Spark of Reason

Gamma-Ray Bubbles on the Sea of Wavelets: Quantifying Existence and Morphology of the Fermi Bubbles

2023-06-18T00:00:00+00:00

tl;dr

The discovery of the Fermi Bubbles has led to a lot of interesting speculation about high energy phenomena originating at the center of the Milky Way. The analysis tools applied both in the original discovery and for testing subsequent physical hypotheses leave room for improvement, particularly in terms of moving from qualitative to quantitative assessment of the results. Here we describe one potential approach leveraging Haar wavelets to capture the expected multi-scale nature of structure in all-sky gamma-ray maps, coupled with statistics to quantify the tradeoffs between detection of detail and “false detections” resulting from photon counting noise.

Click here to read the full article

Using JVM Clojure for Google Cloud Functions

2020-09-22T00:00:00+00:00

I recently ran into a requirement where a Google Cloud Function (GCF) seemed a good fit. I wanted to use Clojure for this, at least as a first cut, but the examples I found were centered around ClojureScript/NodeJS, which wound up being a non-starter for various boring reasons. Googling about turned up essentially nothing about how to use JVM Clojure for this purpose. The GCF story for Java is about as easy as it can get, just implement a known interface, uberjar, and deploy with the gcloud tool.

My first attempt in Clojure used gen-class, but deployment resulted in this exception:

"Exception in thread "main" java.lang.ExceptionInInitializerError
	at clojure.lang.Namespace.<init>(Namespace.java:34)
	at clojure.lang.Namespace.findOrCreate(Namespace.java:176)
	at clojure.lang.Var.internPrivate(Var.java:156)
	at ck.proxysql_notifier.<clinit>(Unknown Source)
	at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
	at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance(NativeConstructorAccessorImpl.java:62)
	at java.base/jdk.internal.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:45)
	at java.base/java.lang.reflect.Constructor.newInstance(Constructor.java:490)
	at com.google.cloud.functions.invoker.NewHttpFunctionExecutor.forClass(NewHttpFunctionExecutor.java:51)
	at com.google.cloud.functions.invoker.runner.Invoker.startServer(Invoker.java:243)
	at com.google.cloud.functions.invoker.runner.Invoker.main(Invoker.java:129)
Caused by: java.io.FileNotFoundException: Could not locate clojure/core__init.class, clojure/core.clj or clojure/core.cljc on classpath.
	at clojure.lang.RT.load(RT.java:462)
	at clojure.lang.RT.load(RT.java:424)
	at clojure.lang.RT.<clinit>(RT.java:338)
	... 11 more" 

First step was to verify that clojure/core__int.class made it in the jar. It did. Next guess was some kind of class loader issue. I’ve actually run into this scenario several times, where some service requires a Java class implementation, said service uses its own class loader, and when the class is loaded you run afoul of the way Clojure uses class loaders to support its dynamic features. It can be confusing, because it’s clear that the Clojure classes are available in the uberjar, but you get an error that they’re not found. Given that I’ve hit this problem more than once, it’s surprising how little is written about it. This post reminded me of how I had solved this problem in the past, using setContextClassLoader. And this Slack thread further reminded me that my past solutions used a simple “shim” class, because the class loader needs to be set before the Clojure runtime is loaded. I thought I should document the solution here, since I encounter this problem infrequently enough to forget the solution between instances.

This solution is specific to implementing a GCF in Clojure, but the general pattern holds in other cases, which is to implement whatever interfaces the service or framework requires as a Java class, which in turn calls into Clojure code implementing the actual logic. Here’s the Clojure:

(ns sparkofreason.cloud-function
  (:require [cheshire.core :as json]
  (:import (com.google.cloud.functions HttpRequest HttpResponse))
  
(defn service
  [^HttpRequest request ^HttpResponse response]
  (let [body (json/parse-stream (.getReader request))
        response-writer (.getWriter response)]
    (println "Received " body)
    (.write response-writer "ok")))

Pretty boring stuff, deserialize the request body JSON, print it out (which will appear in the Stackdriver logs), and return “ok” for the response. The Java wrapper looks like this:

package com.sparkofreason.cloud_function;

import com.google.cloud.functions.HttpRequest;
import com.google.cloud.functions.HttpResponse;
import com.google.cloud.functions.HttpFunction;
import clojure.java.api.Clojure;
import clojure.lang.IFn;

public class MyCloudFn implements HttpFunction {

  static {
    Thread.currentThread().setContextClassLoader(MyCloudFn.class.getClassLoader());
    IFn require = Clojure.var("clojure.core", "require");
    require.invoke(Clojure.read("sparkofreason.cloud-function");
  }
  private static final service_impl = Clojure.var("sparkofreason.cloud-function", "service");
  
  @Override
  public void service(HttpRequest request, HttpResonse response)
    throws Exception {
    service_impl.invoke(request, response);
  }
}

For the interop, I’m just following Alex Miller’s example of calling Clojure from Java. The key part is the call to setContextClassLoader. We put this in the static constructor before any Clojure stuff happens, to ensure the class loader is set so that our service or framework will have visibility to the classes which get loaded when you start poking at clojure.java.api.Clojure.

You’ll then need to build and deploy this to your service/framework, which for GCF looks like this:

Call java -c on the java file, output the class to some folder like “classes”.
Build an uberjar using some Clojure tool (I used depstar) including the “classes” (or whatever) directory in the classpath (e.g. :extra-paths ["classes"] in a :build alias if using deps.edn).
In your CLI, go to the folder containing the uberjar.
Use the gcloud functions deploy command to deploy your cloud function.
Test with curl or whatever, POSTing some JSON for the body. You should see ok returned as the result, and whatever you sent for the body printed in the Stackdriver logs.

The Could not locate clojure/core__init.class error can be mysterious in this type of interop scenario, so hopefully if you run into that case, this post will save you some time. Note that I just through this together quickly from memory, at some point I’ll make a little example repo and update this post. If you try the code before and find errors before I get that done, please DM @sparkofreason on the clojurians slack.

In the Beginning, There Were Programs

2019-08-21T00:00:00+00:00

Order

In the beginning, there were programs. Programs generally consisted of statements which ran in order. The order was originally an actual physical ordering: instructions on a sequential tape, or a sequence of punch cards. “Order” later became order of lines or “statements” in a text file. Some code may be conditionally executed, and we could jump around with GOTO’s, loops, subroutines, functions, etc. But programs basically consisted of chunks of statements executed in order.

In the beginning, all code executed in a local environment. The hardware hid nasty details from us, such as the delay between issuing a memory-write command on the CPU and that value being available for read. Our statements executed on single thread, and we didn’t worry much about “effects” and potential synchronization issues, because everything was made to appear synchronous.

In the beginning, input was static. We had a batch of data that went in to our program, and later we’d get some batch of output. The program was ephemeral, lasting only long enough to either process the input or perhaps fail. Programming languages perhaps were not “functional” as defined today, but the program itself (often) exhibited mathematical purity.

Chaos

Fast forward to today. Batch programs still exist, but much of the effort in software deals with distributed “always on” systems:

mobile/web clients (often themselves containing significant business logic),
microservices,
various persistent stores (databases, KV stores, immutable logs, message queues, etc.),
third-party services,
and so on.

For such applications, we no longer have the nice clean situation of a single batch of input, transformed by sequential statements to produce a unique batch of output. There are multiple points of input (client, message queues, responses to requests to DBs or other services), these change over time with the state of the system, with no guarantees of ordering. We can try to force such guarantees, but in real distributed system this almost always leads to undesirable effects such as poor performance.

In the beginning, we could rely on the local and sequential nature of code execution. Many logical constraints of the system were enforced simply as temporal constraints: we can assume X is true at line 50 because we asserted X at line 49. Pseudocode example:

var x = 1
x == x + 1

The assignment x == x + 1 does not have to be surrounded by and if statement checking that x is defined. We did it in the preceding line, and assume it to be true. And that’s a good thing. Having the compiler guarantee such logical constraints as a consequence of ordering relieves us of a lot of typing and mental overhead. We like it so much, we often try to write code the same way even when such guarantees can’t be made.

async function foo(x) {
    var y = await makeHttpRequest(x)
    y == y + 1
    var result = await writeDatabase(y)
    return result
}

...


if Rec.x > 5 {
    result = await foo(Rec.x)
} else {
    result = false
}

The async/await pattern is one of many techniques for making asynchronous code feel the same as old-school sequential code. Sometimes that abstraction works, but it can lead to complexity and make it difficult to reason about your code. What if, while waiting for the response to makeHttpRequest, Rec.x was changed to 4 by some other thread of execution? Is it still valid to take the response and write it to the database? And what if the database write failed? And so forth. The sequential abstraction, the idea that the code will execute in the order written, only helps us when the implied logical constraint can be enforced as a temporal constraint: if Y occurs after X in the code, then Y is always valid once X has executed.

A similar example can occur with user interfaces:

if Rec.X > 5 {
    textBox.onchange = async function (newText) { 
                                var x = await makeHttpRequest(newText) 
                                ...
                             }
}

Is it still valid to send the result of the textBox.onchange event if Rec.X changes?

Observations

Dynamic Input

The examples above all exhibit dynamic inputs, inputs that change with the execution or state of the system. A HTTP request often implies that we expect a response (assuming it isn’t “fire and forget”). We provide a callback function which is executed if a response is received, and perhaps different code to handle errors. By making the request, we’ve created a new input to our system, a place where the “outside world” will provide some response. Other examples include event callbacks for UI elements, handlers for message queues, and so forth. Abstractly, these are all the same.

Let’s call all such “dynamic inputs” requests. A request is the abstraction indicating our program can receive some input from the outside world, regardless of the implementation details. A response is that input data. Assume the minimum about requests and responses:

A request might not receive a response.
A response is always associated with a specific request instance.
A request receives at most a single (logical) response.
The order of responses to requests is not guaranteed.
A request might become invalid while a response is “in flight” (more on this below).

Stateful

Requests are part of the system state. That state is generally implementation specific, as is what you can interrogate or modify, which can make testing a headache. For HTTP service requests, we might need to inject some sort of mock implementation of the service, which not only responded to requests with the appropriate data, but also verified that requests were made as required. Maybe we’d use Selenium or some other browser mock to drive testing of requests to the user interface, something else to mock message queues, and so forth.

The state describing requests may also depend on business logic. A request could be issued based on some condition. Some other request then receives a response that changes state rendering the first request invalid. But we have no control over the response arriving. Once a request is invalid, we need to ensure that the response is ignored, for example, don’t execute the code in the callback. Otherwise we open the possibility of nasty race condition bugs, and must test such scenarios directly.

Coupling

Requests represent interfaces with the outside world, systems that are potentially “far away” in both space and time, and not under our direct control. Coupling can occur in at least two ways

Logical coupling, like the specifics of what is sent in an HTTP request or database query;
Implementation coupling, such as how your language runtime and the OS wire up sending an HTTP request and dealing with the response, if/when it comes.

Abstractions which allow requests to appear as “normal” sequential code cause such coupling to occur deep in the guts of your code. I feel this is a questionable practice. Say you were building an electronic device, which allowed a user to input numbers, and had other interfaces which maybe sent signals to other devices, etc. You wouldn’t build this thing where the keypad and other interface points were buried inside the device, requiring disassmbly to be accessed. The same thing applies in code. Burying requests in your implementation increases the pain for reasoning about and testing your code. These points where we interface with users or other systems are generally critically important, and should be exposed at the boundaries of our system.

And unlike the electronic box analogy, the interfaces are potentially changing over time. We should be able to query the system and see exactly what requests are pending. And those requests should be abstracted as just data describing the request, explicitly part of the system state. That allows us to focus on business logic, without getting tangled up in the implementation details of interfacing with users or other external services and systems. The code which handles the actual implementation details of wiring up those requests can be separated from the business logic, and thus replaced ad hoc for testing.

R-cubed: Reification of Request/Response

Example

We will use tic-tac-toe as our example. A human will compete against an AI service via a browser client. The usual rules will apply, and additionally we will allow the human to reset the game if things aren’t going well.

Design

A “component” in an R-cubed system could be anything with persistent state, dedicated business rules, and interfaces. The boundaries of what comprises a component are a design decision, but obvious candidates would be UI clients and stateful microservices. The actor model may be helpful in thinking about components, since the state of the component should only be updated by responses to requests resulting from the business logic applied to the current state.

Each R-cubed component requires three pieces:

Business Logic - Implementation of the logical requirements of your application. For tic-tac-toe, these include determining if the game is over (some player won or tie game), which player moves next, or resetting the game state to start a new match. The business logic also maintains the state, and transformation of that state when a request receives a response. The state in the tic-tac-toe example would include the current game board (which squares are empty, or have an X or O), and the current set of valid requests. Requests will be
- MoveRequest for the current player and each empty square;
- ResetRequest when it is the human player’s turn.
Effectors - Effectors implement effects based on the current business logic state. Effectors must therefore be able to query that state. The effectors for tic-tac-toe will be
- View - renders the current UI based on the business logic state, and wires up events for user inputs corresponding to valid requests.
- AI - calls the AI service to get the next move when it’s the computer’s turn, handles the response.
Data flow - some implementation which allows effectors to
- Get updated query results when business logic state is changed
- Provide responses to requests back to the business logic.

An R-cubed component has the following lifecycle:

Initialize business logic state
Effectors run queries against current state
Effects (rendering UI, HTTP requests, etc.) are performed based on query results.
Wait until a response is received from a pending request.
Send the response to the business logic.
Business logic updates state based on response data.
Goto (2) until component is terminated.

Business logic state updates from responses must be serialized, i.e. each update must run to completion before processing another response. Race conditions are thus avoided, as the state changes from a response may invalidate other pending requests.

Implementation

Enforcing Logical Constraints

Before diving into the specifics of the tic-tac-toe implementation, we examine some further choices to be made around the implementation of the business logic. Effectors and data flow are pretty much just “plumbing”, and you will choose the techniques and implementations best suited for your particular effects, programming language, and runtime requirements. The business logic is often the “money code” (hence the name), and bugs there tend to hurt. Consider the following scenario in our tic-tac-toe game:

Human makes a move
A request is sent to the AI service to get the computer’s move
Human realizes they chose badly, and pushes the Reset button before the response is received from the AI.
Board resets to a new game
Response is received from the AI

What happens at step (5)? The correct action would be to ignore the response, which means we removed or otherwise invalidated the associated MoveRequest from the business logic state. We could just be careful to write code to do that explicitly: when Reset is pushed, delete all of the MoveRequest’s. What if additional functionality were added to future versions that could invalidate requests to the AI? We’d have to be disciplined enough to delete the MoveRequest’s there as well.

Words like “careful” and “disciplined”, when applied to programming, imply a high likelihood of creating incorrect code. Why do tools like static type checkers or runtime data validators exist? So you don’t have to be careful. You could write code with no type validation whatsoever, try to remember the type of every variable, shape of every compound data structure, signature of every function, and so forth. But why? That’s the boring shit computers are really good at: ensuring constraints are not violated, everywhere and always. Such tools allow us to dedicate more mental energy to the stuff that rings the cash register: implementing the business requirements.

The constraints here are not about data type or shape, but logical statements of the form if X then assert Y, where X and Y are logical assertions based on the business logic state. An example could be if x == 5 then assert y == -1. When the value of x becomes 5, we want the state to contain the fact that y has the value -1, which may imply a state change. If x subsequently became 4, we want to retract the previously asserted fact y == -1. Returning to our tic-tac-toe example: if player == computer AND square_5 == empty then assert MoveRequest(player == computer, square == square_5). If the condition becomes false by hitting Reset (or any other cause), the MoveRequest will be retracted, thus avoiding the race condition with the AI service response.

The general classification of such functionality is called logic programming. The specific type of logic programming we will employ is foward chaining rules with truth maintenance.

Maali

Maali is a Clojure library, built on the excellent clara-rules library. clara-rules is an implementation of forward-chaining rules with truth maintenance. Maali adds some functionality which I found useful for R-cubed:

clara-rules defines rules as Clojure var’s via the defrule macro, and groups them under Clojure namespaces. Maali allows collections of rules to be defined under a single var with a defrules macro. Correspondingly, session creation in clara-rules specifies the namespaces containing the rules included in the session, while in Maali you just provide the rule collection vars. The same applies to queries, e.g. defquery -> defqueries. (Aside: I think this choice was mostly a matter of personal preference, though it may have facilitated dynamic reloading of rules in ClojureScript, a la figwheel.)
Maali provides some specific tooling around R-cubed for wiring up data flow, creating requests, handling responses, and dealing with cancellation.
Maali provides a base set of rules for maintaining logical consistency of requests/responses.
Maali was written with spec’ed Clojure maps as the representation of fact entities. It is possible that it could be adapted to use defrecord, which may be somewhat faster.

The Clojure DSL used to define rules and queries in Maali is largely the same as that in the underlying clara-rules, so most of the clara-rules documentation applies. Differences will be highlighted in the code examples below.

R-cubed in Maali

(defrules
  ...
  [::move-request!
   "If the game isn't over, request ::Moves from the ::CurrentPlayer for
    eligible squares."
   [:not [::GameOver]]
   [::CurrentPlayer (= ?player player)]
   [?moves <- (acc/all) :from [::Move]]
   [::common/ResponseFunction (= ?response-fn response-fn)]
   =>
   (let [all-positions (set (range 9))
         empty-positions (set/difference  all-positions (set (map ::position ?moves)))
         requests (map #(common/request {::position % ::player ?player} ::MoveResponse ?response-fn) empty-positions)]
     (apply rules/insert! ::MoveRequest requests))]

  [::move-response!
   "Handle response to ::MoveRequest by inserting a new ::Move and switch
    ::CurrentPlayer to the opponent."
   [?request <- ::MoveRequest (= ?position position)]
   [::MoveResponse (= ?request Request) (= ?position position) (= ?player player)]
   [?current-player <- ::CurrentPlayer]
   =>
   (rules/insert-unconditional! ::Move {::position ?position ::player ?player})
   (rules/upsert! ::CurrentPlayer ?current-player assoc ::player (next-player ?player))]

  ...
)

Here are the rules used for request/response for the tic-tac-toe moves. The full code can be viewed in the maali-simple repository. The defrules macro accepts one or more rule definitions. A rule definition is a vector defined as

The rule name. Clojure’s namespaced keywords are handy here, since rule names must be unique. I like suffixing rule names with ! because they represent conditional state transitions. Queries simply bind data with no state change, so no ! on query names.
An optional doc string.
One or more clauses (the if part of the rule)
The symbol => (read as then or implies).
Assertions (or general effects, more on that below.)

The ::reset-board-request! rule is read as

IF
- No fact of type ::GameOver exists;
- AND we can bind the value of the ::player attribute of the ::CurrentPlayer entity to the ?player variable;
- AND Bind all of the existing ::Move entities to the ?moves variable (aside: this is always possible in clara, if no ::Move entities exist then ?moves will b an empty collection);
- AND we can bind the ?response-fn variable to the value of the :response-fn attribute on the ::common/ResponseFunction entity.
THEN
- Conditionally insert a new ::MoveRequest’s (constructed using the common/request function) for all squares not containing a move.

Note that common is an alias for the provisdom.maail.common namespace, and rules aliases provisdom.maali.rules. The :: syntax in Clojure is shorthand for “use the current namespace on this keyword”, so ::move-request! expands to :provisdom.simple.rules/move-request!. The stuff around ::common/ResponseFunction is a convenience for wiring up the data flow dynamically, basically allows effectors to provide a response to a specific request without having to know about the details of the rules code.

The then part of our rule inserts ::MoveRequest’s for the empty squares and the current player. These fact entities are maps with an associated spec ::MoveRequest that serves as the “type” of the entity. The insert! function in clara-rules does not require the entity type to be explicitly stated. For defrecords, the type is just part of the object metadata. The Maali functions which manipulate fact entities require the entity type to be explicitly specified, and the provided data is validated against the spec. The insert in this case is conditional, which means that it is subject to truth maintenance. If bindings/conditions in the if clauses were to change, then the ::MoveRequest’s would be automatically retracted. Had we inserted this fact directly into the session (without it being part of a rule), or had we used the insert-unconditional! function, the fact would not be managed by truth maintenance.

The conditional vs. unconditional point is important in R-cubed. Requests will usually (always?) be conditional, reflecting the dependence of the valid inputs on the business logic state. Responses, however, come from the “outside world”. Responses don’t depend on anything in your business logic, and are unconditional, inserted directly into the rules session working memory. The logical consequence is that facts asserted as part of a response rule are unconditional as well. Look at the `::move-response! rule:

IF we can
- Bind the request of type ::MoveRequest to the ?request variable, and the ::position attribute of the ::MoveRequest to ?position;
- AND find a ::MoveResponse whose ::common/Request attribute matches ?request, ::position attribute matches ?position, and binds ?player to ::player;
- AND Bind ?current-player to the ::CurrentPlayer fact entity;
THEN
- Do an unconditional insert of a ::Move for the ?position and ?player specified in the response;
- AND Update the ::CurrentPlayer entity to be the other player.

The ::MoveResponse is the input received from either the human or AI service. The resulting ::Move fact is thus necessarily unconditional, because its existence and value depends only on the response, not on the rest of the state. To further that point: once we’re done with the ::MoveResponse, we’re going to delete it (we’ll see how below), because we don’t want stale input hanging around. If ::Move were logically dependent on ::MoveResponse, then deleting ::MoveResponse would cause truth maintenance to retract the ::Move, and the game would never progress past an empty board. A benefit of using forward-chaining rules in R-cubed is the explicit specification of which data is a logical consequence of the current state, and what follows from external input.

The upsert! on ::CurrentPlayer is similar. ::CurrentPlayer starts as an initial fact inserted into the session when the game is started, and so is unconditional. The upsert! function is essentially a shortcut for the following:

(rules/retract! ::CurrentPlayer ?current-player)
(rules/insert-unconditional! ::CurrentPlayer (assoc ?current-player ::player (next-player ?player)))

We don’t bother suffixing rules/upsert! with -unconditional. Logically all upserts must be unconditional. Here’s what happens insert-unconditional! above were replaced with insert!:

The current value of the ::CurrentPlayer fact is bound to ?current-player.
?current-player is retracted.
A new value of ::CurrentPlayer is inserted.
Truth maintenance sees that the ?current-player binding for the if clauses in this rule has changed, and so retracts the newly inserted ::CurrentPlayer value.

So upsert! is always unconditional. To be otherwise would lead to logical contradictions in your rules, essentially stating “X implies not X”.

Requests are conditional, and subject to truth maintenance. The ::MoveRequest’s created by the ::move-request! will be automatically retracted whenever the if-bindings are modified:

The value of the ::CurrentPlayer changes
OR The current set of ::Move’s changes

(Technically, also add OR the ::ResponseFunction changes, but that shouldn’t happen). So, when the ::move-response! rule fires, all of the (now stale) ::MoveRequest facts will be retracted automagically by truth maintenance, which saves us some bookkeeping code. ::MoveResponse however is unconditional, and unless we explicitly retract it, is going to hang around. This is a memory leak if nothing else, and could cause further problems by spuriously firing rules with old input. We could be “disciplined” and explicitly retract the response fact in any rule that processes responses, but that’s just asking for bugs.

Instead we can include rules that establish the logical relationships between requests and responses. From provisdom.maali.common:

;;; Common rules for request/response logic.
(defrules rules
  [::cancel-request!
   "Cancellation is a special response that always causes the corresponding
    request to be retracted. Note that the ::retract-orphan-response! rule
    below will then cause the cancellation fact to also be retracted."
   [?request <- ::Cancellable]
   [::Cancellation (= ?request Request)]
   =>
   (rules/retract! (rules/spec-type ?request) ?request)]

  [::retract-orphan-response!
   "Responses are inserted unconditionally from outside the rule engine, so
    explicitly retract any responses without a corresponding request."
   [?response <- ::Response (= ?request Request)]
   [:not [?request <- ::Request]]
   =>
   (rules/retract! (rules/spec-type ?response) ?response)])

We won’t discuss ::cancel-request! here. ::retract-orphan-response! is the rule of interest:

IF we can
- Find a ::Response fact with an associated ::Request attribute bound to ?request;
- AND there exists no ::Request entity in the state with the value ?request;
THEN
- Retract the response.

This covers two scenarios:

We processed a response, which changed the state such that the request was retracted. ::retract-orphan-response! ensures that the response entity is also retracted.
Something else invalidated the request while the response was “in flight” from an external source, in which case when the effector inserts the response it gets automatically removed, avoiding potential race conditions.

Effectors

R-cubed separates the code performing effects from the logic requesting those effects. Some “disclipline” may be required. Most programming languages don’t provide a way to guarantee that business logic code contains no effects. Maali (and the underlying clara-rules) allows you to write arbitrary Clojure code in the then part of the rule, so you could do all kinds of stuff there, like mutating the UI, putting stuff in a database, etc. Don’t do that. Restrict the then clauses to the following (for Maali, or equivalent operations in your language)

insert!
insert-unconditional!
retract!
upsert!
Any computations which are functionally pure
Debug output, like println, which doesn’t affect the state of the business logic or effectors.

Everything else goes in effectors. Business logic remains functionally pure, which will enable reasoning and testing.

The view effector for tic-tac-toe is responsible for changing the view in response to business logic state, as well as wiring up user input and providing any input as responses. An excerpt is shown below:

...

(defn click-handler
  [request]
  (when request
    (let [response (select-keys request [::simple/player ::simple/position])])
      #(common/respond-to request response)))

;;; Markup and styling from https://codepen.io/leesharma/pen/XbBGEj

(defn tile
  [session position]
  (let [c (click-handler (rules/query-one :?request session ::simple/move-request :?position position :?player :o))
        marker (rules/query-one :?player session ::simple/move :?position position)
        win? (rules/query-one :?winning-square session ::simple/winning-square :?position position)]
    [:td {:id (str position)
          :class (cond-> "tile"
                   win? (str " winningTile")
                   c (str " clickable"))
          :on-click c}
     (condp = marker
       :x "X"
       :o "O"
       "")]))

...

The click-handler function is going to provide the response to a user click on an empty square. The ::MoveRequest and ::MoveResponse specs are defined in provisdom.simple.rules:

...

(s/def ::player #{:x :o})
(s/def ::position (s/int-in 0 9))

...

(def-derive ::MoveRequest ::common/Request (s/keys :req [::position ::player]))
(def-derive ::MoveResponse ::common/Response (s/keys :req [::position ::player]))

...

def-derive is a macro defined in provisdom.maali.rules which defines a Clojure spec and establishes an “is a” relationship with some other spec (via Clojure’s derive function). So a ::MoveRequest is an instance of ::common/Request with additional attributes ::player and ::position. That hierarchy proves handy sometimes, in particular allowing us to write a generic ::retract-orphan-response! rule that applies to all entities deriving from ::common/Request and ::common/Response.

The common/respond-to function is a helper that allows effectors to be ignorant of the data flow wiring. All that is required is to call it with the request and response, assuming the request was created with the common/request function as we showed above. We don’t show it here, but this will insert the response, fire the rules, and alert the effectors that the business logic state has changed.

The tile function is responsible for the rendering and event-handling (when relevant). tile is called from another function which is rendering the board as an HTML table, and so returns the markup (as hiccup) for a <td> element. The session argument contains the business logic state, and position is the board position of the square being rendered. provisdom.maali.rules/query-one is a convenience method which executes a query against the business logic state and returns the first result (useful when you know there will only ever be a single result). The relevant queries for tile are (from provisdom.simple.rules):

(defqueries queries
  [::move-request [:?position :?player] [?request <- ::MoveRequest (= ?position position) (= ?player player)]]
  [::move [:?position] [?move <- ::Move (= ?position position) (= ?player player)]]
  [::winning-square [:?position] [?winning-square <- ::WinningSquare (= ?position position)]]
  ...
)

The ::move-request query is parameterized by ?position and ?player, so we pass in the position argument supplied to tile, and :o for player, since the human player is always “O” in this game. If the session contains a ::MoveRequest for the specified position (empty square) AND it is the human’s turn to play, rules/query-one will return that ::MoveRequest; otherwise it returns nil. That value is in turn passed to click-handler, which returns a function to handle a click event if there is a valid request (i.e. the square can be selected by the human player); otherwise it returns nil. tile similarly executes the queries for other relevant facts, providing information to render the <td> with conditional CSS classes and event handling.

The core AI effector code is

   (when (not-empty (rules/query-partial session ::simple/move-request :?player :x))
     (let [moves (map :?move (rules/query-partial session ::simple/move))
           board (simple/squares->board moves)
           next-move (ai-fn board)
           {::simple/keys [position player] :as move-request} 
              (rules/query-one :?request session ::simple/move-request :?position next-move :?player :x)]
       (common/respond-to move-request {::simple/position position ::simple/player player})))

The pattern is similar to the view. We check if there are ::MoveRequest’s for the computer (provisdom.maali.rules/query-partial allows query execution specifying only a subset of query arguments). If so, we gather up all the existing moves, construct the board configuration, and pass that to the AI service to get the next move. We then find the ::MoveRequest for thoe AI’s chosen move, and respond appropriately.

Testing

The purpose of testing software is to inform our beliefs about “correctness”, that it performs according to our specifications. The discussion of how R-cubed enables testing probably warrants its own long discussion. We’ll hit a couple of high points here.

First, remember that while forward-chaining and truth maintenance simplifies R-cubed implementations, they aren’t strictly required. But we accrue an additional benefit by declaring business logic as rules. Looking at the rule definitions, they very much resemble the sort of conditional statements employed in various testing scenarios. Suppose that we weren’t using rules, and instead of having the ::move-request! rule we had a move-requests function which took in the current state and returned the valid move requests. We then might write some unit tests for move-requests, supplying various test-cases, and then checking the output with conditional statements. Those conditions would appear very much the same as the rule definition. This is key: forward chaining with truth maintenance implies that the runtime guarantees the assertions to follow from the conditions, at least at the scope of a single rule. So we don’t need to test that directly. Now, it may be that when combined with other rules, you induce some logical contradiction. Using rules doesn’t get you out of testing, but it does provide some guarantees at a lower level, and allows more testing effort to be spent at a level more like “integration testing”, where nastier bugs are likely to surface. Such bugs are often the result of logical contradictions between rules, which tend to be very obvious, for example, when firing the rules truth maintenance won’t converge, but bounces back and forth between the offending rules.

Rules aside, R-cubed facilitates direct testing of the business logic. Effects have been completely removed from the business logic. The requests for effects are data, contained in the business logic state, and where applicable responses are just supplied as data. The implementation specifics of the effects are decomplected. The connection between business logic and effectors can (should?) be set at runtime, as determined by your data flow. Swapping out effector implementations for test mocks (or any alternative implementation) is therefore straightforward, without requiring we drag in dependency injection, mocking frameworks, and the like. The business logic itself is intrinsically synchronous and pure. Asynchronous handling is pushed to the effectors. For any state, we can ask for the set of pending requests, and assuming we have sufficient metadata describing the expected responses, can randomly and automatically provide response data. Some example test code for tic-tac-toe is shown below:

;;; TESTING

(defn check-invariants
  [session]
  (let [moves (map :?move (rules/query-partial session ::simple/move))
        move-requests (map :?request (rules/query-partial session ::simple/move-request))
        game-over (rules/query-one :?game-over session ::simple/game-over)
        winner (rules/query-one :?player session ::simple/winner)]
    (let [counts (into {} (map (juxt key (comp count val)) (group-by ::simple/player moves)))
          xs (or (:x counts) 0)
          os (or (:o counts) 0)]
      ; Make sure we don't have any extra moves. :x goes first so should be
      ; either one ahead or equal to :o.
      (when (or (< 1 (- xs os)) (> 0 (- xs os)))
        (throw (ex-info "Invariant violation: extra moves" {:counts counts}))))
    ; If all the squares are full, the game should be over.
    (when (= 9 (count moves))
      (when (not game-over)
        (throw (ex-info "Invariant violation: game should be over" {}))))
    ; Smart AI should never lose
    (when smart-ai
      (when (= :o winner)
        (throw (ex-info "Invariant violation: smart AI should never lose" {}))))
    ; In teaching mode, the user should never lose
    (when teaching-mode
      (when (= :x winner)
        (throw (ex-info "Invariant violation: human should never lose in teaching-mode" {}))))
    (let [mr-pos (set (map ::simple/position move-requests))
          m-pos (set (map ::simple/position moves))]
      ; Can't request a move for a square that's already been used.
      (when (not-empty (set/intersection mr-pos m-pos))
        (throw (ex-info "Invariant violation: moves and move requests should not have overlapping positions" {}))))))

(defn abuse-simple
  [session-atom iterations]
  (add-watch session-atom :check-invariants
             (fn [_ _ _ session]
               (check-invariants session)))
  (loop [i 0]
    (if (< i iterations)
      (do
        (if (rules/query-one :?game-over @session-atom ::simple/game-over)
          ; If the game is over, just reset
          (let [req (rules/query-one :?request @session-atom ::simple/reset-request)]
            (if req
              (common/respond-to req)
              (throw (ex-info "Should have reset request for game over" {}))))
          ; if the game is not over, then play
          (if (> 0.01 (rand))
            ; Once in awhile, be a jerk and reset the game.
            (when-let [req (rules/query-one :?request @session-atom ::simple/reset-request)]
              (common/respond-to req))
            (let [reqs (rules/query-partial @session-atom ::simple/move-request)]
              (if (not-empty reqs)
                ; If legal moves exist, choose one at random
                (let [{::simple/keys [position player] :as req} (:?request (rand-nth reqs))]
                  (common/respond-to req {::simple/position position ::simple/player player}))))))
        (recur (inc i)))
      (remove-watch session-atom :check-invariants))))

check-invariants are conditions we want to test. Most of these are for additional app-level features we didn’t discuss here. For example, the final implementation of tic-tac-toe allows the user to switch between “dumb” and “smart” modes, which either randomly selects a move or does an exhaustive search of all possible future game moves and chooses the best one. Smart mode should never lose, if the AI is correctly implemented.

abuse-simple runs the tests for the specified number of iterations. Each iteration checks the game state and then randomly chooses a request for which a response is provided. The add-watch statement at the top of abuse-simple subscribes to changes in the business logic state, and calls check-invariants for every change. We are simulation testing at the application level, rather than the function level.

We can further expand the scope of integration testing to include effectors, if/when it makes sense. A good example would be to connect the view effector, let it run, and watch for exceptions, indications of rendering errors, or whatever. This video shows the results applied to tic-tac-toe. About the first half of the video has a longish delay between iterations, while the second half reduces this. We can take it even further, and interact with the UI while the simulation is running, as shown in this video.

The tic-tac-toe application doesn’t require any sort of generation of response data. The only input is click events (or equivalently the move choice from the AI service), and so the request data completely determines the response. The Maali implementation of TodoMVC does utilize generation of response data based both on response specs and request data:

(def request->response
  {::todo/EditRequest             ::common/Response
   ::todo/UpdateDoneRequest       ::todo/UpdateDoneResponse
   ::todo/RetractTodoRequest      ::common/Response
   ::todo/CompleteAllRequest      ::common/Response
   ::todo/RetractCompletedRequest ::common/Response
   ::todo/VisibilityRequest       ::todo/VisibilityResponse})

... 

(defn gen-response
  [request]
  (let [response (sg/generate (s/gen (request->response (rules/spec-type request))))]
    (assoc response ::common/Request request)))

(defn gen-visibility-response
  [visibility-request]
  (let [response (gen-response visibility-request)]
    (assoc response ::todo/visibility (sg/generate (s/gen (::todo/visibilities visibility-request))))))

gen-response will generate response data based on the spec for the ::Response entity expected for a given ::Request spec. gen-visibility-response picks a visibility filter based on the valid options in the ::VisibilityRequest. Those options change with the business logic state, so must be generated dynamically, rather than from a static spec. Here is another video, showing the simulation test for TodoMVC connected to the view effector.