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This post is part of a series exploring Concepts, Techniques, and Models of Computer Programming by Van Roy and Haridi. Check the blog index for more.

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Chapters 3 and 4 of Concepts, Techniques, and Models of Computer Programming (CTM) cover the definition of declarativeness and its application in concurrent programing. As noted in the previous post in this series which mostly covered Chapter 3, one of the limitations of the declarative paradigm is its inability to deal with the “real world.”[3] Declarative programming is pure, but not always realistic. The “real world” includes concurrency, the basic definition of which is “A set of activities that execute independently.” In other words, in the real world, things operate both in tandem with and independently from each other. Not everything can be neatly partitioned as declarative programming can sometimes require. Dealing with concurrency in programs is notoriously challenging, but not by necessity. The authors have developed a simple mantra:

“Concurrency can be simple.”

They demonstrate the basic means by which a program can be made concurrent as follows. Consider this simple program in the declarative kernel language:

A function Gen takes two variables L and H. It waits 100 milliseconds. It terminates if L is greater than H, else it recurs on a constructed list with L as the head and a new list beginning with L+1 as the tail. When run with {Gen 1 10}, it would return a list [1 2 3 4 5 6 7 8 9 10] Below the function definition, the 1..10 list is bound to Xs, and Ys is bound to the results of mapping over the elements of Xs and squaring them. The results of the list are then shown with Browse.

The concurrent or threaded version uses the same definition for Gen, and only adds the thread keyword:

The result is that the results are incrementally displayed in Browse as they are calculated. The reason to put a Delay call in Gen is to illustrate the point that concurrency has the effect of making ‘atomic’ calculations ‘incremental’. Note that nothing else about the program needed to change in order to make it concurrent: just add threads and you’re good. This is the dream of concurrent programming.

This post will cover the parts of Chapter 4 which define concurrency and its application to declarative programming. We will see the semantics of threads in the extended kernel language, get a glimpse at programming with streams, and I will attempt to tie the lessons of declarative concurrency to the current state of programming tools. I’m not covering everything in this chapter by a long shot - it is very dense. I’m intentionally not covering error handling or exceptions, which might rankle some, especially in the context of streams. If you want to know more about this, I suggest that you read the chapter: the authors have some good answers for you. Our next post will finish out Chapter 4 by taking a look at Declarative concurrency and its interaction with a fascinating language construct known as laziness.

#### What is Concurrency?

Declarative programming has been shown to be a surprisingly rich and capable paradigm which can be applied in a variety of circumstances if the developer is aware of the involved tradeoffs. The declarative kernel language is small and flexible enough that adding the ability to execute code concurrently ends up being simple, at least from a programming language design standpoint.

“Our approach to concurrency is a simple extension to the declarative model that allows more than one executing statement to reference the store.”

A new instruction, thread, is added to the existing kernel, which gives us the following language:

The entire data-driven concurrent kernel language, including the new thread instruction. [3]

The ability for the kernel language to express concurrent programs means that under the right conditions, things can be happening at the same time. The authors do an excellent job of describing what “at the same time” really means, and it’s worth going through the terminology so that we can thoroughly understand the implications of declarative concurrency.

It is said that all operations in a program have a global sequence and that threads do an interleaving execution over this sequence. A scheduler is responsible for choosing work for threads. Concurrency in the kernel language relies on the existence of single assignment or dataflow variables, the properties of which provide both immutability guarantees and a coordination point for external computation with respect to their bound/unbound state.

An execution is nondeterministic if the choice of which thread to execute becomes visible to the programmer. In the concurrent declarative kernel language, nondeterminism is never visible. Simply put, this lack of visible nondeterminism can be attributed to the fact that there is simply no choice but to wait if a variable is not yet bound. There is no chance that two threads will write to the same variable, since variables can only be assigned a value once. Therefore all “reads” will be deterministic and at worse you cannot predict exactly when “writes” will happen.

The scheduler which runs the concurrent kernel language is assumed to fairly select threads to do work, and never lets any thread starve. Threads can be either be ready or suspended, depending on if they have work to do, or are waiting on other calculations to be complete before their work can proceed. Let’s take a closer look at how threads integrate into the semantics of the kernel language and how it executes in our abstract machine.

This section builds on the abstract machine discussed in this earlier post in the series.

Adding threads to the existing declarative kernel language is a matter of adding a thread operation. This operation extends the abstract machine by allowing multiple semantic stacks to have access to the same data store.

Intuitively, the difference between a sequential and a concurrent program is reflected in how we introduce concurrency into the abstract machine: before, one total order was possible because only one environment was executed. After, a causal order is guaranteed by the scheduling algorithm and the existence of multiple stacks, each represented by a thread.

We still have the concepts of a single assignment store ($\sigma$), an environment ($E$), a semantic statement ($< S >, E$), and a semantic stack ($ST$). We extend the concept of an execution state and computation to allow for multiple semantic stacks. An execution state becomes a pair ($MST,\sigma$) where MST is a multiset (which we can think of as a list for our purposes) of semantic stacks and $\sigma$ is the single assignment store. A computation becomes a sequence of execution states which starts at the beginning of the list of semantic stacks, and ends at its end. The choice of which semantic stack to evaluate is up to the scheduler (the implementation of the scheduler is another fascinating subject that this post does not do justice).

Consider the following small sample concurrent program:

This program only has one place to begin, on the first line. B is introduced into an environment in a semantic stack and then the next line is reached. thread never blocks, but peels off the work into its own semantic stack to be executed at the scheduler’s convenience. The next line is reached. If B has been bound by the work done in the computation in the previous step, then this line will display yes and the program will be complete. There are no circumstances under which this program would behave in any other way under the given semantics.

#### What is Declarative Concurrency?

It has been shown that the “threadless” programs in the preceding chapters are declarative, and we have defined what concurrency means. So what does it mean for a program to be both declarative and concurrent? We know that the basis of declarativeness is that the output of a program should be a mathematical function of its input. Two issues arise with concurrent programming, however - termination is not guaranteed thus output is difficult to measure, and definition as functional is challenging, because programs inputs and outputs can both contain unbound variables. Simply put, we can think of declarative concurrency as concurrency with no observable nondeterminism, but lets spend some time with the technical definition:

“A concurrent program is declarative if the following holds for all possible inputs. All executions with a given set of inputs have one of two results: (1) they all do not terminate or (2) they all eventually reach partial termination and give results that are logically equivalent.”

For programs which do not terminate, we don’t need to illustrate much – they just won’t terminate, and that is true of any time you run them, regardless of externalities.

What does partial termination mean? Since we cannot rely on total termination in a programming paradigm with streams that can grow indefinitely, we can rely on a partial termination, defined as a stopping point when calculations are temporarily exhausted. Consider the following program:

This program will run as long as there are values in Xs to be processed. If there are none, the program will simply be in a state of partial termination. How can we assert the logical equivalence of the results of a program such as this? We can essentially rely on our intuition, but a technical explanation exists. Each state of partial termination contains enough information for us to quantify in terms of constraints. These constraints allow us to compare states in terms of bound and unbound variables and the values to which they may be bound. Since equivalence on these constraints is defined (but outside the scope of this post), we can assert equivalence on partial termination states even if the total order present in the sequential version doesn’t hold. As long as the causal order is maintained, and no nondeterminism is visible, our concurrent programs can be considered declarative.

#### Programming With Streams

Streams are given extensive treatment by the authors in Chapter 4 and are referred to as one of the most convenient and reasonable ways to program with declarative concurrency. A special case of stream programming is covered, known as deterministic stream programming, where “each stream object always knows for each input where the next message will come from.” This is a declarative means of stream programming - non-deterministic stream programming is covered in Chapter 5, Message-Passing Concurrency. Though this sounds limiting, some very interesting examples are covered.

The concept behind streams are that they are convenient ways to declaratively express computation as communication between threads. The authors description, as usual, is compact and thorough:

“A stream is a potentially unbounded list of messages, i.e., it is a list whose tail is an unbound dataflow variable. Sending a message is done by extending the stream by one element: bind the tail to a list pair containing the message and a new unbound tail. Receiving a message is reading a stream element.”

Streams and dataflow variables have a natural affinity and the authors capitalize on this insight. They give a nice definition and demonstration of basic use of streams, and begin to explore patterns useful in stream programming, even using streams to perform digital logic simulations.

Declaring a stream looks like this:

Here is how you incrementally extend a stream:

And a program that combines these concepts to form a basic producer/consumer pattern:

Producer and consumer each run in their own threads, operating on the shared dataflow variable Xs. As data is appended to the stream by Generate, it is consumed by Sum. The case statement in Sum blocks when there are no available values to bind, and calculates values when they are there to be read. As the authors say, “Waiting for a dataflow variable to be bound is the basic mechanism for synchronization and communication in the declarative concurrent model.”

You can use this same basic program to have multiple consumers and producers, or create a pipeline of filters:

And when streams are generalized to “a recursive procedure that executes in its own thread and communicates with other stream objects through input and output streams,” things really start to get wild: simple declarative concurrency primitives when combined can produce powerful results.

#### Conclusion

The authors have shown us yet again that simple extension of the semantics of the kernel language can make very sophisticated programs possible with seemingly limited resources. Concurrency and its application in modern software design is of paramount importance as our “free lunch” has long been over but we struggle in denial against its reality, often wielding primitive, wasteful tools.[2] Our tools rely on syntactic and semantic constructions which force us to amortize the costs of writing our programs over a very long period of time - they are easy to create, but difficult to maintain. Some of these constructions include (faux, overloaded) Object Orientation, global state, and mutability.

Mutability refers to the ability of the programmer to change the value of an object after it has been instantiated (object is an abstract name given to any assignable quantity that developers have access to). Much discussion has been raised specifically surrounding the connection between mutability and the inability for our tools to properly handle concurrency in a reasonable way, and in fact we are making progress.[1] Several active programming languages, including the Mozart platform that the CTM book constructs, Clojure, which runs on the Java Virtual Machine, and Haskell all have embraced the value of immutability and the leverage it gives programming language designers in providing simpler concurrency.

Beginning professional developers who jump right in to programming with mutable, global state, objects, and concurrency rightfully believe that “concurrency in LANGUAGE X is Hard.” Unfortunately, many people extend that to “programming with concurrency is Hard.” They don’t seek other paradigms because they think that the complexity is necessary. They think it is capital-H Hard and the truth is that it doesn’t have to be.

#### Works Cited

All quotes unless otherwise cited from Van Roy and Haridi.

[1] Hickey, Rich. Index of Published Talks HTML Page

[2] Sutter, Herb. A Fundamental Turn Toward Concurrency in Software Dr. Dobbs Software Journal. Available here.

[3] Van Roy and Haridi. Concepts, Techniques, and Models of Computer Programming MIT Press, hardcover, ISBN 0-262-22069-5, March 2004