskell thread. The binding of resources to threads in Haskell is mostly for convenience (e.g. for easier state resources, organization) and occasionaly for safety (e.g. for FFI resources, OpenGL TLS, GLFW event queues, etc.). But within this limited scope, Sirea does model automatic code distribution. Partitions are named by type. A concrete signal (S Foo x) specifies a signal exists in partion Foo. A unique thread for that partition will be created (based on a Partition typeclass) when the partition is needed.

The bcross behavior allows signals to move between Sirea partitions:

    bcross :: (BCross b, Partition p, Partition p') => b (S p0 x) (S pf x)

The automatic code distribution aspect is obvious when some behaviors are presented as occurring in another partition than the one you started in. Consider foo >>> bcross >>> bar. Here, the bar behavior may be computed in a different partition than the partition in which foo was computed. Information bout bar must be delivered to the second partition.

While Sirea is currently constrained quite severely to live within one Haskell process, I would like to eventually explore lifting Sirea to operate in open distributed systems. This can potentially be achieved by using higher level behaviors that compile to a mix of Sirea-local and remote behaviors (where the remote shards are more constrained). Since I'm considering something similar to support client-side RDP for sirea-webapps (pages as dynamic behaviors, compiling some code to JavaScript for a client browser) I am considering to provide a limited variation of this feature as part of sirea-webapps.

Even without distributed behaviors, Sirea can interact with distributed resources. This is achieved by modeling a local proxy to a remote resource. The proxy can expose failure modes, e.g. when the network is not available.

Temporal Behaviors

It takes time for signals to propagate through a behavior. If you twiddle a few bits in the input signal, it might be microseconds to milliseconds before you see bits twiddling in the output. Short term, it is often convenient and harmless to pretend that the latency is zero. But, as application behaviors grow in scale, it can prove harmful: the physical latency grows faster than logical latency, and signal updates straggle through the network, falling behind real time. Eventually, you get signal updates telling you what you should have done many milliseconds ago, when it is too late to handle them.

Those straggling updates can be used for retroactive corrections to state, providing RDP a degree of eventual consistency. But for many effects - e.g. sounds played, images rendered - a signal too late is no good.

Use of explicit, logical delay provides developers more control over their RDP computations.

    bdelay :: (BDelay b) => DT -> b x x

The behavior bdelay will delay a signal logically. Fundamentally, the idea is to turn straggling updates into future updates: instead of an update too late, the update might arrive a little early (based on the distance between logical and real time). Future updates are subject to speculative evaluation, anticipation, and buffering. The delay can mask variance in physical latency, hiding scheduler hiccups and similar.

Choosing too large a delay has its own disadvantages: most reactive or real time systems have a tight latency budget, beyond which the quality of the system rapidly degrades. Further, it results in larger buffers and memory overheads. So developers in RDP are under some pressure to specify delays that are large enough but not too large. Fortunately, developers do not need to be very precise or accurate; most resources are robust to an occasional straggler, and the window for "good enough" is quite large in most problem domains. In many cases, computation latencies can be entirely subsumed by communication latencies, i.e. such that developers only add delay at bcross.

The bdelay behavior be applied to components signals in a complex signal type (e.g. bfirst bdelay 0.01 to delay the first signal 10 milliseconds). This is why RDP has asynchronous products and sums for its signal types. But when signals become asynchronous, it is often desirable to synchronize them for an operation. Some operations in Sirea will implicitly synchronize: bzip, bmerge, or bdisjoin. But a behavior for an explicit synchronization barrier is also available:

    bsynch :: (BDelay b) => b x x

The bsynch behavior will take every concrete signal in x and delay it to match the signal with the highest logical latency. This allows developers to synchronize signals without being explicitly aware of their latencies. Synchronization barriers can be very useful for controlling side-effects, ensuring multiple resources and subsystems operate in concert.

Behavior Implementation and Extension

A behavior is compiled into a concrete dataflow network that uses Haskell IO for propagation. This network is then activated by the first signal update. Signal updates are also used to deactivate the behavior, i.e. by indicating the signal is inactive after a certain time. The use of bcross allows different parts of a behavior to compute in different partitions, where each partition is represented by a different Haskell thread.

Between partitions, signal updates are batched into one outbox for each destination. The contents of those outboxes are delivered atomically at the end of the step. At the start of each step, ALL available batches are processed. Multiple updates for one signal will "piggyback" (be combined into one update). A bounded-buffer mechanism is applied at the batch-level between partitions, ensuring fairness and controlling space costs.

Step-driven batch processing ensures an atomic "snapshot" view of other partitions within and between rounds. Snapshot consistency is weaker than "glitch freedom": by observing one resource through lenses of two different partitions, temporary inconsistency is possible. But snapshot consistency eliminates "local" glitches, which are the cause of most problems.

Within each step, updates are processed in three phases. First, every link with a pending update is "touched" to indicate an update will be coming on that link. Second, every local update is processed, with bcross updates going to the relevant outbox. Third, mailboxes are delivered.

Touch and the Update Ordering Problem

The update ordering problem is a performance concern for push-based reactive systems with complex or ad-hoc acyclic dependencies. For example, assume a system whose dependency graph looks like:

    a--b--c--d--e--k
     \/ \/ \/ \/  /
     /\ /\ /\ /\ /
    f--g--h--i--j

In this graph, dependencies flow left to right along the lines. For example, c depends on b and g. Assuming there are pending updates on a and f, there are multiple orderings in which the updates could be processed:

    a,f,b,g,c,h,d,i,e,j,k -- an optimal update ordering
    a,b,h,d,j,k,c,i,e,k,g,c,d,e,k,f,b,h,d,j,k,g,h,c,d,e,i,e,j,k -- a non-optimal ordering

I do not present a worst-case ordering. The worst-case ordering is exponentially worse than the best case. If you know the dependencies, a toplogical sort will provide an optimal ordering. However, for RDP, the dynamic behaviors and openly shared resources (state, demand monitors) make it difficult to determine the dependencies. The "touch" technique used by Sirea is a simple, dynamic solution to the problem: a "touch" is a promise of a pending update. When g is touched by a and f, g knows to wait for an update from both before pushing its own update. By propagating all touches before propagating any updates, the update ordering will be optimal.

A risk when we touch is that we might later decide that an update can be filtered or delayed, so we don't have a real update in that step. When that happens, we'll send an idle rather than a real update.

Robust Cycle Handling

RDP behaviors do not directly express cycles, but can indirectly introduce feedback cycles through external resources. For example:

    readFile "foo.txt" >>> bdelay 0.1 >>> bfmap foo >>> writeFile "foo.txt"

This behavior presumably models a 10Hz cycle that continuously reads and writes the same file assuming there are no filesystem errors or write conflicts. The frequency determined by bdelay 0.1 - each cycle delays 0.1 seconds. This delay is logical (i.e. the thread is not paused), but ultimately results in a corresponding wall-clock delays and thread frequencies.

Note: RDP developers are not encouraged to use cyclic feedback. It is possible, and sometimes unavoidable (due to unknown dependencies in open systems), but feedback is difficult to control and reason about. Fine-grained resources, e.g. using separate state resources for requests and results, can help avoid cycles.

A concern for partition-local cycles is that the touch mechanism may result in a cyclic wait. To resolve this, there is also a test for partition-local cycles that involves passing a unique identifier and listening for the same value. Detected partition-local cycles are then broken across the next step, ensuring progress. For performance reasons involving potential rework, it is preferable to detect cycles and perform as much processing within each step as possible.

Concrete Links and Updates

I've mentioned signal updates, touch, idle, and test for partition-local cycles. These operations are directly reflected in the LnkUp type that is used to implement behaviors:

    data LnkUp a = LnkUp
        { ln_touch  :: IO ()
        , ln_update :: StableT -> T -> Sig a -> IO ()
        , ln_idle   :: StableT -> IO ()
        , ln_cycle  :: Set Unique -> IO ()
        }

This is used under-the-hood. Most users of Sirea shouldn't need to know or use LnkUp, but it occasionally will be valuable for developing new resource adapters or special behaviors.

Parallelism and Performance

Sirea RDP is an excellent target for parallelism in Haskell for a few reasons:

• the (x :&: y) asynchronous products clarify data dependencies. This makes it easier for developers to judge where introducing parrallelism is advantageous. Very little parallelism will be wasted.
• the concrete signal type (S p a) (implemented by Sig a) provides a clean separation between the spatial and temporal aspects of data. It is easy, in Sirea, to specify that the spatial computations occur in parallel while the temporal "spine" of the signal is left to incremental, sequential processing.
• the use of signal updates with explicit stability supports speculative evaluation and optimistic concurrency, similar to lightweight time warp protocols. (Parallelism via optimistic concurrency is really trading efficiency for latency and robustness, but is a very nice way to use that extra CPU.)
• use of bcross models distributed behaviors, potentially multi-processor systems, which are inherently parallel.
• state resources are explicit and external to RDP, and persistent; there is no risk of lazy, parallel folds becoming space leaks.

Sirea provides several convenience functions for developers to control the timing of computations on data:

    bstrat :: (BFmap b) => b (S p (Eval a)) (S p a)
    bseq :: (BFmap b) => b (S p a) (S p a)
    bspark :: (BFmap b) => (x -> ()) -> b (S p x) (S p x)
    bforce :: (BFmap b) => (x -> ()) -> b (S p x) (S p x)
    bstratf :: (BFmap b, Functor f) => (forall e . f e -> e) -> b (S p (f x)) (S p x)

bspark is the most accessible mechanism to add parallelism to a Sirea behavior. It will spin off one spark for each value in a signal, but for only a few values at a time (incrementally, relative to stability), and downstream clients will wait on this computation to finish (as though it were strict). This eliminates risk of losing parallelism, but has the disadvantage of not being very compositional. The reduction (x -> ()) is any sequential strategy, usually rnf from Control.DeepSeq. The bforce behavior is similar but will evaluate in the current partition's thread. A potentially useful idiom is to use bspark just before bcross, such that lazy values are computed "in transit".

The bstrat and bseq behaviors are more primitive. The bstrat will not directly evaluate anything, but will prepare the inner Eval a to evaluate when later computing the signal up to Just a | Nothing. The bseq behavior will, over time, incrementally evaluate the signals up to Just a | Nothing. These are usually paired. The Eval type is an identity monad from Haskell's parallel package. If developers desire to use another pure evaluator type, such as Monad.Par, they might simply use bstratf runParAsync.

The above behaviors are a Sirea user's primary tools to control the whens and wheres of lazy evaluation. But lazy evaluation is not the only performance concern. Other concerns involve caching, memoization, choking signals, and eliminating redundant updates.

At the moment, Sirea unfortunately lacks standard idioms for memoization and caching. The traditional Haskell tricks for memoization (e.g. expressed in Luke Palmer's memocombinators package) can certainly be applied, but I fear those may accummulate too much memory over time. I've been exploring designs for windowed memoization, possibly using history with exponential decay (via a sequence or ringbuffers).

The notion of choking signals involves skipping high-frequency intermediate updates to a signal and showing only the occasional snapshot. This is a very different notion from filtering signals. Choking is inherently a stateful concept because it must hold onto information about the past (at the very least, when the last snapshot was selected). The motivation for choking is usually to either dampen feedback cycles (a dubious application) or to support a fast producer in feeding a slow consumer. In Sirea, choking will be modeled always with support of intermediate stateful resources, and I'm considering creating a dedicated resource just for choking. (Some resources may also perform their own ad-hoc choking, e.g. an OpenGL resource might not display faster than the framerate demanded even if there are many possible intermediate frames.)

An intelligent choke might support a signifigance function, i.e. choking based on time, but allowing a few extra values through if the values are somehow interesting.

For eliminating redundant updates, Sirea does have a ready answer:

    badjeqf :: (BFmap b, Eq x) => b (S p x) (S p x) -- adjacent equality filter

This behavior can improve performance by eliminating many redundant signal updates. There is some cost to perform the filter, of course, so it should be used judiciously. But there may be significant downstream savings for bfmap, bzap, and similar, and much rework avoided. (NOTE: bconst has a simple variation of badjeqf built into it; this is the main advantage of using bconst instead of bfmap . const.)

Behaviors as Arrows

If you are familiar with the Arrows abstraction, invented by John Hughes circa 2000, then you have probably recognized several of the operators presented above: (>>>), (***), (&&&), (+++), (|||), first, second, left, right. Sirea presents RDP as an arrowized model, albeit using bfmap instead of arr, and RDP offers many valuable properties not promised by arrow laws. Haskell's Control.Arrow class is not used. If you are unfamiliar with Arrows, or somewhat intimidated by them, do not fret! Like Monads, Arrows are best learned by using them, by osmosis and exposure, by understanding and manipulating toy examples. If you're feeling comfortable with the syntax and structure of RDP from the README so far, I do recommend reading Understanding Arrows in the Haskell wikibook.

Resources

Resources exist outside the RDP program, but may be programmatically accessed by RDP behaviors. Resources generally include sensors, actuators, and state. Specific examples include keyboard, mouse, graphics display, sound output, filesystem, database, network. External services and FFI can be usefully treated as resources. Signals to resources tend to represent continuous queries or commands.

Collectively, the continuous queries and commands are called demands. The word "demand" was chosen because its definitions and connotations in English fits in many ways. Demands may be for information (queries). Demands may be for action (orders, commands). Demand has connotations of authority and force that mere "requests" do not. Demand, as the word is used for markets and utilities, suggests continuity, concurrency, duration, variation over time. At any given moment, there may be many demands on a resource.

Resources in RDP are demand-driven. At any given instant, the a resource is influenced by the set of active demands on it. And, since signals may represent live queries, each distinct signal may have a distinct response.

The breadth and variety of of sensors, human input devices, output devices, and foreign services is enormous. Further, for every resource, there are many API design choices that affect performance, portability, safety, and ease of use. Users of Sirea, especially early adopters, must occasionally step outside of RDP composition to develop resource adapter (preferably in a BSD3-licensed package prefixed with sirea-).

The process of adapting a resource typically involves introducing a thread (to provide resource-specific polling, maintenance, or event loops) and making some state accessible to behaviors. Also, resources often have dependencies on other resources, configuration information, or state. It is convenient to push most logic into RDP, and to model a resource as exclusively controlled by another RDP application or agent.

• Partitions introduce threads with programmable actions between RDP steps
• PCX simplifies access to state for resource proxies and adapters
• BCX will distribute a PCX context object to primitive behaviors
• AgentResource models resources as controlled by separate RDP apps
• DemandMonitor pushes ad-hoc demand-tracking logics up into RDP

Those are explained in detail in the associated modules.

Sirea 1.0 will include packages supporting the most commonly accessible resources - mouse, keyboard, graphics, web, state, filesystem, sound, time. Developers should (hopefully!) need to write adapters only for more domain specific or esoteric resources and services, and even then only for resources that nobody else has adapted effectively. But when those situations occur, the aforementioned features will keep it from being too onerous.

Specific resources will be discussed in their corresponding packages. However, a few broad resources and idioms will be discussed here.

State

RDP is stateless logic on a stateful grid: the motivation for developing RDP behaviors is, ultimately, to observe and influence stateful resources towards some end. Even sensors and actuators are, abstractly, means to observe and influence a stateful environment. State is always external to RDP behaviors. Orthogonal persistence is very natural. The precise temporal semantics make concurrent shared state much easier in RDP than it would be in most imperative models.

However, programmers from imperative backgrounds must learn new ways of thinking about state and controlling it. RDP influence on state is commutative, idempotent, and continuous. There are many systems that have these characteristics:

• tuple space systems where demands insert or delete tuples on a set
• rules based systems where demands impose rules that predictably influence state
• timed state systems where states are animated by timeouts, cooldowns, or schedules
• machine learning where the state is implicit to a learning or clustering model, but is not easy to control.
• history based state which simply records the values pushed to it, possibly with some expiration or decay model

A simplistic rules-based state model is the reactive state transition system. The resource is in some state, initially 0. Each demand adds a directed bridge between states, such as (4,5). The state follows a predictable path across these bridges, going as far as it can. If rule (0,4) is added, the state will transition from 0 to 4 then immediately from 4 to 5 (assuming the (4,5) bridge is still available). Ambiguity might be resolved predictably by favoring the lowest numbered state. An instantaneous cycle might be resolved by settling in the lowest state.

Reactive state transition could serve a similar purpose as a state machine. It could be augmented with time, e.g. by adding a cooldown time to each transition. It could also be augmented with a stack, e.g. for a "structured" state transition system that requires every trip to be a round trip (a very useful constraint).

There are much more expressive rules systems available, e.g. based on term rewriting or temporal logic.

An advantage of universally external state (besides orthogonal persistence) is the reduced competition or interference between state models. RDP behaviors can easily orchestrate many heterogeneous state resources, and developers may introduce new ones if those from sirea-state prove insufficient.

An important restriction on state in RDP is that state cannot hold onto dynamic behaviors. This restriction is valuable for security, resource management, and persistence. Sirea enforces this property via Haskell's type system. In a distributed system, this can be structurally enforced at serialization. To record a behavior statefully (e.g. for mobile agent abstractions), represent that behavior as code or data, then compile that code into the dynamic behavior.

Demand Monitors

Resources may be influenced by the set of active, concurrent demands. Thus, a simple, useful resource could respond to demands with the set of active, concurrent demands. This concept is called the demand monitor, and is of great practical value for RDP systems. Demand monitors and a few variants are among the few resources provided by sirea-core.

Demand monitors don't directly respond to demand with the set of demands. (An artificial requirement to provide a demand just to observe demands would be inconvenient, and would reduce stability.) Instead, there are two separate facets of a demand monitor: one to receive demands, one to monitor demands. Each distinct demand monitor resource is represented in RDP by a unique pair of behaviors. Demands received by a particular demand monitor are only observable to systems that hold the corresponding monitor facet.

    B (S p x) (S p ())   -- receives demands
    B (S p ()) (S p [x]) -- monitors demands

The basic demand monitor actually returns a Haskell list in some indeterminate order. Not all demands developers might wish to monitor have an Ord class. In that case, it is up to developers to provide the extra discipline to treat the list as a set. However, there are variations that will return a sorted, uniquified set of demands.

One variation of demand monitor is possibly the simplest useful resource: the activity monitor. An activity monitor is essentially a demand monitor for the unit signal: the monitor responds with a simple boolean indicating whether there is any demand at all.

    B (S p ()) (S p ())   -- receives activity
    B (S p ()) (S p Bool) -- monitors activity

Demand monitors and activity monitors are typically composed into more complex behaviors to track demands and use of resources. Demand monitors are also useful as a volatile blackboard for communication between agents, or as a registry for publishing available services or plugins (dynamic behaviors).

Demand monitors have a severe weakness: a large set of demands will tend to be much less stable than any of the contributing signals. This is because an update to any constituent signal will require an update to the monitored signal. A suggested practice for demand monitors is to use many fine-grained demand monitors, one for each role or responsibility. Also, if possible, favor variations of demand monitors that narrow the set of responses (e.g. the activity monitor or a k-maximum monitor).

Anticipation

Reactive Demand Programming is designed to pervasively support speculative evaluation: each signal update carries information about that signal's future, from tens of milliseconds up to a few seconds in the future. Though information about the future is not always stable or accurate, many resources can easily leverage this speculative information:

• A file-system adapter can asynchronously pre-load files that it anticipates it will need in a second.
• A world model might leverage projected updates to improve the quality of current estimates and predictions.
• A constraint model might use projected future constraints to choose solutions that can be expected to remain stable for longer.
• A robotic arm might use speculative commands to plan a smoother motion.

Note: Early RDP designs have bpeek :: DT -> B (S p x) (S p (Maybe x)), such that developers could anticipate on ad-hoc signals. Unfortunately, bpeek breaks merge equivalence: (bpeek 0.1 +++ bpeek 0.1) >>> bmerge is not equivalent to bmerge >>> bpeek 0.1 because the former will anticipate periods of inactivity where the latter does not. Merge equivalence is essential for dynamic behaviors because it allows us to treat dynamic behaviors semantically as if they are continuously expired and replaced. Anticipation now is leveraged only at resources, but remains useful.

Resource Management

Resources in RDP systems are generally demand-driven, i.e. driven by the set of demand signals that query or influence the resource.

Demand driven resource management is naturally very robust: If a demand signal is disrupted for any reason (e.g. decision, network failure, switching dynamic behaviors), it will be removed from the set of demands on the resource. If all demands are removed, the resource can return to an idle or hibernation state, and resource proxies (handles, buffers, etc.) can be removed from process memory. Conversely, when demand on a resource is introduced - or some time before, using anticipation - it is easy to load the necessary resources, prepare local proxies and buffers, and so on.

RDP structurally enforces a property called duration coupling: for every behavior, the input signal has the same activity of the output signal (modulo delay). Basically, you only get a value while you're demanding one. Duration coupling ensures that, when demand is disrupted upstream, it is disrupted downstream after a very predictable latency. It also makes job control and shutdown very easy in RDP. An application is halted but cutting the initial demand signal, and this naturally propagates through the entire RDP behavior.

Demand driven resource management is sufficient for most cases, especially those relevant within a single process.

Stateful resource management can still be expressed, if necessary: model a separate RDP agent to observe state and maintain the demands on behalf of the client. This might be necessary in a distributed system, for long-term disruption tolerance, possibly by a mobile agent abstraction (push code to the remote partition that can compile to an RDP behavior). As with any explicit resource management, discipline and design are necessary to use it safely.

RDP is designed to support resource management and sane partial failures in open distributed systems with buggy or malign services and clients. RDP has no need for global GC, ephemeron tables, or messy hand-written timeouts.

Resource Discovery

RDP supports runtime discovery of resources via first-class dynamic behaviors. Discovery of resources will be achieved through an intermediate resource (e.g. broker, registry, matchmaker). By discovering and reactively utilizing available resources, RDP applications can adapt themselves for their environments. Rather than a static configuration, RDP applications can continue to adapt as the environments change over time.

Resources are always external to RDP behaviors. Consequently, RDP lacks an equivalent to the new expression often used in OOP - no newIORef or newUnique. (Use of new plays havoc with dynamic behaviors, orthogonal persistence, extensibility, and declarative properties.) Fortunately, simple resource discovery idioms can achieve the same purpose:

• compute stable unique locators for resources
• locate resource in an abstract resource space

A locator might involve URLs, session keys, domain values, and so on. The stability of the locator should be on the same order as the desired lifetime. The abstract resource space is a resource that can be navigated via arbitrary locators to find useful resources, generally in a default state.

A tree-shaped resource space, where each subtree is a recursive resource space, is nearly ideal:

• path names can be stabilized using meaningful domain values
• can be securely partitioned; no path from child to parent
• subtree-level operations feasible: reset, clone, splice
• parent can easily observe and influence child resources
• readily supports orthogonal persistence and versioning

You're probably thinking, "hey, that's basically a filesystem!" And you're right. A filesystem metaphor to manage resources is superior in every way to use of new. The tree structure is discoverable, extensible, auditable, persistable, securable, composable, and suitable for declarative access. With a little discipline to ensure stability of schema and locators, the tree structure effectively supports live programming. The ability to audit and discover resources is useful for visual presentation, developer awareness, and debugging.

Sirea includes abstractions for resource discovery: PCX supports type-based resource discovery (via Data.Typeable) and a ResourceSpace uses strings for discovery. Users of Sirea, at least those not involved with developing resource adapters, should never need new.

(Note: one may also provide resources or services. An agent becomes a service provider by publishing a dynamic behavior and metadata to a shared registry, such that potential clients can discover it.)

First-Class Frameworks and Overlay Networks

RDP provides a feature I've never seen in another paradigm: effective support for first-class, composable frameworks. Leveraging first-class behaviors, bidirectional reactive dataflow, and support for effects, many systems that would require painful inversion of control and concurrent event managers in an imperative OOP model can be represented as straight behaviors in RDP. Since frameworks are just behaviors, multiple frameworks are easily composed and will have precise, predictable concurrency properties.

Similarly, RDP is suitable for modeling first-class overlay networks: a single behavior can span many partitions and manage communication between them. By publishing a few services for external agents, these overlay networks can introduce ad-hoc patterns for communication. They can also perform many network-layer optimizations, such as caching or content-delivery.

My intuition is that these features make RDP far more expressive than I have yet imagined or fathomed. At the moment, I only imagine to use frameworks for easy staged metaprogramming: to model compilers, service brokers, etc.

Ad-Hoc Control Flow and Workflow

Programming with control flow is implicitly, and pervasively, stateful. To achieve scalability, developers redundantly duplicate the implicit state to make it explicit, e.g. with Command Patterns and queues and Object Relational Mappers. Implicit state in control flow models seems to be a source of many scalability woes.

RDP is not implicitly stateful. RDP is not a control-flow paradigm.

However, RDP systems can model explicit state resources, and RDP systems easily react to changes in state by causing more changes in state. With some cooperative discipline and design, developers can model any control flow component: mailboxes, stacks, queues, data streaming, promise pipelining, barriers, etc.. RDP is very expressive for modeling ad-hoc control flow systems. Further, many of RDP's fringe benefits survive the control-flow abstraction: orthogonal persistence, precise logical concurrency, speculative evaluation and anticipation, ability to audit and debug control state in live systems. Finally, control flow will be at higher levels, since the underlying RDP can handle a lot of drudge-work for data gathering, data synchronization, job control, and low-level resource management.

With a little abstraction, RDP could prove to be an expressive and pleasant foundation for a hybrid declarative-imperative programming style. The flexibility and fring benefits are especially valuable for workflows, which are essentially problem-specific, persistent control flows.

But I strongly encourage developers to favor declarative designs. Imperative abstraction invites imperative issues. Control flow should be a technique approached with second thoughts and reluctance. Simpler declarative effects will often suffice.