egg Sequences 3

Sequences (as introduced earlier) are a good way to abstract lists of homogeneous data. We are only allowed to see one piece of data at a time and we don't know (until we get there) where the end of the data is. Indeed, sequences can be infinite.

This promotes the use of streaming algorithms which allow us to process very large data sets (i.e. ones that cannot all fit into memory at one time).

However, there is a hidden danger here:

Sequences may promote sequential processing of data

The hint's in the name!

Sequential processing on today's multi-core computers is rightly frowned upon. We should be writing code that is either explicitly parallel or gives the compiler and/or run-time the opportunity to parallelize. But sequential list processing, where you primarily only process the head of the list before moving on to the tail elements, goes all the way back to Lisp; over sixty years ago! It's no wonder these concepts are so deeply ingrained.

Sequences are often reduced via accumulation. As Guy Steel hints at in "Four Solutions to a Trivial Problem", accumulation can be difficult to automatically parallelize. The abandoned Fortress project was an attempt to mitigate this.

The egg language (not in the same league!) is designed to be easy to learn, but I would like some aspects of concurrency and parallelization to be accessible, even if only as a taste of more complex paradigms. Microsoft's PLINQ demonstrates that it is possible to build parallel execution on top of sequences, but I need to do a lot more research in this area. In particular, do I need to worry about this as part of the language specification as opposed to a library, like PLINQ?

egg Sequences 2

Last time we saw how various curly-brace programming languages deal with sequences, if at all. Now we'll concentrate on sequence generation.

Generators

In these examples, I'll use JavaScript because the syntax is more concise, but similar effects have be achieved with C#.

Consider this code:

  // JavaScript

  function* countdown() {

    yield 10;

    yield 9;

    yield 8;

    yield 7;

    yield 6;

    yield 5;

    yield 4;

    yield 3;

    yield 2;

    yield 1;

  }

  for (var i of countdown()) {

    console.log(i);

  }

This obviously counts down from 10 to 1. (I say "obviously" but that wasn't strictly true for me. I used "in" instead of "of" in the for loop and got nothing out. Good luck, learners!)

The first improvement we'd probably want to make is to use a loop:

  // JavaScript

  function* countdown() {

    for (var n = 10; n > 0; --n) {

      yield n;

    }

  }

  for (var i of countdown()) {

    console.log(i);

  }

Next, we could parameterize the countdown:

  // JavaScript

  function* countdown(x) {

    for (var n = x; n > 0; --n) {

      yield n;

    }

  }

  for (var i of countdown(10)) {

    console.log(i);

  }

Nice. But what exactly is "countdown" and what does it return? If you bring up a Chrome console and type in the last snippet, you can get useful insights:

So, "countdown" is a function; no surprise there! But a call to "countdown(10)" produces a suspended "Generator" object with a couple of scopes. This gives an insight into what is happening under the hood.

A JavaScript generator function returns a object that implements the iterator protocol. This consists of the "next()" member function, which, in turn, allows the use of "for ... of" loops and spread syntax:

  > console.log(...countdown(10))

  10 9 8 7 6 5 4 3 2 1

Yield

The JavaScript yield operator differs from the return statement in a couple of fundamental ways.

Firstly, "yield" is resumable. If a function terminates with a "return" statement (including an implicit return at the end), that's it: game over; the function has finished. With a yield, the function may resume at a later date. This implies that the state of the function (e.g. local variables, exception try blocks, etc.) must be preserved when a "yield" is executed so that the generator can continue exactly where it left off. This is a coroutine.

Secondly, a JavaScript "yield" is an operator that produces a value. It is an expression. This allows the caller to pass information back into the iterator function. A "return" is a statement.

Coroutines

If generator functions produce coroutines, what sort of coroutines do they produce?

The various flavours of coroutines are discussed at length in the following papers:

• Revisiting Coroutines, Ana Lucia de Moura and Roberto Ierusalimschy, 2004
• Boost Coroutines, Oliver Kowalke, 2009
• Yield: Mainstream Delimited Continuations, Roshan P. James and Amr Sabry, 2011

Symmetric versus Asymmetric

Symmetric coroutines can yield to any arbitrary coroutine; asymmetric coroutines can only yield to their "caller". It has been shown that you can build symmetric coroutines from asymmetric ones, and vice versa. Asymmetric coroutines are generally considered to be easier for humans to understand; for one thing, they maintain the notion of caller and callee. Both JavaScript and C# implement asymmetric coroutines.

Stackful versus Non-stackful

Stackful coroutines can yield anywhere, including from functions called by coroutine. Non-stackful coroutines can only can only suspend their execution when the control stack is at the same level that it was at creation time. Non-stackful coroutines have the advantage that yields are unambiguous in cases where one co-routine has explicitly called another. Both JavaScript and C# implement non-stackful coroutines.

Internal-only versus Externalised

This only applies to coroutines that are generators. Internal-only yields can only be used inside foreach-like statements; for example, CLU iterators are internal-only. Externalised yields provide an interface for calling the coroutine at arbitrary call-sites. Both JavaScript and C# implement externalised yields (via the "iterator protocol" and "IEnumerator interface" respectively).

Unidirectional versus Bidirectional

This is my own nomenclature. Unidirectional coroutines use yield statements; i.e. no value can be passed from the caller back to the callee upon resumption. Bidirectional coroutines use yield expressions. In reality, bidirectional coroutines can be approximated using unidirectional ones:

  // JavaScript: bidirectional

  function* generator() {

    // blah blah

    var y = yield x; // caller returns 'y'

    // blah blah

  }

  // JavaScript: unidirectional

  function* generator() {

    // blah blah

    var xy = { x: x };

    yield xy; // caller adds 'xy.y'

    var y = xy.y;

    // blah blah

  }

JavaScript implements bidirectional coroutines; C# implements unidirectional coroutines.

Implementation

Under the hood, calls to JavaScript generator functions create objects that encapsulate the logic of the body of the function and maintain the state. We could do this by hand:

  // JavaScript

  function countdown(x) {

    var n = x;

    return {

       next: function() {

         return (n > 0) ? {value: n--, done: false}

                        : {done: true};

       }

    };

  }

But this is tedious and error-prone, not to mention ugly. Another option is to convert the generator body to resumable code automatically. This usually entails producing a finite state machine that replicates the functionality. There are at least two tools that do this:

1. Google's Traceur, and
2. Facebook's Regenerator.

Both produce genuinely scary code.

Perhaps the best solution is to support resumable function bodies natively. On code designed to run on a virtual machine, this is not so difficult. However, for efficiency, generators will probably be run via a different (stackless) code path from standard function calls. This is what the current egg implementation does, and I suspect this is also true for Chrome's generators too. C# on the other hand rewrites the function.

egg Sequences 1

Sequences of items are a recurring theme in programming, but different computer languages have differing levels of support for them. For the purposes of these posts, I'm going to define a sequence as:

1. Zero or more homogeneous elements
2. Elements may be repeated
3. Elements have a position (or positions, in the case of repeated elements) within the sequence
4. The only operation allowed for a consumer is to fetch the next element; this may fail if we have reached the end of the sequence
5. Sequences may be endless

This definition is known by many names in different languages (lists, enumerations, streams, iterations, etc.) but I'll stick with "sequence" to avoid ambiguity.

Let's break down the definition. Point 1 sounds quite restrictive: what if we want a sequence of integers and strings? This isn't really a problem in a language with composable types; we just define the type of the elements in our sequence to be the union of all the expected, individual types. In egg, we could use the hold-all "any" (or "any?" if we want nulls too).

Point 4 hints that, from a programming point of view, the consumer of a sequence doesn't see very much. But what does it need to see?

Support in Existing Languages

Rust has a very good interface for what it calls iterators. It has a single member function that returns the next element or nothing:

    // Rust

    fn next(&mut self) -> Option;

JavaScript has a similar protocol. The single member returns an object with two fields ("value", which may be undefined, and "done", which is a Boolean):

    // JavaScript

    function next();

Other languages are, in my opinion, a bit inferior in this respect. C# defines an enumerator interface with three members:

    // C#

    public T Current { get; }

    public bool MoveNext();

    public void Reset();

My two concerns with C#'s "IEnumerator<T>" are:

• Getting the next element is not an atomic operation: you need to move to the next element and then read it.
• The "Reset" method suggests that sequences are always "replayable". This is rarely the case (see the comment in the source).

In Java 8, sequences are named "iterators". The interface has four members:

    // Java

    default void forEachRemaining(Consumer action)

    boolean hasNext();

    T next();

    default void remove();

The first is a helper that can be overridden to optimise sequence operations. The next two exhibit the same atomicity problem that C#'s interface has. The final "remove" method is just plain strange. Needless to say, the default implementation throws a "not supported" exception.

C++ iterators are heavily templated and do not, in general, work via interfaces (though see Boost for some work towards this). Iterators in C++ are often bi-directional.

Atomicity

As I mentioned above, C# and Java have potential atomicity problems. In the vast majority of cases, these never appear or can be avoided by using additional locks. However, sequences can be a useful building block in concurrent systems (e.g. CSP), so native atomicity is a desirable feature.

For example, imagine a sequence of tasks being used as a queue of work for two or more consumers. If the consumers cannot atomically fetch the next work item from the sequence, there is the potential for work items to be accidentally skipped or even performed twice.

For that reason, if written in C++17, one interface for sequences could be:

    // C++

    template<typename T> class Sequence {

      virtual ~Sequence() {}

      virtual std::optional<T> next() = 0;

    };

This is effectively the Rust interface above.

Sequence Functions in egg

In egg, we can simplify this interface (for integers) to a single function signature:

    // egg

    void|int next()

We could have used the following:

    // egg

    int? next()

But that would mean that sequences could not contain null values.

The type of a sequence function for integers is therefore "(void|int)()" which is somewhat ugly. I originally thought that abbreviating this to "int..." would be quite intuitive, but quickly ran into syntax problems (see later). At present, I am toying with the idea of using "int!" as a shorthand, based on some fuzzy notion that other languages using "!" when dealing with channels.

Thus, if a function took two integer sequences and merged them in some way, the signature could be:

    // egg

    int! merge(int! left, int! right)

This implies that sequences are first-class entities: what R. P. James, and A. Sabry call "externalised yields" that can be used outside of the "for-each" control statement.

However, this only deals with consumers of sequences. How does one produce a sequence in the first place?

Sequence Generators

One way to create a sequence is via a container that permits iteration. Most languages that support the "for-each" control statement allow you to iterate around elements in an array, for example.

    // JavaScript

    var a = [10, 20, 30];

    for (var v of a) {

      process(v);

    }

However, one of the strengths of sequences is that the elements can be generated on-demand or lazily. Indeed, some sequences are infinite, so populating a container with all the elements of a sequence may be impractical or impossible.

Both C# and JavaScript have the "yield" keyword. C, C++ and Java have non-standard mechanisms for achieving similar effects, but they are not part of the language.

Here's a generator function to produce the infinite, zero-based, Fibonacci sequence in JavaScript:

    function* fibonacci() {

      var a = 0;

      var b = 1;

      for (;;) {  

        yield a;

        var c = a + b;

        a = b;

        b = c;

      }

    }

And in C#:

    public IEnumerable<int> fibonacci() {

      int a = 0;

      int b = 1;

      for (;;) {

        yield return a;

        int c = a + b;

        a = b;

        b = c;

      }

    }

The syntax is slightly different, but the fundamentals appear similar. Surely that means that generator functions are trivial to implement? Alas, no.

Next time, I'll discuss why generators are so complicated under the surface. In the mean-time, might I again suggest this paper as some bed-time reading?

egg Garbage Collection 2

In the first part of this thread, I introduced a less intrusive tracing garbage collector that I'm working on for the egg programming language. One of the questions I left hanging was determining which nodes in the basket are "roots". That is, which nodes are pointed to directly from outside the basket?

Roots and Concurrency

At some stage in the future, I'd like to switch the garbage collection to be concurrent. This poses additional problems. Imagine you are inserting a parent node and a child node into the basket and the parent is a root. How do you do this whilst the garbage collector is concurrently running? You have to be very careful of the order of operation so that the collector doesn't accidentally evict your nodes before you've had the chance to finalise all the links.

One solution is to ensure all the new nodes are roots and then downgrade most of them after linking them together. This implies that downgrading nodes, from root to non-root, needs to be an efficient operation.

Another potential requirement is "locking" nodes when a subsystem other than the garbage collector is using them; you don't want the collector to pull the rug from under their feet.

Hard and Soft References

To try to solve these issues, I've been experimenting with "soft" and "hard" references. These shouldn't be confused with "weak" references; that's an orthogonal concern. A soft reference is a link between two nodes in the same basket; these are the links that the tracing garbage collector follows. A hard reference is a link to a node that uses traditional reference counting. Unlike soft references, hard references do not need to know which node they are pointing from, only where they are pointing to. Indeed, hard references do not even need to be to or from nodes within a basket. In these respects, hard references are similar to "std::shared_ptr" in C++.

In egg, the "Collectable" base class can be the target of both soft and hard references. To be the target of a soft reference, the "Collectable" node must be a member of exactly one basket. When the node was added to it's basket, the basket obtained a single hard reference to it. This single hard reference is maintained no matter how many soft references there are to it from within the basket; it is only relinquished when the node is evicted from the basket.

Here's an overview:

• When a node is added to a basket, the basket takes a hard reference to it.
• Nodes can have zero or more additional hard references to them.
• The garbage collector only considers nodes for eviction if they have a hard reference count equal to one, i.e. the only hard reference to them is from the basket.
• Nodes that have hard references in addition to the single reference from the basket are considered "roots" and are effectively locked.
• Nodes can only be added to a basket by supplying a hard reference. This overcomes the race condition causing premature eviction of partially constructed networks.
• Nodes can be made a "root" simply by creating an external hard reference to it. When the last external hard reference is lost, the node is no longer a "root" and is a candidate for eviction from the basket if it is not accessible from some other root.

Practical Considerations

When I started implementing soft references, I found they are incredibly difficult to construct properly. The reason is that soft references need to know both the source and target of the reference. If you are constructing an instance, "source", of a class that contains a soft reference to another node, "target", you can easily end up creating a reference between "source" and the partially constructed "target". If an exception is thrown within the constructor (or a function called from it) it can be very difficult to untangle the links safely.

The solution I'm using at the moment creates all the links as hard references and then demotes them to soft references later on. This has the added advantage of not adding nodes to the basket at all in the event of an exception being thrown part-way through the initial creation of the network.

Another facility I added to make constructing soft references less error-prone is "basket inference". Usually, the sequence of events is:

1. Add the target to the basket, if it's not already added
2. Add the source to the basket, if it's not already added
3. Create a soft reference from the source to the target

Instead, the basket (which must be the same for both source and target) is inferred where possible; the source or target are added to the basket as necessary. This usually works because it's highly unlikely that neither the source nor the target have been added to a basket already.

egg Boolean operators

Here's an interview-style question:

What are the Boolean operators in C++?

Of course, it's a trick question; there are two flavours of "Boolean operator":

• Operators that take Boolean operands, and/or
• Operators that return Boolean values

So let's be more concrete. Which standard C++ operators can you substitute for "◊" to make the following well-formed?

    // C++
    bool a = false;
    bool b = true;
    auto c = a ◊ b;

It turns out that any C++ operator that can be applied to integers can be substituted, including shift operators like "<<". Because of the history of the introduction of "bool" values into the language, they often get type-promoted to integers silently. For example, "c" has type "int" in the following:

    // C++
    bool a = false;
    bool b = true;
    auto c = a << b;

Whilst the following holds true:

    // C++
    assert((false - true) == -1);

The list of C++ operators that take Boolean operands and return Boolean values is much smaller:

• a == b
• a != b
• a < b
• a <= b
• a >= b
• a > b
• a && b
• a || b
• !a

In Java, Boolean values seem to be treated more carefully. It adds the "&", "|" and "^" operators.

Let's not even think about JavaScript!

I've been extending my test coverage of egg scripts (using OpenCppCoverage) and have come across this inconsistency. As part of the effort to make egg easy to learn by reducing surprise, I'm shying away from automatic type promotion (although I suspect integer-to-float promotions will always be warranted). Therefore, I decided to add explicit Java-style Boolean operators to egg.

    // egg
    bool a = foo();
    bool b = bar();
    var c1 = a & b; // 'c1' is bool
    var c2 = a | b; // 'c2' is bool
    var c3 = a ^ b; // 'c3' is bool

And, while I'm at, I'll add the following operators for orthogonality:

    // egg
    bool a = foo();
    bool b = bar();
    a &&= b; // Same as 'if (a) { a = b; }'
    a ||= b; // Same as 'if (!a) { a = b; }'
    int? c = baz();
    c ??= 123; // Same as 'if (c == null) { c = 123; }'

The last operator is particularly useful when dealing with default parameters.

And then we have the rabbit-hole of the missing "^^" and "^^=" operators...

Postscript

I also noticed today that spaceships are set to invade C++20. I will resist such an invasion of egg!