Day 15: Junction transformers

Consider a junction of digits:

say any 0..9; # OUTPUT: any(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

This carries 'any' as a type of operation and 0..9 as a list of eigenstates internally. In a smartmatch context, this can match any object that can smartmatch against any of its digit eigenstates. While the list of these is not exposed, there is a means of traversing its contents.

The ~~ smartmatch operator delegates to the ACCEPTS method on the RHS prior to a Bool coercion on its result. For example, we’ll depend on Code.ACCEPTS directly as a means of injecting behaviour into a smartmatch:

sub sum(Mu $topic is raw) {
    my $sum is default(0);
    sub sum($topic) { cas $sum, * + $topic }
    &sum.ACCEPTS: $topic;

say sum any 0..9; # OUTPUT:
# 45

say sum 0 & (9 ^ 9) & 0; # OUTPUT:
# 18

In this case, it forwards a single argument (its “topic”) to an invocation of itself, allowing us to take a sum of eigenstates.

We give &sum a closure to give us fresh $sum for each call. Because the $topic of the inner &sum has no type, it carries a Mu type like the outer $topic, but will autothread a Junction:D argument over Any eigenstates. Because the outer $topic is explicitly typed Mu and is raw however, it will leave both junctions and containers on input alone. Note that autothreading recurses over Junction:D eigenstates, and while we could use +=, a Junction implementation may be parallel.

If we’re going to just accept one argument given a junction, it could just as well be a Mu eigenstate instead of the junction itself. Mu.ACCEPTS can thread its topic over Mu instead of Any given a Mu:U invocant (Mu:D is NYI; Any:D defaults to &[===]). Similarly, Junction.CALL-ME threads its invocant over Mu. Because a junction will not shortcircuit as it is threaded, these can be chained to traverse one’s eigenstates recursively:

class JMap does Callable {
    has &!transform is built(:bind);

    multi method ACCEPTS(::?CLASS:U: Mu $topic is raw) {
        self.bless: transform => {
    multi method ACCEPTS(::?CLASS:D: Mu $topic is raw) {
        &!transform.ACCEPTS: -> Mu $thread is raw {
            $thread.ACCEPTS: $topic

    proto method CALL-ME(Mu) {*}
    multi method CALL-ME(::?CLASS:U: Mu $topic is raw) {
        self.ACCEPTS: $topic
    multi method CALL-ME(::?CLASS:D: &function) is raw {

say JMap(any 0..9)(*[]); # OUTPUT:
# any(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

say JMap(any 0..9)(2 ** *); # OUTPUT:
# any(1, 2, 4, 8, 16, 32, 64, 128, 256, 512)

say JMap(0 & (9 ^ 9) & 0)(?*); # OUTPUT:
# all(False, one(True, True), False)

JMap gets its one chance to thread a Junction:D as a type object, so we forward the junction to map before its Callable. After a CALL-ME, we wind up with either a callable or a new junction of callables that is invokable, but does not qualify as Callable itself. Despite ACCEPTS being typed with a Mu topic over JMap, the threading of junctions still wins in a dispatch.

JMap can process the eigenstates of a junction generically, but carries overhead in its autothreading in CALL-ME prior to any smartmatching against the result. If you have a particular Callable in mind with which to map, this JTransformer template can be followed:

class JTransformer does Callable is repr<Uninstantiable> {
    multi method ACCEPTS(Mu --> Code:D) { ... }

    method CALL-ME(Mu $topic is raw) {
        self.ACCEPTS: $topic

In general, a CALL-ME would be used to thread its Mu $topic is raw through ACCEPTS. Instead of instantiating the invocant, this would return a bare block or anon sub, which would perform a tailored smartmatch operation given the threaded Mu in its context and a topic from any later smartmatch on said code object.

If a junction produced by CALL-ME is cached, the ACCEPTS candidate written can shoulder part of its resultant thunk’s work to make that cheaper to smartmatch, e.g. by preprocessing the path to a particular block. It can be cheapened further in this sense by subtyping Mu directly in lieu of the default Any for a simpler dispatch, though it becomes more difficult to work with in doing so:

class JTransformer is Mu does Callable is repr<Uninstantiable> { ... }

A practical example of a JTransformer-like class is the internal class Refine that backs my Kind subsets’ refinements (where clauses) as of v1.0.3. Because it’s dabbling in metaobjects (e.g. Mu, Junction), Any cannot be assumed, but at the same time, junctions can allow for complex checks against multiple metaroles. If a metaobject threaded by its ACCEPTS call cannot typecheck as Mu for any reason, it will substitute a block wrapping a low-level typecheck against it, otherwise thunking a boolification of an ACCEPTS call.

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