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diff --git a/posts/2024-07-03-frp-with-propagators.md b/posts/2024-07-03-frp-with-propagators.md new file mode 100644 index 0000000..cfb0e30 --- /dev/null +++ b/posts/2024-07-03-frp-with-propagators.md @@ -0,0 +1,1147 @@ +title: Functional reactive user interfaces with propagators +date: 2024-07-08 08:30:00 +tags: lisp, scheme, guile, frp +summary: A look at a prototype functional reactive web UI using the propagator paradigm +--- + +I’ve been interested in functional reactive programming (FRP) for +about a decade now. I even wrote a couple of +[blog](/posts/functional-reactive-programming-in-scheme-with-guile-2d.html) +[posts](/posts/live-asset-reloading-with-guile-2d.html) back in 2014 +describing my experiments. My initial source of inspiration was +[Elm](https://elm-lang.org/), the Haskell-like language for the web +that [once had FRP](https://elm-lang.org/news/farewell-to-frp) as a +core part of the language. From there, I explored the academic +literature on the subject. + +(Sidenote: The Elm of 10 years ago looks quite different than the Elm +of today and I don’t know where to find that time-traveling Mario demo +that sent me down this path in the first place. That demo was really +cool! I’ll update this post later if I can find an archive of it.) + +Ultimately, I created and then abandoned a library that focused on +[FRP for games](/projects/sly.html). It was a neat idea, but the +performance was terrible. The overhead of my kinda-sorta FRP system +was part of the problem, but mostly it was my own inexperience. I +didn’t know how to optimize effectively and my implementation +language, [Guile](https://gnu.org/s/guile), did not have as many +optimization passes as it does now. Also, realtime simulations like +games require much more careful use of heap allocation. + +I found that, overhead aside, FRP is a bad fit for things like +scripting sequences of actions in a game. I don’t want to give up +things like coroutines that make it easy. I’ve learned how different +layers of a program may call for different programming paradigms. +Functional layers rest upoin imperative foundations. Events are built +on top of polling. Languages with expression trees run on machines +that only understand linear sequences. You get the idea. A good +general-purpose language will allow you to compose many paradigms in +the same program. I’m still a big fan of functional programming, but +single paradigm languages do not appeal to me. + +Fast forward 10 years, I find myself thinking about FRP again in a new +context. I now work for the [Spritely +Institute](https://spritely.institute) where we’re researching and +building the next generation of [secure, distributed application +infrastructure](https://spritely.institute/goblins). We want to demo +our tech through easy-to-use web applications, which means we need to +do some UI programming. So, the back burner of my brain has been +mulling over the possibilities. What’s the least painful way to build +web UIs? Is this FRP thing worth revisiting? + +The reason why FRP is so appealing to me (on paper, at least) is that +it allows for writing interactive programs *declaratively*. With FRP, +I can simply describe the *relationships* between the various +time-varying components, and the system wires it all together for me. +I’m spared from *callback hell*, one of the more frightening layers of +hell that forces programs to be written in a kind of +[continuation-passing +style](https://en.wikipedia.org/wiki/Continuation-passing_style) where +timing and state bugs consume more development time as the project +grows. + +## What about React? + +In the time during and since I last experimented with FRP, a different +approach to declarative UI programming has swept the web development +world: [React](https://react.dev/). From React, many other similar +libraries emerged. On the minimalist side there are things like +[Mithril](https://mithril.js.org/) (a favorite of mine), and then +there are bigger players like [Vue](https://vuejs.org/). The term +“reactive” has become overloaded, but in the mainstream software world +it is associated with React and friends. FRP is quite different, +despite sharing the declarative and reactive traits. Both help free +programmers from callback hell, but they achieve their results +differently. + +The React model describes an application as a tree of “components”. +Each component represents a subset of the complete UI element tree. +For each component, there is a template function that takes some +inputs and returns the new desired state of the UI. This function is +called whenever an event occurs that might change the state of the UI. +The template produces a data structure known as a “virtual +[DOM](https://developer.mozilla.org/en-US/docs/Web/API/Document_Object_Model)”. +To realize this new state in the actual DOM, React diffs the previous +tree with the new one and updates, creates, and deletes elements as +necessary. + +With FRP, you describe your program as an acyclic graph of nodes that +contain time-varying values. The actual value of any given node is +determined by a function that maps the current values of some input +nodes into an output value. The system is bootstrapped by handling a +UI event and updating the appropriate root node, which kicks off a +cascade of updates throughout the graph. At the leaf nodes, +side-effects occur that realize the desired state of the application. +Racket’s [FrTime](https://docs.racket-lang.org/frtime/) is one example +of such a system, which is based on Greg Cooper’s 2008 PhD +dissertation [“Integrating Dataflow Evaluation into a Practical +Higher-Order Call-by-Value +Language”](https://cs.brown.edu/people/ghcooper/thesis.pdf). In +FrTime, time-varying values are called “signals”. Elm borrowed this +language, too, and there’s currently a [proposal to add signals to +JavaScript](https://github.com/tc39/proposal-signals). Research into +FRP goes back quite a bit further. Notably, Conal Elliot and Paul +Hudak wrote [“Functional Reactive +Animation”](http://conal.net/papers/icfp97/icfp97.pdf) in 1997. + +## On jank + +The scope of potential change for any given event is larger in React +than FRP. An FRP system flows data through an acyclic graph, updating +only the nodes affected by the event. React requires re-evaluating +the template for each component that needs refreshing and applying a +diff algorithm to determine what needs changing in the currently +rendered UI. The virtual DOM diffing process can be quite wasteful in +terms of both memory usage and processing time, leading to jank on +systems with limited resources like phones. Andy Wingo has done some +interesting analyses of things like [React +Native](https://wingolog.org/archives/2023/04/21/structure-and-interpretation-of-react-native) +and +[Flutter](https://wingolog.org/archives/2023/04/26/structure-and-interpretation-of-flutter) +and covers the subject of jank well. So, while I appreciate the +greatly improved developer experience of React-likes (I wrote my fair +share of frontend code in the jQuery days), I’m less pleased by the +overhead that it pushes onto each user’s computer. React feels like +an important step forward on the declarative UI trail, but it’s not +the destination. + +FRP has the potential for less jank because side-effects (the UI +widget state updates) can be more precise. For example, if a web page +has a text node that displays the number of times the user has clicked +a mouse button, an FRP system could produce a program that would do +the natural thing: Register a click event handler that replaces the +text node with a new one containing the updated count. We don’t need +to diff the whole page, nor do we need to create a wrapper component +to update a subset of the page. The scope is narrow, so we can apply +smaller updates. No virtual DOM necessary. There is, of course, +overhead to maintaining the graph of time-varying values. The +underlying runtime is free to use mutable state, but the user layer +must take care to use pure functions and persistent, immutable data +structures. This has a cost, but the per-event cost to refresh the UI +feels much more reasonable when compared to React. From here on, I +will stop talking about React and start exploring if FRP might really +offer a more expressive way to do declarative UI without too much +overhead. But first, we need to talk about a serious problem. + +## FRP is acyclic + +FRP is no silver bullet. As mentioned earlier, FRP graphs are +typically of the acyclic flavor. This limits the set of UIs that are +possible to create with FRP. Is this the cost of declarativeness? To +demonstrate the problem, consider a color picker tool that has sliders +for both the red-green-blue and hue-saturation-value representations +of color: + + + +In this program, updating the sliders on the RGB side should change +the values of the sliders on the HSV side, and vice versa. This forms +a cycle between the two sets of sliders. It’s possible to express +cycles like this with event callbacks, though it’s messy and +error-prone to do manually. We’d like a system built on top of event +callbacks that can do the right thing without strange glitches or +worse, unbounded loops. + +## Propagators to the rescue + +Fortunately, I didn’t create that diagram above. It’s from Alexey +Radul’s 2009 PhD dissertation: [“Propagation Networks: A Flexible and +Expressive Substrate for +Computation”](https://dspace.mit.edu/bitstream/handle/1721.1/49525/MIT-CSAIL-TR-2009-053.pdf). +This paper dedicates a section to explaining how FRP can be built on +top a more general paradigm called *propagation networks*, or just +*propagators* for short. The paper is lengthy, naturally, but it is +written in an approachable style. There isn’t any terse math notation +and there are plenty of code examples. As far as PhD dissertations +go, this one is a real page turner! + +Here is a quote from section 5.5 about FrTime (with emphasis added by +me): + +> FrTime is built around a custom propagation infrastructure; it +> nicely achieves both non-recomputation and glitch avoidance, but +> unfortunately, the propagation system is **nontrivially +> complicated**, and **specialized for the purpose of supporting +> functional reactivity**. In particular, the FrTime system **imposes +> the invariant that the propagation graph be acyclic**, and +> guarantees that it will **execute the propagators in +> topological-sort order**. This simplifies the propagators +> themselves, but greatly complicates the runtime system, especially +> because it has to **dynamically recompute the sort order** when the +> structure of some portion of the graph changes (as when the +> predicate of a conditional changes from true to false, and the other +> branch must now be computed). That complexity, in turn, makes that +> runtime system **unsuitable for other kinds of propagation**, and +> even makes it **difficult for other kinds of propagation to +> interoperate** with it. + +So, the claim is that FRP-on-propagators can remove the acyclic +restriction, reduce complexity, and improve interoperability. But +what are propagators? I like how the book [“Software Design for +Flexibility”](https://mitpress.mit.edu/9780262045490/software-design-for-flexibility/) +(2021) defines them (again, with emphasis added by me): + +> “The propagator model is built on the idea that the basic +> computational elements are propagators, **autonomous independent +> machines interconnected by shared cells through which they +> communicate**. Each propagator machine continuously examines the +> cells is is connected to, and adds information to some cells based +> on computations it can make from information it can get from others. +> **Cells accumulate information and propagators produce +> information**.” + +Research on propagators goes back a long way (you’ll even find a form +of propagators in the all-time classic [“Structure and Interpretation +of Computer +Programs”](https://sarabander.github.io/sicp/html/3_002e3.xhtml#g_t3_002e3_002e5)), +but it was Alexey Radul that discovered how to unify many different +types of special-purpose propagation systems so that they could share +a generic substrate and interoperate. + +Perhaps the most exciting application of the propagator model is AI, +where it can be used to create “explainable AI” that keeps track of +how a particular output was computed. This type of AI stands in stark +contrast to the much hyped mainstream machine learning models that +hoover up our planet’s precious natural resources to produce black +boxes that generate [impressive +bullshit](https://link.springer.com/article/10.1007/s10676-024-09775-5). +But anyway! + +The diagram above can also be found in section 5.5 of the +dissertation. Here’s the description: + +> “A network for a widget for RGB and HSV color selection. Traditional +> functional reactive systems have qualms about the circularity, but +> general-purpose propagation handles it automatically.” + +This color picker felt like a good, achievable target for a prototype. +The propagator network is small and there are only a handful of UI +elements, yet it will test if the FRP system is working correctly. + +## The prototype + +I read Alexey Radul’s dissertation, and then read chapter 7 of +Software Design for Flexibility, which is all about propagators. Both +use Scheme as the implementation language. The latter makes no +mention of FRP, and while the former explains *how* FRP can be +implemented in terms of propagators, there is (understandably) no code +included. So, I had to implement it for myself to test my +understanding. Unsurprisingly, I had misunderstood many things along +the way and my iterations of broken code let me know that. +Implementation is the best teacher. + +After much code fiddling, I was able to create a working prototype of +the color picker. Here it is below: + + + +This prototype is written in Scheme and uses +[Hoot](https://spritely.institute/hoot) to compile it to WebAssembly +so I can embed it right here in my blog. Sure beats a screenshot or +video! This prototype contains a minimal propagator implementation +that is sufficient to bootstrap a similarly minimal FRP +implementation. + +## Propagator implementation + +Let’s take a look at the code and see how it all works, starting with +propagation. There are two essential data types: Cells and +propagators. Cells accumulate information about a value, ranging from +*nothing*, some form of *partial information*, or a complete value. +The concept of partial information is Alexey Radul’s major +contribution to the propagator model. It is through partial +information structures that general-purpose propagators can be used to +implement logic programming, probabilistic programming, type +inference, and FRP, among others. I’m going to keep things as simple +as possible in this post (it’s a big enough infodump already), but do +read the propagator literature if phrases like “dependency directed +backtracking” and “truth maintenance system” sound like a good time to +you. + +Cells start out knowing *nothing*, so we need a special, unique value +to represent nothing: + +```scheme +(define-record-type <nothing> + (make-nothing) + %nothing?) +(define nothing (make-nothing)) +(define (nothing? x) (eq? x nothing)) +``` + +Any unique (as in `eq?`) object would do, such as `(list ’nothing)`, +but I chose to use a record type because I like the way it prints. + +In addition to nothing, the propagator model also has a notion of +*contradictions*. If one source of information says there are four +lights, but another says there are five, then we have a contradiction. +Propagation networks do not fall apart in the presence of +contradictory information. There’s a data type that captures +information about them and they can be resolved in a context-specific +manner. I mention contradictions only for the sake of completeness, +as a general-purpose propagator system needs to handle them. This +prototype does not create any contradictions, so I won’t mention them +again. + +Now we can define a cell type: + +```scheme +(define-record-type <cell> + (%make-cell relations neighbors content strongest + equivalent? merge find-strongest handle-contradiction) + cell? + (relations cell-relations) + (neighbors cell-neighbors set-cell-neighbors!) + (content cell-content set-cell-content!) + (strongest cell-strongest set-cell-strongest!) + ;; Dispatch table: + (equivalent? cell-equivalent?) + (merge cell-merge) + (find-strongest cell-find-strongest) + (handle-contradiction cell-handle-contradiction)) +``` + +The details of *how* a cell does things like merge old information +with new information is left intentionally unanswered at this level of +abstraction. Different systems built on propagators will want to +handle things in different ways. In the propagator literature, you’ll +see generic procedures used extensively for this purpose. For the +sake of simplicity, I use a dispatch table instead. It would be easy +to layer generic merge on top later, if we wanted. + +The constructor for cells sets the default contents to nothing: + +```scheme +(define default-equivalent? equal?) +;; But what about partial information??? +(define (default-merge old new) new) +(define (default-find-strongest content) content) +(define (default-handle-contradiction cell) (values)) + +(define* (make-cell name #:key + (equivalent? default-equivalent?) + (merge default-merge) + (find-strongest default-find-strongest) + (handle-contradiction default-handle-contradiction)) + (let ((cell (%make-cell (make-relations name) '() nothing nothing + equivalent? merge find-strongest + handle-contradiction))) + (add-child! (current-parent) cell) + cell)) +``` + +The default procedures used for the dispatch table are either no-ops +or trivial. The default `merge` doesn’t merge at all, it just +clobbers the old with the new. It’s up to the layers on top to +provide more useful implementations. + +Cells can have neighbors (which will be propagators): + +```scheme +(define (add-cell-neighbor! cell neighbor) + (set-cell-neighbors! cell (lset-adjoin eq? (cell-neighbors cell) neighbor))) +``` + +Since cells accumulate information, there are procedures for adding +new content and finding the current strongest value contained within: + +```scheme +(define (add-cell-content! cell new) + (match cell + (($ <cell> _ neighbors content strongest equivalent? merge + find-strongest handle-contradiction) + (let ((content* (merge content new))) + (set-cell-content! cell content*) + (let ((strongest* (find-strongest content*))) + (cond + ;; New strongest value is equivalent to the old one. No need + ;; to alert propagators. + ((equivalent? strongest strongest*) + (set-cell-strongest! cell strongest*)) + ;; Uh oh, a contradiction! Call handler. + ((contradiction? strongest*) + (set-cell-strongest! cell strongest*) + (handle-contradiction cell)) + ;; Strongest value has changed. Alert the propagators! + (else + (set-cell-strongest! cell strongest*) + (for-each alert-propagator! neighbors)))))))) +``` + +Next up is the propagator type. Propagators can be *activated* to +create information using content stored in cells and store their +results in some other cells, forming a graph. Data flow is not forced +to be directional. Cycles are not only permitted, but very common in +practice. So, propagators keep track of both their input and output +cells: + +```scheme +(define-record-type <propagator> + (%make-propagator relations inputs outputs activate) + propagator? + (relations propagator-relations) + (inputs propagator-inputs) + (outputs propagator-outputs) + (activate propagator-activate)) +``` + +Propagators can be *alerted* to schedule themselves to be re-evaluted: + +```scheme +(define (alert-propagator! propagator) + (queue-task! (propagator-activate propagator))) +``` + +The constructor for propagators adds the new propagator as a neighbor +to all input cells and then calls `alert-propagator!` to bootstrap it: + +```scheme +(define (make-propagator name inputs outputs activate) + (let ((propagator (%make-propagator (make-relations name) + inputs outputs activate))) + (add-child! (current-parent) propagator) + (for-each (lambda (cell) + (add-cell-neighbor! cell propagator)) + inputs) + (alert-propagator! propagator) + propagator)) +``` + +There are two main classes of propagators that will be used: +**primitive propagators** and **constraint propagators**. Primitive +propagators are directional; they apply a function to the values of +some input cells and write the result to an output cell: + +```scheme +(define (unusable-value? x) + (or (nothing? x) (contradiction? x))) + +(define (primitive-propagator name f) + (match-lambda* + ((inputs ... output) + (define (activate) + (let ((args (map cell-strongest inputs))) + (unless (any unusable-value? args) + (add-cell-content! output (apply f args))))) + (make-propagator name inputs (list output) activate)))) +``` + +We can use `primitive-propagator` to lift standard Scheme procedures +into the realm of propagators. Here’s how we’d make and use an +addition propagator: + +```scheme +(define p:+ (primitive-propagator +)) +(define a (make-cell)) +(define b (make-cell)) +(define c (make-cell)) +(p:+ a b c) +(add-cell-content! a 1) +(add-cell-content! b 3) +;; After the scheduler runs… +(cell-strongest c) ;; => 4 +``` + +It is from these primitive propagators that we can build more +complicated, compound propagators. Compound propagators compose +primitive propagators (or other compound propagators) and lazily +construct their section of the network upon first activation: + +```scheme +(define (compound-propagator name inputs outputs build) + (let ((built? #f)) + (define (maybe-build) + (unless (or built? + (and (not (null? inputs)) + (every unusable-value? (map cell-strongest inputs)))) + (parameterize ((current-parent (propagator-relations propagator))) + (build) + (set! built? #t)))) + (define propagator (make-propagator name inputs outputs maybe-build)) + propagator)) +``` + +By this point you may be wondering what all the references to +`current-parent` are about. It is for tracking the parent/child +relationships of the cells and propagators in the network. This could +be helpful for things like visualizing the network, but we aren’t +going to do anything with it today. I’ve omitted all of the other +relation code for this reason. + +Constraint propagators are compound propagators whose inputs and +outputs are the same, which results in bidirectional propagation: + +```scheme +(define (constraint-propagator name cells build) + (compound-propagator name cells cells build)) +``` + +Using primitive propagators for addition and subtraction, we can build +a constraint propagator for the equation `a + b = c`: + +```scheme +(define p:+ (primitive-propagator +)) +(define p:- (primitive-propagator -)) +(define (c:sum a b c) + (define (build) + (p:+ a b c) + (p:- c a b) + (p:- c b a)) + (constraint-propagator 'sum (list a b c) build)) +(define a (make-cell)) +(define b (make-cell)) +(define c (make-cell)) +(c:sum a b c) +(add-cell-content! a 1) +(add-cell-content! c 4) +;; After the scheduler runs… +(cell-strongest b) ;; => 3 +``` + +With a constraint, we can populate any two cells and the propagation +system will figure out the value of the third. Pretty cool! + +This is a good enough propagation system for the FRP prototype. + +## FRP implementation + +If you’re familiar with terminology from other FRP systems like +“signals” and “behaviors” then set that knowledge aside for now. We +need some new nouns. But first, a bit about the problems that need +solving in order to implement FRP on top of general-purpose +propagators: + +* The propagator model does not enforce any ordering of *when* + propagators will be re-activated in relation to each other. If + we’re not careful, something in the network could compute a value + using a mix of fresh and stale data, resulting in a momentary + “glitch” that could be noticeable in the UI. + +* The presence of cycles introduce a crisis of identity. It’s not + sufficient for every time-varying value to be treated as its own + self. In the color picker, the RGB values and the HSV values are + two representations of *the same thing*. We need a new notion of + identity to capture this and prevent unnecessary churn and glitches + in the network. + +For starters, we will create a “reactive identifier” (needs a better +name) data type that serves two purposes: + +1) To create shared identity between different information sources +that are *logically* part of the same thing + +2) To create localized timestamps for values associated with this identity + +```scheme +(define-record-type <reactive-id> + (%make-reactive-id name clock) + reactive-id? + (name reactive-id-name) + (clock reactive-id-clock set-reactive-id-clock!)) + +(define (make-reactive-id name) + (%make-reactive-id name 0)) + +(define (reactive-id-tick! id) + (let ((t (1+ (reactive-id-clock id)))) + (set-reactive-id-clock! id t) + `((,id . ,t)))) +``` + +Giving each logical identity in the FRP system its own clock +eliminates the need for a global clock, avoiding a potentially +troublesome source of centralization. This is kind of like how +[Lamport timestamps](https://en.wikipedia.org/wiki/Lamport_timestamp) +are used in distributed systems. + +We also need a data type that captures the value of something at a +particular point in time. Since the cruel march of time is unceasing, +these are *ephemeral* values: + +```scheme +(define-record-type <ephemeral> + (make-ephemeral value timestamps) + ephemeral? + (value ephemeral-value) + ;; Association list mapping identity -> time + (timestamps ephemeral-timestamps)) +``` + +Ephemerals are boxes that contain some arbitrary data with a bunch of +shipping labels slapped onto the outside explaining from whence they +came. This is the partial information structure that our propagators +will manipulate and add to cells. + +Here’s how to say “the mouse position was (1, 2) at time 3” in code: + +```scheme +(define mouse-position (make-reactive-id ’mouse-position)) +(make-ephemeral #(1 2) `((,mouse-position . 3))) +``` + +We need to perform a few operations with ephemerals: + +1) Test if one ephemeral is *fresher* (more recent) than another + +2) Compose the timestamps from several inputs to form an aggregate +timestamp for an output, but only if all timestamps for each distinct +identifier match (no mixing of fresh and stale values) + +3) Merge two ephemerals when cell content is added + +```scheme +(define (ephemeral-fresher? a b) + (let ((b-inputs (ephemeral-timestamps b))) + (let lp ((a-inputs (ephemeral-timestamps a))) + (match a-inputs + (() #t) + (((key . a-time) . rest) + (match (assq-ref b-inputs key) + (#f (lp rest)) + (b-time + (and (> a-time b-time) + (lp rest))))))))) + +(define (merge-ephemerals old new) + (cond + ((nothing? old) new) + ((nothing? new) old) + (else (if (ephemeral-fresher? new old) new old)))) + +(define (merge-ephemeral-timestamps ephemerals) + (define (adjoin-keys alist keys) + (fold (lambda (key+value keys) + (match key+value + ((key . _) + (lset-adjoin eq? keys key)))) + keys alist)) + (define (check-timestamps id) + (let lp ((ephemerals ephemerals) (t #f)) + (match ephemerals + (() t) + ((($ <ephemeral> _ timestamps) . rest) + (match (assq-ref timestamps id) + ;; No timestamp for this id in this ephemeral. Continue. + (#f (lp rest t)) + (t* + (if t + ;; If timestamps don't match then we have a mix of + ;; fresh and stale values, so return #f. Otherwise, + ;; continue. + (and (= t t*) (lp rest t)) + ;; Initialize timestamp and continue. + (lp rest t*)))))))) + ;; Build a set of all reactive identifiers across all ephemerals. + (let ((ids (fold (lambda (ephemeral ids) + (adjoin-keys (ephemeral-timestamps ephemeral) ids)) + '() ephemerals))) + (let lp ((ids ids) (timestamps '())) + (match ids + (() timestamps) + ((id . rest) + ;; Check for consistent timestamps. If they are consistent + ;; then add it to the alist and continue. Otherwise, return + ;; #f. + (let ((t (check-timestamps id))) + (and t (lp rest (cons (cons id t) timestamps))))))))) +``` + +Example usage: + +```scheme +(define e1 (make-ephemeral #(3 4) `((,mouse-position . 4)))) +(define e2 (make-ephemeral #(1 2) `((,mouse-position . 3)))) + +(ephemeral-fresher? e1 e2) ;; => #t +(merge-ephemerals e1 e2) ;; => e1 + +(merge-ephemeral-timestamps (list e1 e2)) ;; => #f + +(define (mouse-max-coordinate e) + (match e + (($ <ephemeral> #(x y) timestamps) + (make-ephemeral (max x y) timestamps)))) +(define e3 (mouse-max-coordinate e1)) +(merge-ephemeral-timestamps (list e1 e3)) ;; => ((mouse-position . 4)) +``` + +Now we can build a primitive propagator constructor that lifts +ordinary Scheme procedures so that they work with ephemerals: + +```scheme +(define (ephemeral-wrap proc) + (match-lambda* + ((and ephemerals (($ <ephemeral> args) ...)) + (match (merge-ephemeral-timestamps ephemerals) + (#f nothing) + (timestamps (make-ephemeral (apply proc args) timestamps)))))) + +(define* (primitive-reactive-propagator name proc) + (primitive-propagator name (ephemeral-wrap proc))) +``` + +## Reactive UI implementation + +Now we need some propagators that live at the edges of our network +that know how to interact with the DOM and can do the following: + +1) Sync a DOM element attribute with the value of a cell + +2) Create a two-way data binding between an element’s `value` attribute +and a cell + +3) Render the markup in a cell and place it into the DOM tree in the +right location + +Syncing an element attribute is a directional operation and the +easiest to implement: + +```scheme +(define (r:attribute input elem attr) + (let ((attr (symbol->string attr))) + (define (activate) + (match (cell-strongest input) + (($ <ephemeral> val) + (attribute-set! elem attr (obj->string val))) + ;; Ignore unusable values. + (_ (values)))) + (make-propagator 'r:attribute (list input) '() activate))) +``` + +Two-way data binding is more involved. First, a new data type is used +to capture the necessary information: + +```scheme +(define-record-type <binding> + (make-binding id cell default group) + binding? + (id binding-id) + (cell binding-cell) + (default binding-default) + (group binding-group)) + +(define* (binding id cell #:key (default nothing) (group '())) + (make-binding id cell default group)) +``` + +And then a reactive propagator applies that binding to a specific DOM +element: + +```scheme +(define* (r:binding binding elem) + (match binding + (($ <binding> id cell default group) + (define (update new) + (unless (nothing? new) + (let ((timestamp (reactive-id-tick! id))) + (add-cell-content! cell (make-ephemeral new timestamp)) + ;; Freshen timestamps for all cells in the same group. + (for-each (lambda (other) + (unless (eq? other cell) + (match (cell-strongest other) + (($ <ephemeral> val) + (add-cell-content! other (make-ephemeral val timestamp))) + (_ #f)))) + group)))) + ;; Sync the element's value with the cell's value. + (define (activate) + (match (cell-strongest cell) + (($ <ephemeral> val) + (set-value! elem (obj->string val))) + (_ (values)))) + ;; Initialize element value with the default value. + (update default) + ;; Sync the cell's value with the element's value. + (add-event-listener! elem "input" + (procedure->external + (lambda (event) + (update (string->obj (value elem)))))) + (make-propagator 'r:binding (list cell) '() activate)))) +``` + +A simple method for rendering to the DOM is to replace some element +with a newly created element based on the current ephemeral value of a +cell: + +```scheme +(define (r:dom input elem) + (define (activate) + (match (cell-strongest input) + (($ <ephemeral> exp) + (let ((new (sxml->dom exp))) + (replace-with! elem new) + (set! elem new))) + (_ (values)))) + (make-propagator 'dom (list input) '() activate)) +``` + +The `sxml->dom` procedure deserves some further explanation. To +create a subtree of new elements, we have two options: + +1) Use something like the +[`innerHTML`](https://developer.mozilla.org/en-US/docs/Web/API/Element/innerHTML) +element property to insert arbitrary HTML as a string and let the +browser parse and build the elements. + +2) Use a Scheme data structure that we can iterate over and make the +relevant `document.createTextNode`, `document.createElement`, +etc. calls. + +Option 1 might be a shortcut and would be fine for a quick prototype, +but it would mean that to generate the HTML we’d be stuck using raw +strings. While string-based templating is commonplace, we can +certainly [do +better](https://www.more-magic.net/posts/structurally-fixing-injection-bugs.html) +in Scheme. Option 2 is actually not too much work and we get to use +Lisp’s universal templating system, +[`quasiquote`](https://www.gnu.org/software/guile/manual/r5rs/Quasiquotation.html), +to write our markup. + +Thankfully, [SXML](https://en.wikipedia.org/wiki/SXML) already exists +for this purpose. SXML is an alternative XML syntax that uses +s-expressions. Since Scheme uses s-expression syntax, it’s a natural +fit. + +Example: + +```scheme +'(article + (h1 "SXML is neat") + (img (@ (src "cool.jpg") (alt "cool image"))) + (p "Yeah, SXML is " (em "pretty neato!"))) +``` + +Instead of using it to generate HTML text, we’ll instead generate a +tree of DOM elements. Furthermore, because we’re now in full control +of how the element tree is built, we can build in support for reactive +propagators! + +Check it out: + +```scheme +(define (sxml->dom exp) + (match exp + ;; The simple case: a string representing a text node. + ((? string? str) + (make-text-node str)) + ((? number? num) + (make-text-node (number->string num))) + ;; A cell containing SXML (or nothing) + ((? cell? cell) + (let ((elem (cell->elem cell))) + (r:dom cell elem) + elem)) + ;; An element tree. The first item is the HTML tag. + (((? symbol? tag) . body) + ;; Create a new element with the given tag. + (let ((elem (make-element (symbol->string tag)))) + (define (add-children children) + ;; Recursively call sxml->dom for each child node and + ;; append it to elem. + (for-each (lambda (child) + (append-child! elem (sxml->dom child))) + children)) + (match body + ((('@ . attrs) . children) + (for-each (lambda (attr) + (match attr + (((? symbol? name) (? string? val)) + (attribute-set! elem + (symbol->string name) + val)) + (((? symbol? name) (? number? val)) + (attribute-set! elem + (symbol->string name) + (number->string val))) + (((? symbol? name) (? cell? cell)) + (r:attribute cell elem name)) + ;; The value attribute is special and can be + ;; used to setup a 2-way data binding. + (('value (? binding? binding)) + (r:binding binding elem)))) + attrs) + (add-children children)) + (children (add-children children))) + elem)))) +``` + +Notice the calls to `r:dom`, `r:attribute`, and `r:binding`. A cell +can be used in either the context of an element (`r:dom`) or an +attribute (`r:attribute`). The `value` attribute gets the additional +superpower of `r:binding`. We will make use of this when it is time +to render the color picker UI! + +## Color picker implementation + +Alright, I’ve spent a lot of time explaining how I built a minimal +propagator and FRP system from first principles on top of +Hoot-flavored Scheme. Let’s *finally* write the dang color picker! + +First we need some data types to represent RGB and HSV colors: + +```scheme +(define-record-type <rgb-color> + (rgb-color r g b) + rgb-color? + (r rgb-color-r) + (g rgb-color-g) + (b rgb-color-b)) + +(define-record-type <hsv-color> + (hsv-color h s v) + hsv-color? + (h hsv-color-h) + (s hsv-color-s) + (v hsv-color-v)) +``` + +And procedures to convert RGB to HSV and vice versa: + +```scheme +(define (rgb->hsv rgb) + (match rgb + (($ <rgb-color> r g b) + (let* ((cmax (max r g b)) + (cmin (min r g b)) + (delta (- cmax cmin))) + (hsv-color (cond + ((= delta 0.0) 0.0) + ((= cmax r) + (let ((h (* 60.0 (fmod (/ (- g b) delta) 6.0)))) + (if (< h 0.0) (+ h 360.0) h))) + ((= cmax g) (* 60.0 (+ (/ (- b r) delta) 2.0))) + ((= cmax b) (* 60.0 (+ (/ (- r g) delta) 4.0)))) + (if (= cmax 0.0) + 0.0 + (/ delta cmax)) + cmax))))) + +(define (hsv->rgb hsv) + (match hsv + (($ <hsv-color> h s v) + (let* ((h' (/ h 60.0)) + (c (* v s)) + (x (* c (- 1.0 (abs (- (fmod h' 2.0) 1.0))))) + (m (- v c))) + (define-values (r' g' b') + (cond + ((<= 0.0 h 60.0) (values c x 0.0)) + ((<= h 120.0) (values x c 0.0)) + ((<= h 180.0) (values 0.0 c x)) + ((<= h 240.0) (values 0.0 x c)) + ((<= h 300.0) (values x 0.0 c)) + ((<= h 360.0) (values c 0.0 x)))) + (rgb-color (+ r' m) (+ g' m) (+ b' m)))))) +``` + +We also need some procedures to convert colors into the hexadecimal +representations we’re used to seeing: + +```scheme +(define (uniform->byte x) + (inexact->exact (round (* x 255.0)))) + +(define (rgb->int rgb) + (match rgb + (($ <rgb-color> r g b) + (+ (* (uniform->byte r) (ash 1 16)) + (* (uniform->byte g) (ash 1 8)) + (uniform->byte b))))) + +(define (rgb->hex-string rgb) + (list->string + (cons #\# + (let lp ((i 0) (n (rgb->int rgb)) (out '())) + (if (= i 6) + out + (lp (1+ i) (ash n -4) + (cons (integer->char + (let ((digit (logand n 15))) + (+ (if (< digit 10) + (char->integer #\0) + (- (char->integer #\a) 10)) + digit))) + out))))))) + +(define (rgb-hex->style hex) + (string-append "background-color: " hex ";")) +``` + +Now we can lift the color API into primitive reactive propagator +constructors: + +```scheme +(define-syntax-rule (define-primitive-reactive-propagator name proc) + (define name (primitive-reactive-propagator 'name proc))) + +(define-primitive-reactive-propagator r:rgb-color rgb-color) +(define-primitive-reactive-propagator r:rgb-color-r rgb-color-r) +(define-primitive-reactive-propagator r:rgb-color-g rgb-color-g) +(define-primitive-reactive-propagator r:rgb-color-b rgb-color-b) +(define-primitive-reactive-propagator r:hsv-color hsv-color) +(define-primitive-reactive-propagator r:hsv-color-h hsv-color-h) +(define-primitive-reactive-propagator r:hsv-color-s hsv-color-s) +(define-primitive-reactive-propagator r:hsv-color-v hsv-color-v) +(define-primitive-reactive-propagator r:rgb->hsv rgb->hsv) +(define-primitive-reactive-propagator r:hsv->rgb hsv->rgb) +(define-primitive-reactive-propagator r:rgb->hex-string rgb->hex-string) +(define-primitive-reactive-propagator r:rgb-hex->style rgb-hex->style) +``` + +From those primitive propagators, we can build the necessary +constraint propagators: + +```scheme +(define (r:components<->rgb r g b rgb) + (define (build) + (r:rgb-color r g b rgb) + (r:rgb-color-r rgb r) + (r:rgb-color-g rgb g) + (r:rgb-color-b rgb b)) + (constraint-propagator 'r:components<->rgb (list r g b rgb) build)) + +(define (r:components<->hsv h s v hsv) + (define (build) + (r:hsv-color h s v hsv) + (r:hsv-color-h hsv h) + (r:hsv-color-s hsv s) + (r:hsv-color-v hsv v)) + (constraint-propagator 'r:components<->hsv (list h s v hsv) build)) + +(define (r:rgb<->hsv rgb hsv) + (define (build) + (r:rgb->hsv rgb hsv) + (r:hsv->rgb hsv rgb)) + (constraint-propagator 'r:components<->hsv (list rgb hsv) build)) +``` + +At long last, we are ready to define the UI! Here it is: + +```scheme +(define (render exp) + (append-child! (document-body) (sxml->dom exp))) + +(define* (slider id name min max default #:optional (step "any")) + `(div (@ (class "slider")) + (label (@ (for ,id)) ,name) + (input (@ (id ,id) (type "range") + (min ,min) (max ,max) (step ,step) + (value ,default))))) + +(define (uslider id name default) ; [0,1] slider + (slider id name 0 1 default)) + +(define-syntax-rule (with-cells (name ...) body . body*) + (let ((name (make-cell 'name #:merge merge-ephemerals)) ...) body . body*)) + +(with-cells (r g b rgb h s v hsv hex style) + (define color (make-reactive-id 'color)) + (define rgb-group (list r g b)) + (define hsv-group (list h s v)) + (r:components<->rgb r g b rgb) + (r:components<->hsv h s v hsv) + (r:rgb<->hsv rgb hsv) + (r:rgb->hex-string rgb hex) + (r:rgb-hex->style hex style) + (render + `(div + (h1 "Color Picker") + (div (@ (class "preview")) + (div (@ (class "color-block") (style ,style))) + (div (@ (class "hex")) ,hex)) + (fieldset + (legend "RGB") + ,(uslider "red" "Red" + (binding color r #:default 1.0 #:group rgb-group)) + ,(uslider "green" "Green" + (binding color g #:default 0.0 #:group rgb-group)) + ,(uslider "blue" "Blue" + (binding color b #:default 1.0 #:group rgb-group))) + (fieldset + (legend "HSV") + ,(slider "hue" "Hue" 0 360 (binding color h #:group hsv-group)) + ,(uslider "saturation" "Saturation" (binding color s #:group hsv-group)) + ,(uslider "value" "Value" (binding color v #:group hsv-group)))))) +``` + +Each color channel (R, G, B, H, S, and V) has a cell which is bound to +a slider (`<input type="range">`). All six sliders are identified as +`color`, so adjusting *any of them* increments `color`’s timestamp. +The R, G, and B sliders form one input group, and the H, S, and V +sliders form another. By grouping the related sliders together, +whenever one of the sliders is moved, *all members* of the group will +have their ephemeral value refreshed with the latest timestamp. This +behavior is *crucial* because otherwise the `r:components<->rgb` and +`r:components<->hsv` propagators would see that one color channel has +a fresher value than the other two and *do nothing*. Since the +underlying propagator infrastructure does not enforce activation +order, reactive propagators *must* wait until their inputs reach a +consistent state where the timestamps for a given reactive identifier +are all the same. + +With this setup, changing a slider on the RGB side will cause a new +color value to propagate over to the HSV side. Because the +relationship is cyclical, the HSV side will then attempt to propagate +an equivalent color value back to the RGB side! This could be bad +news, but since the current RGB value is equally fresh (same +timestamp), the propagation stops right there. Redundant work is +minimized and an unbounded loop is avoided. + +And that’s it! Phew! + +Complete source code can be found +[here](https://git.dthompson.us/software-design-for-flexibility/tree/chapter-7/propagators.scm). + +## Reflections + +I think the results of this prototype are promising. I’d like to try +building some larger demos to see what new problems arise. Since +propagation networks include cycles, they cannot be garbage collected +until there are no references to any part of the network from the +outside. Is this acceptable? I didn’t optimize, either. A more +serious implementation would want to do things like use `case-lambda` +for all n-ary procedures to avoid consing an argument list in the +common cases of 1, 2, 3, etc. arguments. There is also a need for a +more pleasing domain-specific language, using Scheme’s macro system, +for describing FRP graphs. + +Alexey Radul’s dissertation was published in 2009. Has anyone made a +FRP system based on propagators since then that’s used in real +software? I don’t know of anything but it’s a big information +superhighway out there. + +I wish I had read Alexey Radul's disseration 10 years ago when I was +first exploring FRP. It would have saved me a lot of time spent +running into problems that have already been solved that I was not +equipped to solve on my own. I have even talked to Gerald Sussman (a +key figure in propagator research) *in person* about the propagator +model. That conversation was focused on AI, though, and I didn’t +realize that propagators could also be used for FRP. It wasn’t until +more recently that friend and colleague [Christine +Lemmer-Webber](https://dustycloud.org/), who was present for the +aforementioned conversation with Sussman, told me about it. There are +so many interesting things to learn out there, but I am also so tired. +Better late than never, I guess! + +Anyway, if you made it this far then I hope you have enjoyed reading +about propagators and FRP. ’Til next time! |