Trade Logic - what mechanisms would a system need?

The mechanisms that a Trade Logic system would need

Previously

I introduced and specified Trade Logic, and posted a fair bit about it.

Now

Here's another post that's mostly a bullet-point list. In this post I try to mostly nail down all the mechanisms TL needs in order to function as intended. Some of it, notably the treatment of selector bids, is still only partly defined.

The mechanisms that a TL system needs

• Pre-market
  • Means to add definitions (understood to include selectors and bettable issues)
    • Initiated by a user
    • A definition is only accepted if it completely satisfies the typechecks
    • Definitions that are accepted persist.
• In active market
  • Holdings
    • A user's holdings are persistent except as modified by the other mechanisms here.
  • Trading
    • Initiated by a user
    • User specifies:
      • What to trade
      • Buy or sell
      • Price
      • How much
      • How long the order is to persist.
    • A trade is accepted just if:
      • The user holds that amount or more of what he's selling.
      • It can be met from booked orders
      • It is to be retained as a booked order
    • Booked orders persist until either:
      • Acted on
      • Cancelled
      • Timed out
  • Issue conversion
    • Initiated by a user
    • User specifies:
      • What to convert from
      • What to convert to
      • How much
    • A trade is accepted just if:
      • It's licensed by one of the conversion rules
      • User has sufficient holdings to convert from
• Selectors - where the system meets the outside world. Largely TBD.
  • As part of each selector issue, there is a defined mechanism that can be invoked.
    • Its actions when invoked are to:
      • Present itself to the outside world as invoked.
        • Also present its invocation parameters.
        • But not reveal whether it was invoked for settlement (randomly) or as challenge (user-selected values)
      • Be expected to act in the outside world:
        • Make a unique selection
        • Further query that unique result. This implies that selector issues are parameterized on the query, but that's still TBD.
        • Translate the result(s) of the query into language the system understands.
        • Present itself to the system as completed.
      • Accept from the real world the result(s) of that query.
        • How it is described to the system is TBD. Possibly the format it is described in is yet another parameter of a selector.
    • How an invocable mechanisms is described to the system is still to be decided.
    • (NB, a selector's acceptability is checked by the challenge mechanism below. Presumably those selectors that are found viable will have been defined in such a way as to be randomly inspectable etc; that's beyond my scope in this spec)
  • Challenge mechanism to settle selector bets
    • Initiated by challengers
      • (What's available to pro-selector users is TBD, but probably just uses the betting mechanism above)
    • Challenger specifies:
      • The value that the choice input stream should have. It is basically a stream of bits, but:
        • Where split-random-stream is encountered, it will split and the challenger will specify both branches.
        • Challenger can specify that from some point on, random bits are used.
      • Probably some form of good-faith bond or bet on the outcome
    • The selector is invoked with the given values.
    • Some mechanism queries whether exactly one individual was returned (partly undecided).
    • The challenge bet is settled accordingly.
  • There may possibly also be provision for multi-turn challenges ("I bet you can't specify X such that I can't specify f(X)") but that's to be decided.
• Settling (Usually post-market)
  • Public fair random-bit generating
    • Initiated as selectors need it.
    • For selectors, some interface for retrieving bits just as needed, so that we may use pick01 etc without physically requiring infinite bits.
      • This interface should not reveal whether it's providing random bits or bits given in a challenge.
  • Mechanism to invoke selectors wrt a given bet:
    • It decides:
      • Whether to settle it at the current time.
      • If applicable, "how much" to settle it, for statistical bets that admit partial settlement
    • Probably a function of:
      • The cost of invoking its selectors
      • Random input
      • An ancillary market judging the value of settlement
      • Logic that relates the settlement of convertible bets. (To be decided, probably something like shares of the ancillary markets of convertible bets being in turn convertible)
    • Being activated, it in fact invokes particular selectors with fresh random values, querying them.
    • In accordance with the results of the query:
      • Shares of one side of the bet are converted to units
      • Shares of the other side are converted to zeros.
      • But there will also be allowance for partial results:
        • Partial settlement
        • Sliding payoffs

Trade Logic pick-boolean

Trade Logic pick-boolean

Previously

I initially said that the basic choice operator in TL was pick01, which outputs a random scalar between 0 and 1.

What's wrong with pick01 as basic

It occurs to me that picking a random scalar is not the most basic thing we could do.

It also occurred to me that pick01 as defined needs to provide infinite precision, which of course isn't physically realizable.

It couldn't be sensibly defined to generate both exact 0 and exact 1.

And the fact that I forget whether its interval was left-closed or right-closed suggests that there's a problem there.

So pick-boolean

So from infinite to minimal: pick-boolean is analogous to pick01, except that it outputs a bit, not a scalar.

But it shouldn't be unary

The temptation is to make pick-boolean unary. But if we did, it wouldn't be like other unary predicates. When two instances of these pick-boolean have the same inputs (ie, none), the outputs are not neccessarily the same. This lack of referential transparency potentially infects the outputs of any predicate that uses pick-boolean. This would restrict and complicate the conversions we are allowed to make.

So instead, let's provide a system random stream. A "random output" predicate such as pick-boolean will actually be ternary; its args will be:

• Input bitstream
• Output bitstream
• Output random

This has the nice property that it gives us an upper bound on a proposition's sample space: It's the difference in position between the input stream and the output stream. Of course, that is not always predetermined.

We said earlier that bettable propositions had no arguments, and we need these to be bettable, so we have to revise slightly: A definition is bettable if its only inputs and outputs are system random streams, which will be a type.

There's another way this treatment is helpful: Sometimes we want to sample to settle issues (population bets). Such issues can sample by using the random stream argument, which feeds any selectors that are involved.

Random stream arguments also help validate selectors by challenge - the challenger specifies the bitstream. In this one case, the output bitstream is useful. It gives the various random calls an ordering, otherwise the challenger couldn't specify the bitstream.

Stream splitting

But sometimes a single stream doesn't work nicely. A predicate like pick01 may need to use arbitrarily many bits to generate arbitrary precision. So what can it do? It shouldn't consume the entire stream for itself, and it shouldn't break off just a finite piece and pass the rest on.

So let's provide split-random-stream. It inputs a random stream and outputs two random streams. We'll provide some notation for a challenger to split his specified stream accordingly.

Can't be built by users

We will provide no way to build an object of this new type from first principles. Users can get two of them from one by using split-random-stream, but can't get one from none. So the only way to have one is to get it from an input. Ultimately any proposition that uses a random stream must get it from system mechanisms of proposition resolution such as sampling and challenging.

New pieces

So let's define these built-ins:

• Type: random-stream, the type of the system's random stream. No built-in predicate has any mode that outputs this type but doesn't also input it.
• split-random-stream, ternary predicate that inputs a random stream and outputs two random streams.
• pick-boolean, a ternary predicate outputting a bit.
• Type: lazy scalar. A lazy scalar can only be compared with given precision, not compared absolutely. So any comparison predicates that take this also manage precision, possibly by inputting an argument giving the required precision.
• pick01, ternary, outputs a lazy scalar.
• Convenience
  • Maybe pick-positive-rational, similar but picking binarily from a Stern-Brocot tree.
  • Maybe pick-from-bell-curve, similar but picking lazily from the standard bell curve.

Kernel WYSIWYG Digraphs

Kernel WYSIWYG rooted digraphs

Previously

I said in comments that I view backquote as a WYSIWYG tree ctor, analogous to `list'.

That's not fully general

But backquote doesn't suffice to construct the most general form of open structure of pairs, a rooted digraph. Those require the ability to share objects between multiple parents.

Things that don't do the job

One could write shared objects by naming objects in a `let' form and including them by name. That's not WYSIWYG, though. WYSIWYG would at least present the objects in place once, as #N# / #N= reader notation does.

But that's in the reader. It's not available to general code.

What to do

One could:

• Enclose the whole construction in an empty `let'.
• Provide a combiner expanding to ($sequence ($define! x DEF) x)

Signals, continuations, and constraint-handling

Signals, continuations, constraint-handling, and more

Previously

I wrote about mutability and signals and automatically forcing promises where they conflict with required types.

Signals for Constraint-handling

Constraint-handling, and specifically the late-ordered evaluation it uses, could be treated by signals. Something like this:

• Promises are our non-ground objects. They are, if you think about it, analogous to Prolog variables.
  • They can be passed around like objects.
  • But they're not "really" objects yet.
  • For them to "succeed", there must be some value that they can take.
  • That value can be determined after they are passed.
  • Everything else is either ground or a container that includes one or more of them.
• As I already do in Klink, use of an non-ground argument is detected where it's unacceptable.
  • Generally, they're unacceptable where a type is expected (eg they're acceptable as arguments to cons)
• Unlike what I do now, non-ground unacceptables send signals to a scheduler.
  • This implies that each evaluation is uniquely related to (owned by) one scheduler.
  • That signal passes as objects
    • the continuation as object.
    • The promise to be forced.
• It is the job of the scheduler to ensure that the resulting computation completes.
  • In appropriate circumstances, eg with resource-quotas, or when doing parallel searches, it is reasonable to not complete.

An analogy

Computations whose flow can't be changed are analogous to constant objects and flow-changable ones analogous to mutable ones.

Another use: Precision

This mechanism could also be useful for "dataflow" precision management. Here the objects are not exactly promises, but they are incomplete in a very precise way. They are always numbers but their precision can be improved by steps.

Combiners that require more precision could signal to their generators, which could signal back their new values, propagating back their own requirements as needed. This is very manageable.

Apply-continuation and signals can mutually define

apply-continuation, while it could be used to implement signals, can also be implemented by signals between evaluations. It signals a scheduler to schedule the given continuation and deschedule the current continuation.

Done this way, it gives a scheduler flexibility. This might appear to make analysis more difficult. But a simple (brain-dead) scheduler could do it exactly the continuation way: exactly one evaluation is "in control" at all times. This might be the default scheduler.

In both cases this functionality is a neither-fish-nor-fowl hybrid between objects and computational flow. ISTM it has to be so.

signals allow indeterminate order

One mixed blessing about signals is that since they are "broadcast" 1-to-N, it can be indeterminate what is to be evaluated in what order.

• Pro: This gives schedulers flexibility.
• Con: Computations can give different results.
  • Continuation-based scheduling doesn't neccessarily do better. It could consult "random" to determine the order of computations.
• Pro: Signals and their schedulers give us another handle to manage evaluation order dependency. A scheduler could co-operate with analysis by:
  • Promising that evaluations will behave "as if" done in some particular order.
  • Taking into account analysis
  • Providing information that makes analysis easier, short of simulating the scheduler.
    • Probably promising that no signals escape the scheduler itself, or only a few well-behaved ones do.
• Pro: Regardless of the scheduler, analysis can treat signals as a propagating fringe. Everything not reached by the fringe is unaffected.

Should signal-blockers cause copies?

I suggested earlier that combiners might promise non-mutation by blocking mutation signals out.

One way to code this is to make such combiners deep-copy their arguments. Should this situation automatically cause copies to be made? ISTM yes.

• Not an issue: User confusion. There is no case where a user reasonably expects different functionality than he gets.
  • He might expect a function to mutate an object and it doesn't - but why is he expecting that of a function that doesn't claim to mutate anything and moreover explicitly blocks that from happening? Bad docs could mislead him, but that's a documentation issue.
• Not an issue: Performance.
  • Performance is always secondary to correctness.
  • Performance can be rescued by
    • copy-on-write objects
    • immutable objects
    • Analysis proving that no mutation actually occurs.

Thoughts on the structure of Klink Libraries

Klink Libraries

Previously

I blogged some ideas about Library paths for Klink, the Kernel implementation I wrote. I listed several desiderata, based on lessons from the past. I also blogged about how I'd like bridge the gap between package as used by developer and package as used by user.

Additional desiderata

• (The desiderata from the previous blog post, plus:)
• Should co-operate well with development. Switching from use to development shouldn't require gross changes or compete with library support.
• Can fetch libraries automatically with reasonable power and control
  • In particular, automatable enough to support "remote autoloading" but ultimately should be under the user's control.
• Support clean packaging

Fetching libraries: mostly lean on git

The well-loved version manager git provides most of what I'd want, out of the box:

• Co-operates well with development (More than co-operates, that's what it's usually for)
• Reasonably compact for non-development. You can clone a repo with depth=1
• Fetching
  • Via URL (git protocol or otherwise)
  • Doesn't treat URLs as sexps - only a mild problem.
• Finding out what's there to be fetched, in the sense of available versions (eg, looking for latest stable release)

  git ls-remote --tags URL 
  

  • But we have to distinguish tags and tags^{, which AIUI don't refer to versions.}
• Secure digital signatures are easy
  • Creating them

    git tag -s
    

  • Verifying them

    git-verify
    

  • Some pages about them:
    • http://learn.github.com/p/tagging.html
    • http://progit.org/book/ch2-6.html
• Excluding local customizations from being updated
  • This is possible with .gitignore and some care
  • But customizations will live somewhere else entirely (See below)
• Practices supporting stable releases. git-flow (code and practices) does this.
• NOT a well-behaved heterogenerated tree of libraries.

Of course git does not support knowing that a repo is intended as Kernel code. Looking at filename extensions does, but that seems to require fetching the repo first. For the same reason, it can't easily be any file that "lives" in the repo. It should be something about the repo itself.

So the convention I propose is that the presence of a branch named --kernel-source-release indicates a branch of stable Kernel code. Tags on that branch would indicate available versions, so even if coders are working informally and doing unstable work on "master", only tagged versions would be offered.

But does keeping --kernel-source-release up to date require extra effort for the maintainer? IIUC, git can simply make --kernel-source-release track "master", so if a coder's workflow is organized, he needn't make any extra effort beyond issuing a one-time command. Branch tracking is intended for remotes, but seems to support this.

Should there be other branches, like --kernel-source-unstable or --kernel-source-development? I suspect they're not needed, and any use of unstable branches should be specifically configured by the daring user.

I'm not proposing to permanently tie Klink (much less Kernel) specifically to git forever. But it serves so well and is so well supported that I'm not concerned.

Where to put it all?

That addressed how we can fetch code. In doing so, it put some restrictions on how we can organize the files on disk. So I should at least sketch how it could work on disk.

The easy part

Of course one would configure directories for libraries to live in. Presumably one would distinguish system, local, and user.

The hard part

A mature set of libraries tends to look like a tree. But above, we had to treat each one a separate project.

Approaches:

• Let the namespace tree exactly be the directory tree.
  • Fatal con: Code repos want to "own" all their subdirectories. git will try to control everything in its working tree. It even wants submodules to covary with the working tree.
• Have a dotty namespace where all the components are expressed in one name. So directories have names like "std.math.util.raw"
  • Con: Yuck! There's everything wrong with this.
• Reserve a name for subdirectories and .gitignore it.
  • Con: Every level of subdirectory becomes two levels.
  • Con: Still yuck.
• Require that directories must be either inner nodes or leaves, never both. If a project directory becomes an inner node, move code in it to a directory with a special name, say "%main".
  • Con: Requires moving subdirectories, possibly behind the back of other software.
• Library filespace and project filespace are distinct. Stow the projects into a library tree. They live in some other directory as configured by user.
  • Pro: Clean.
  • Pro: Flexible.
  • Pro: Lets local customizations live outside the project repo, as they should.
  • Con: How is stow to know where a project's "root" in filespace is?
  • Con (that the other approaches had too): Internal project filetree organization can still mess us up. What happens if its code lives in "src" instead of in "."?

I favor the "stow" approach.

Path configuration

But the stow approach still left issues of where exactly to stow things. We can't solve it in the file system. That would result in one of two ugly things:

• Making each project represent the entire library filespace, with its real code living at some depth below the project root.
• Making each project physically live in a mirror of the target filespace. This would have all the problems we were avoiding above plus more.

So I propose per-project configuration data to tell stow about paths. I'd allow binding at least these things:

prefix

The library prefix, being a list of symbols.

parts

List of sub-parts, each being a list, being:

• Type of file as far as library-ing is concerned (source, docs, info, default-customizations, others to be defined. See below).
• file name or directory relative to repo root
  • Or alternatively a URL, eg for a wiki or mailing list associated with the library.
• library name relative to library prefix

For example,

((prefix (std util my-app))
   (parts
      (
         (source
            [,,src,,]
            ())
         (source
            [,,tests,,]
            (tests))
         (info
            [,,doc,,]
            ())
         (default-customizations
            [,,defaults,,]
            ())
         (public-key
            [,,pub_key.asc,,]
            ()))))

That would live in a file with a reserved name, say "%kernel-paths" in the repo root. As the example implies, the contents of that file would be sexps, but it wouldn't be code as such. It'd be bindings, to be evaluated in a "sandbox" environment that supported little or no functionality. The expressions seem to be just literals, so no more is required.

Dependencies and version identity

Surfeit of ways to express version identity

There are a number of ways to indicate versions. All have their strengths:

• ID hash
  • Automatic
  • Unique
  • Says nothing about stability and features
• Release timestamp
  • Easily made automatic
  • Time ordered
  • Nearly unique, but can mess up.
  • Says nothing about stability and features
• Version major.minor.patch
  • Just a little work
  • Expresses stability
  • Expresses time order, but can be messed up.
• Test-satisfaction
  • Lots of work
  • Almost unused
  • Automatically expresses stability and features
  • No good convention for communicating the nature of tests
• `stable', `unstable', `release', `current'.
  • Expresses only stability and currency
• By named sub-features
  • Just a little work
  • Expresses dependencies neatly
  • Expressive
  • Not automatic

I chose sub-feature names, based on how well that works for emacs libraries, a real stress test. That is, I choose for code to express dependencies in a form like:

(require (li bra ry name) (feature-1 feature-2))

Co-ordinating sub-features with version identity

The other forms of version identity still exist as useful data: ID hash, version tags, results of tests. What makes sense to me is to translate them into sets of provided features. Do this somewhere between the repository and the require statement. require would still just see sets of features.

Desiderata for this translation:

• Shouldn't be too much work for the developer.
  • Probably easiest to support automatic rules and allow particular exceptions. With a git-flow workflow, this could almost be automatic. As soon as a feature branch is merged into "master", that version and later versions would be deemed to have a feature of that name.
• Should be expressable at multiple points in the pipeline, at least:
  • Annotations in the source code itself
  • In the repo (In case the source code annotations had to be corrected)
  • Stand-alone indexes of library identities. Such indexes would be libraries in their own right. Presumably they'd also record other version-relevant attributes such as signature and URL.
  • Locally by user
• Should be derivable from many types of data, at least:
  • Branches (eg, everything on "master" branch has the feature stable)
  • Tag text (eg, all versions after (2 3 3) provide foo-feature)
  • Tag signature (eg, check it against a public key, possibly found in the repo)
  • Source code annotations (eg, after coding foo-feature, write (provide-features ear lier fea tures foo-feature))
  • Tests (eg, annotate foo-feature's (sub)test suite to indicate that passing it all means foo-feature is provided)
  • ID
    • To express specific exceptions (eg, ID af84925ebdaf4 does not provide works)
    • To potentially compile a mapping from ID to features
  • Upstream data. Eg, the bundles of library identities might largely collect and filter data from the libraries
• Should be potentially independent of library's presence, so it can be consulted before fetching a version of a library.
• Should potentially bundle groups of features under single names, to let require statements require them concisely.

Dependencies

With sub-features, we don't even need Scheme's modest treatment of dependencies, at least not in require. Instead, we could avoid bad versions by indicating that they lack a feature, or possibly possess a negative feature.

The usual configuration might implicitly require:

• works
• stable
• trusted-source
• all-tests-passed

The set of implicitly required features must be configurable by the user, eg for a developer to work on unstable branches.

Library namespace conventions

On the whole, I like the CPAN namespace conventions. I'd like to suggest these additional (sub-)library-naming conventions:

raw

This interface provides "raw" functionality that favors regular operation and controllability over guessing intentions.

dwim

This interface provides "dwim" functionality that tries to do what is probably meant.

test

This sub-library contains tests for the library immediately enclosing it

testhelp

This sub-library contains code that helps test libraries that use the library immediately enclosing it. In particular, it should provide instances of objects the library builds or operates on for test purposes.

interaction

This library has no functionality per se, it combine one or more functional libraries with an interface (keybindings, menus, or w/e). This is intended to encourage separation of concerns.

inside-out

This library is young and has not yet been organized into a well-behaved namespace with parts. It can have sub-libraries, and their names should evolve to mirror the overall library organization so that it can become a real library.

(inside-out new-app)

user

This user is providing a library that doesn't yet have an official "home" in the namespace. The second component is a unique user-name.

(user tehom-blog/blogspot.com inside-out new-app)
(user tehom-blog/blogspot.com std utility new-util)

Other roots

But there are other files that are relevant to libraries but are not source code. ISTM there's often a benefit in locating them relative to a given library. But they shouldn't have an identity in the library tree itself:

• They're not source
• Libraries mustn't accidentally use their identifier as the name of a normal source file.

So I would define other trees exactly paralleling the library tree. I would include at least:

docs

Organized documentation

info

Documentation specifically as info files

customizations

For customizations relating to a library. Always local.

(customizations std util my-app)

• Format : List of bindings

default-customizations

For the recurring idiom where one initially configures with defaults, and user changes to them are preserved.

• Format : List of lists, each being in the format (name value first-appeared-in-version)

files

General non-source files supporting a library. In particular, in relation to test or examples.

Mutability And Signals

Mutability and Signals

Recently I've been working on Rosegarden, the music sequencer. It uses Qt which uses signals.

Signals implement the Observer pattern, where an object notifies "observers" via signals. A signal is connected to one or more "slots" in other objects. The slots are basically normal methods, except they return nothing (void). When a signal is emitted, Qt arranges for the slots to be called, other than those of deleted objects. So far, I find it works easily and elegantly.

This made me wonder: Could signals take the place of mutability in Scheme? And might that give us both referential transparency and reactiveness simultaneously?

There's not much support for signals for Lisp and Scheme. There's Cells, but it seemed to be conceived of as just a super-spreadsheet. I want to go much further and use signals to re-imagine the basics of object mutation.

Quasi-mutation: The general idea

Basically, we'd use signals between constant objects to fake mutability.

• Objects can't mutate.
• "Slots" are closures.
  • In the observer pattern, eg in Qt, slots are parts of objects. But Scheme is not object-oriented. Even in the presence of object-oriented extensions (CLOS, GOOPS), I don't think that would be right, by the same logic as for generic functions.
  • Closures would typically know a target object. Possibly as environment as record.
• Signals are emitted with respect to particular objects.
  • Not "by objects". Again, we're not object-oriented. We're just indexing on objects.
  • Ability to emit is controlled by access to objects and signal types.
  • Indexing on one particular argument seems overly special, so I contemplate indexing on any relevant arguments. This is again similar to generic functions.
• Signals can be connected to slots.
  • The signals go to where the object's respective signal is connected. They are indexed on objects.
• Constructors connect the signal replaced from the parts to the constructed object.
  • More precisely, to a closure that knows the object.
  • The closure would fully represent the objects' relation. For instance, mutable pairs might have the slots new-car and new-cdr with the obvious meanings.
  • But not for immutable objects. Immutable objects' slots would not be new-car and new-cdr, they would raise error.
  • The constructed object can access its part objects, in appropriate ways by its own lights. For instance, a pair object could retrieve its car and cdr objects.
  • This particular signal replaced is not exposed.
  • The details of replaced will be refined below.
• Slots such as new-car will typically:
  • Construct a near-copy of the object, with the new part in the old part's place. This effectively connects a new version of the object to the new part and disconnects it from the old part.
  • Emit replaced with respect to the object, propagating the change.
• "Normal" setters such as set-car! emit replaced wrt the old object with the new object as value.
  • That's just the classical way. There's plenty of room to do clever new things with signals.
  • As above, doing this to immutable objects causes error.
• Constructed objects behaving this way would include at least:
  • Mutable pairs (and therefore mutable lists and trees)
  • Environments
  • Continuations. While not often considered object-like, continuations have parts such as the current environment and their parent continuations.
• External-world-ish objects such as ports react to signals in their own appropriate way, not neccessarily propagating them further.

As if

Literally implementing ever pair with at least two signals between itself and its car and cdr seems prohibitive if not impossible. Physically, it couldn't be the only mechanism of mutation. So I'm talking about a mechanism that acts as if it's continuous down to basics like pairs and lists, but really uses a more modest mechanism where it can (presumably containment, as now).

Circularity

My blog readers, being smart, will already be wondering what happens when replaced is propagated in a circular structure. Does it propagate forever, crashing the interpreter? That might go something like this: The signal propagates from pair to pair, repeatedly reaching its original location, pointlessly representing more new objects that differ only from the k*N nth cdr, and never finishing because there's always an (k+1)*N nth cdr to represent.

For instance, in the circular list above, suppose we gave object C a new value. It emits (replaced New-C C), which B receives in new-cdr. B emits (replaced New-B C) which both A and old C receive. Leaving aside A's reaction, old C then emits (replaced New-Old-C C) which old B again receives. A is going to be deluged with infinite signals, and we will keep making new copies of old B and old C. Worse, we make many new-Bs when we only have a place for one.

The too-easy answer would be to block all repetitions between the same two objects. That fails, because we re-emit on new copies. So also block repetitions where the objects are the same except that one is replaced by an updated copy?

So as a first draft, I propose that these built-in signal emissions:

• Be each associated with a unique ID
• Refuse to propagate that ID circularly

The ID would be an opaque ID equal? only to itself. It would be unique to a given cascade of emissions. That is, set-car! etc would make fresh IDs but new=car etc would use the ID of the replaced signal that provoked it.

One subtle point: It suffices for the signalled object itself to recognize repititions. Originally I thought repititions would have to be recognized across a transitive closure. But only the original object is connected to by its contents, and connections from new parts to new object don't receive any signal to propagate.

What about structural information?

The above is progress, but it discards structural information.

Consider an application that displays the first N items from a possibly-circular list on screen, and redisplays them just as needed (Say they are formatted in some time-consuming way and different screen locations can't share this work) The display would want to be notified of all the nth cdr occurences of a changed element. The approach above wouldn't permit that.

So when there's circularity, let's switch tactics and use polling to retrieve information as needed. Let any circular object provide a stream of all the replacements that occured in it for a given emission-ID. Applications only read the stream as far as they need to and the rest is not really generated.

But often a slot would prefer to get a simple new object, without replaying all the detailed changes.

Desiderata

To sum up the desiderata on this:

• We want slots to be able to replay detailed changes.
• We want slots to be able to just get a new object
• We don't want mutated objects to have to guess what their target slots want, which may not even be the same for different slots.
• We don't want mutated objects to have to do inordinate (even infinite) work preparing these signals.
• We don't want to make assumptions about the topology of the mutated object. It can be an arbitrary directed graph.

A thought-experiment sequence of operations

The sequence of operations on the circular list above would go something like this. Here I use FOO.N to indicate the nth version of FOO.

• We gave object C.1 a new car, V (we emit replaced.1 to it) Its change is:
  • "Replace car with object V". We'll represent this as
    • The trivial accessor identity.
    • A promise to construct V (Trivial since we started off knowing it)
• replaced.1 reaches C
• We emit replaced.2 for C. Its change is:
  • A disjunction (or) of
    • "Replace what you're holding with C.2"
      • identity
      • A promise to construct C.2
    • "Replace car of it with V"
      • car
      • Promise of V
• replaced.2 reaches B
• We emit replaced.3 for B.1. Its change is:
  • A disjunction (or) of
    • "Replace this with B.2"
      • identity
      • A promise to construct B.2
    • A disjunction (or) of
      • "Replace cdr of this with C.2"
        • cdr
        • A promise to construct C.2
      • "Replace cddr of this with V"
        • cadr
        • Promise of V
• replaced.3 reaches A.1
  • We'll say the promises are not forced yet. If they are, that still forces these following operations to occur first.
• replaced.3 also reaches C.1. Here we encounter a repitition. C.1 has already encountered a signal from this trigger. We don't want to emit another consequence of it to the same places. Instead we want to fold the signals together.

Let's stop operations and look at it

• If we made replaced.4, its change would be:
  • A disjunction (or) of
    • "Replace this with C.2"
      • identity
      • A promise to construct C.2
    • A disjunction (or) of
      • "Replace cdr with B.2"
        • cdr
        • A promise to construct B.2
      • A disjunction (or) of
        • "Replace cddr of this with C.2"
          • cddr
          • Again, a promise to construct C.2
        • "Replace cadr of this with V"
          • caddr
          • Promise of V

So replaced.4 resembles replaced.2. The big change is that instead of "Replace car of this with V", we have a cdr replacement. It pushes "replace with V" down to another cycle of the loop. That doesn't support the "display circular list" example, which was our motivation for doing this. So:

• We need to support something that can mention both the car replacement and the cdr replacement of C.1
• We need to effectively be able to adjust previous signals instead of emitting more.

I first considered and discarded an approach of rewriting the second disjunct into a conjunction.

Now the most tempting approach is to rethink the car replacement operation. It did not fully describe the object, it just described the new car, V.

Let's say that all such operations are in fact constructors, and in the case of "Replace car of it with V", we let the cdr argument default to the current cdr.

Timing issues:

• The default can't be committed to until the signal and its consequents have stopped propagating.
• We know this by Emission-Id.
• So forcing one of these promises first causes the signal to propagate until it's done.

This sounds quite like what I would expect from a solution. Constructors "stand for" the objects they make, as is often the case in RT languages. We are getting a structure that's isomorphic to the original object (circular list of period 2). "Just mutate contents" remains a valid optimization as long as we're in a closed system (And a tempting one; I have to keep reminding myself that we're conceptually replacing mutation with signals so it won't do)

The new structure of replacement info

So replaced.2's replacement info actually looks like:

• A disjunction (or) of
  • "Replace what you're holding with C.2"
    • identity
    • A promise to construct C.2
  • "Construct it with V as car"
    • Arguments
      • car : Promise of V
      • cdr : C.2's cdr value, defaulting to C.1's cdr value.

Default arguments

The action of replaced.3 on C.1 just provides a value for the cdr argument. Re-emission is not needed, nor wanted since at C's cdr the signal has reached a join.

So the default cdr argument is held in a sort of limbo until it's given or not. That's a lot like mutation in itself. So it too is managed by signals:

• "All done". Signal has fully propagated, use defaults for anything not filled.
• "Use this" Accessor Value. After receiving "use this", "All done" has no effect.

These are of course quasi-mutating the stream argument of replace. There's an infinite regress there, but since it is all behind promises that delay evaluation until after this is done, I think we can consider it as if the stream had had one unchanging value forever.

Structure of the change stream

So each "cell" of the stream of operations changes consists of a disjunction on constructors and values, rather than a cons cell. Each disjunct can be:

• A promise of a value
• A promise of a constructor parameterized by promises of values

So it's like an n-ary tree-stream.

Note that this naturally orders the change stream from shallow to deep. If it was ordered from deep to shallow we couldn't find elements in finite time.

This doesn't preclude specialized representations that (say) compact multiple simple cdr accesses to an nthcdr access. These could be represented as additional constructors in the disjunct.

Object identity

Above, I said "constructed object can access a part object", not "a part's value". Since objects no longer ever change value, the difference is subtle. It's just this: the object has a single set of signal connections. So it has a single identity. So there is a trace of object identity remaining.

One could represent identity value-wise by saying that values consist of a (classical) value and an "object-identity" value, and that object-identity values are opaque and unique except as shared by this mechanism. So signals are connected with respect to object-identity values.

It has a flavor of "the long way around", but it lets us treat objects entirely as values.

Object versioning

Different versions of an object have different Object-IDs. Imperatively this wouldn't be anything, since two simultaneous references to the same object can't have different values. But here, one can both mutate an object as far the the world is concerned and hold onto its old value. But it should never be the case that objects are eq? but not equal?. So different versions have different Object-IDs.

The equality predicates

Equality:

equal?

is what it normally is in Scheme or Kernel: The objects have the same current value.

eq?

A and B are eq? just if

• (equal? identity-of-a identity-of-b)

=?

is just an optimization of equal?

Signals and immutability

I mentioned that I was thinking about immutability in regard to this. So far, I've just described how to duplicate mutability with signals.

For immutable objects, some or all slots would still get connections, but would raise error instead of propagating mutation.

But that's only half of the control we should have over mutation. We'd also like to guarantee that certain evaluations don't mutate even mutable objects they have access to, eg their arguments, the environment, and dynamic variables. The "foo!" convention indicates this (negatively) but doesn't enforce anything. "foo!" convention notwithstanding, we'd like to guarantee this from outside an arbitrary call, not from inside trusted combiners.

Blocking signals

So we'd like to sometimes block signals. If signals were emitted anyways, they'd be errors and would not reach their destinations. So if replaced is blocked, code either doesn't try to mutate objects or tries and raises an error. Either is consistent with immutability.

ISTM the simplest way to block signals is to disconnect their existing connections and connect them to error combiners. When the call is done, restore their original connections. However, that doesn't play well with asynchrous execution.

Instead, we'll make a copy of the original object that will (probably lazily) infect its parts with "don't mutate me in this scope".

Scope

For a traditional imperative language, where flow of control and scope are structurally the same, we could block signals in specific scopes, recursively. But for Scheme and Kernel, that won't suffice. What would happen if an object is passed to a continuation and mutated there? We've broken the guarantee that the object wouldn't be mutated. Any time we let objects be passed abnormally, this can happen.

We might try to:

1. raise error if affected objects are passed to continuation applications, or
2. "infect" the other scope with the signal restrictions.

Neither is appealing. In this mechanism, continuing normally is also passing to a less restrictive scope. And continuing normally should behave about the same way as continuing abnormally to the same destination. We also don't want error returns to permanently "freeze" objects.

So ISTM we must distinguish between continuing to a (not neccessarily proper) parent of the restricting scope (normally or otherwise) and continuing elsewhere. Signal blocks are removed just if control reaches a parent. This is essentially how Kernel guards reckon continuation parentage.

Doing this for all object parts

We'd usually want to say that no part of any argument to a combiner can be mutated. It's easy enough to treat signal connections from the root argobject. But we need to "infect" the whole object with immutability, and not infect local objects, which may well be temporary and legitimately mutable.

Since these arguments are ultimately derived from the root argobject, what we can do is arrange for accessors to give immutable objects in their turn. But they have to be only temporarily immutable - blocked, as we said above. And we'd prefer to manage it lazily.

So I propose that accessing a blocked object gives only objects:

• whose replaced signals are re-routed to error, as above, until control "escapes normally" (an improper parent continuation is reached)
• which are in turn blocked, meaning they have the same property infecting all of their accessors.

Non-pair containers

Non-pair containers are not treated by mechanisms like copy-es-immutable. But we want to treat immutably fully, so they have to be treated too. This is the case even for:

• Environments
• Encapsulation types. In this case, their sole accessor is required to do this, as all accessors are.
• Ports. Administrative state or not, they can be immutable.
• Closures. Anything they return is considered accessed and automatically gets this blockingness. Their internal parts (static environment, etc) need not be blocked.
• Continuations. Like closures, what they return is considered accessed and automatically gets this blockingness.

Exemptions

We'd like to be able to exempt particular objects from this. Some combiners mutate an argument but shouldn't mutate anything else. There'd probably be a signal-block spec that would specify this.

Blocking signals to keyed dynamic objects

We can easily extend the above to deal with dynamic environment, but keyed dynamic objects are not so simple. Their accessors would be covered by the above if derived from the argobject or the dynamic environment, but they need not be.

So we need an additional rule: Keyed dynamic objects are blocked if accessed in the dynamic scope of the blocking. That's recursive like other blockings. Keyed rebindings in the dynamic scope aren't, because one might bind a temporary that's legitimately mutable.

Side note: I'd like to see a stylistic convention to differentiate between combiners that mutate their arguments ("foo!") and combiners that mutate something else, meaning either their dynamic environment or a dynamic variable (Say "foo!!")

Interface to be defined

I've already written a lot, so I'll leave this part as just a sketch. To support all this, we need to define an interface.

• A means of defining new signal types
  • Returns a signal emitter
  • Returns a signal identifier for `connect' to use.
• A signal scheduler. By general principles, the user should be able to use his own, at least for exposed signals. It's not too hard to write one with closures and continuations.
• Means for the user to emit signals
• Means for the user to connect and disconnect signals
  • Not exposed for many built-in objects such as pairs.
  • "capture all current", as for blocking
  • "disconnect all"
• block-all-signals: connects all signals to error continuation
  • Possible argument `except'
• (Maybe) block-signal: connects given signal to error continuation
• A "dirty-flag" mechanism, often useful with signals.
• Possibly a priority mechanism.

Some possibilities this raises

• Use the signal scheduling mechanism for managing constraints. Since when we can enforce immutability, constraints become very tempting.
• Provide general signals
• Provide an interface to Lone-COWs, a sort of copy-on-write object optimized for usually being uniquely referenced/owned.
• Supplying "out-of-band" signals to a debugger or similar. They really do need to be out-of-band.
• Provide a broadly applicable interface for redo/undo. It could basically just capture historical copies of objects.

Glorified footnote: Aren't signals a lot like callbacks?

Somewhat. The differences are:

• Signals are N to 1.
• Signals are associated to some sort of signal-type object. One creates a signal of a specific type. In Qt, this is specified as "signal:" members of a class.
• Signals are scheduled more freely.
• Signals to "dead" objects do nothing. Their existence doesn't keep objects alive; in this they are like weak references.
• The sending object does not explicitly track its observers,

Thinking about Immutability in Klink

Previously

Klink is my stand-alone implementation of Kernel by John Shutt.

Types of immutability

There are several types of immutability used or contemplated in Klink.

Complete immutability

Not much to be said.

Pair immutability

A pair that forever holds the same two objects, though those objects' contents may change.

List immutability

For instance, a list where you can change the contents, but not the number of elements.

Recursive structural immutability

An immutable tree of mutable non-pair objects.

Administrative immutability

Eg, what ports typically have. When you read or write to a port, it remains "the same thing" administratively.

Current status in Klink

Complete immutability

Available in C, used in some places such as symbols and strings. AFAICT there's no way to specify its use or non-use in Kernel; some objects just have it because of what they are or how they are created.

Pair immutability

This is the default in Klink. To get mutable pairs, use mcons instead of cons. I was persuaded of this by Getting rid of set-car! and set-cdr! and Racket, also here.

List immutability

No way to have a pair whose car is mutable but whose cdr recursively isn't.

Recursive structural immutability (Tree immutability)

Supported via copy-es-immutable

Administrative immutability

No C flag for it. Like complete immutability, some objects just have it because of what type they are.

Non-recursive structural immutability?

If you read section 4.7.2 of the Kernel report (copy-es-immutable), you may notice that Pair immutability and List immutability are actually extensions. So I figured I should at least advance a rationale for them.

Is non-recursive immutability worth supporting? ISTM it's already strongly suggested by Kernel.

Implied by an informal type

Some combiners take finite lists as arguments; all applicatives require a finite list as argobject. That distinguishes the finite list as at least an informal type. There's a predicate for it, finite-list?, but pairs that "are" finite lists can "become" other sorts of lists (dotted or circular), so it falls short of being a formal type. This seems like an irregularity to me. Structural immutability would solve it.

Implied by implied algorithms

For some combiners (eg reduce), any practical algorithm seems to require doing sub-operations on counted lists. That implies a structurally immutable list, because otherwise the count could theoretically become wrong; in practice it's saved from this by writing the algorithm carefully. So there are at least ephemeral, implied structurally immutable lists present.

Vectors

John once told me that he would eventually like to have vectors in Kernel. Vectors are optimized structurally immutable finite lists.

Opportunity for optimization

There's an opportunity for other optimizations where list immutability is used and recognized. In particular, caching a list's element count is often nice if one can be sure the list count won't change.

Comparison table

Type of immutability	Pair	List	Tree
Special care needed
for shared objects?	No	Only own tail	Yes
Exists in Klink?	Yes	No	Yes
Exists in Kernel?	No	No	Yes
What might be mutable?	car, cdr	elements	leaves