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package csp

import "github.com/thomas11/csp"

The examples from Tony Hoare's seminal 1978 paper "Communicating sequential processes" implemented in Go.

Go's design was strongly influenced by Hoare's paper [1]. Although Go differs significantly from the example language used in the paper, the examples still translate rather easily. The biggest difference apart from syntax is that Go models the conduits of concurrent communication explicitly as channels, while the processes of Hoare's language send messages directly to each other, similar to Erlang. Hoare hints at this possibility in section 7.3, but with the limitation that "each port is connected to exactly one other port in another process", in which case it would be a mostly syntactic difference.

[1] http://blog.golang.org/2010/07/share-memory-by-communicating.html

Implementing these examples, and the careful reading of the paper required to do so, were a very enlightening experience. I found the iterative array of 4.2, the concurrent routines changing their behavior execution of 4.5, and the highly concurrent matrix multiplication of 6.2 to be particularly interesting.

I tried to name routines and variables like in the paper, which explains the now outdated upper-case names. Similarly, I tried to make the function signatures as similar to the paper as possible, so we mostly work directly with channels, where one would hide this implementation detail in real-world code.

The ugly name prefixes like "S33_" make godoc order the types by section of the paper.

Most of the examples have tests, although I have not taken a lot of care to test corner cases. The test of the S53_DiningPhilosophers is not really a test, it simply runs the routine for ten seconds so you can observe the philosophers behavior (use `go test -v`).

Thomas Kappler <tkappler@gmail.com>

csp.go

❖ func S31_COPY(west, east chan rune)

3.1 COPY

> "Problem: Write a process X to copy characters output by process west to process, east."

In Go, the communication channel between two processes (goroutines) is explicitly represented via the chan type. So we model west and east as channels of runes. In an endless loop, we read from west and write the result directly to east.

As an addition to the paper's example, we stop when west is closed, otherwise we would just hang at this point. To indicate this to the client, we close the east channel.

❖ func S32_SQUASH(west, east chan rune)

3.2 SQUASH

> "Problem: Adapt the previous program [COPY] to replace every pair of consecutive asterisks "**" by an upward arrow "↑". Assume that the final character input is not an asterisk."

If we get an asterisk from west, we receive the next character as well and then decide whether to send the upward arrow or the last two characters as-is. Go's UTF8 support allows to treat the arrow like any other character.

❖ func S32_SQUASH_EXT(west, east chan rune)

Hoare adds a remark to 3.2 SQUASH: "(2) As an exercise, adapt this process to deal sensibly with input which ends with an odd number of asterisks." This version handles this case by sending a single asterisk from west to east if west did not supply another character after a timeout, or if west was closed in the meantime.

❖ func S33_DISASSEMBLE(cardfile chan []rune, X chan rune)

3.3 DISASSEMBLE

> "Problem: to read cards from a cardfile and output to process X the stream of characters they contain. An extra space should be inserted at the end of each card."

Trivially translated to Go. We don't need to care about the indices 1 to 80, range handles this for us.

❖ func S34_ASSEMBLE(X chan rune, lineprinter chan []rune)

3.4 ASSEMBLE

> "Problem: To read a stream of characters from process X and print them in lines of 125 characters on a lineprinter. The last line should be completed with spaces if necessary."

❖ func S35_Reformat(cardfile, lineprinter chan []rune)

3.5 Reformat

> "Problem: Read a sequence of cards of 80 characters each, and print the characters on a lineprinter at 125 characters per line. Every card should be followed by an extra space, and the last line should be completed with spaces if necessary."

This is a great example of how easily concurrent processes can be combined in the manner Unix pipes. No extra code is required to let the data flow through the two routines we wrote earlier.

❖ func S36_Conway(cardfile, lineprinter chan []rune)

3.6 Conway's Problem

> "Problem: Adapt the above program to replace every pair of consecutive asterisks by an upward arrow."

The implementation in four lines is a testament to the expressive power of modeling programs as communicating sequential processes.

❖ func S41_DIV(x, y int, res chan struct{ quot, rem int })

4.1 Function: Division With Remainder

> "Problem: Construct a process to represent a function-type subroutine, which accepts a positive dividend and divisor, and returns their integer quotient and remainder. Efficiency is of no concern."

❖ func S42_facM(limit int) chan int

4.2 Recursion: Factorial

> "Problem: Compute a factorial by the recursive method, to a given limit."

This example is fascinating. It introduces the "iterative array" which kept me puzzled for a while, but made for a great a-ha moment when I got it. It's an array of coroutines, so that for a given integer input i, the coroutine at index i knows how to deal with it. By addressing its neighbor coroutines at i-1 and i+1, a coroutine can communicate with the others to break down the overall problem. That sounds pretty abstract and will be clearer in the following examples.

To compute n!, we use the simple recurrence `n! = n * (n-1)!`, with `0! = 1! = 1`. In our iterative array of goroutines, when routine i receives the value x, it sends x-1 up the chain, i.e., to the right in the iterative array. This continues until the value is 0 or 1 and we hit the base case of the recursion. The coroutines then pass values back down the chain, i.e. leftwards, starting with 1. When routine i receives a result passed back down the chain, it multiplies it with x and passes on the result. When it arrives at routine 0, n! is computed.

The caller doesn't see this process. We only need to expose goroutine 0, which can compute any factorial by passing the value up the chain and waiting for the result. Any factorial up to the limit of the length of the iterative array, that is, which has to be given when creating the factorial iterative array.

Go models communication between goroutines with explicit channel values, so in this implementation the iterative array is an array of channels. When we create it, we launch the corresponding goroutines at the same time.

❖ func S45_ParIntSet(limit int) (chan int, chan S45_HasQuery, chan chan int, chan S45_LeastQuery)

4.5 Recursive Data Representation: Small Set of Integers

> "Problem: Same as above, but an array of processes is to be used to achieve a high degree of parallelism. Each process should contain at most one number. When it contains no number, it should answer "false" to all inquiries about membership. On the first insertion, it changes to a second phase of behavior, in which it deals with instructions from its predecessor, passing some of them on to its successor. The calling process will be named S(0). For efficiency, the set should be sorted, i.e. the ith process should contain the ith largest number."

We use the iterative array technique from 4.2 again here.

I found this exercise to be the trickiest one. The *least* operation had me puzzled for a while. I tried to make it work, analogous to the other three, with a single channel used both to communicate with the client and to communicate internally between the goroutines.

❖ func S51_Buffer(bufSize int) (consumer chan int, producer chan int)

5.1 Bounded Buffer

> "Problem: Construct a buffering process X to smooth variations in the speed of output of portions by a producer process and input by a consumer process. The consumer contains pairs of commands X!more( ); X?p, and the producer contains commands of the form X!p. The buffer should contain up to ten portions."

This is exactly what Go's buffered channels provide. We will do it manually here. Even that would be trivial using a `select` containing both the producer receive and the consumer send, so we'll do it without select. The implementation strictly follows Hoare's pseudo-code from the paper.

We do actually use `select`, but only for single channel operations, in order to exploit the semantics of its `default` case: try the channel operation, but don't block if the other end isn't ready, instead just skip it and continue.

5.3 Dining Philosophers (Problem due to E.W. Dijkstra)

> "Problem: Five philosophers spend their lives thinking and eating. The philosophers share a common dining room where there is a circular table surrounded by five chairs, each belonging to one philosopher. In the center of the table there is a large bowl of spaghetti, and the table is laid with five forks (see Figure 1). On feeling hungry, a philosopher enters the dining room, sits in his own chair, and picks up the fork on the left of his place. Unfortunately, the spaghetti is so tangled that he needs to pick up and use the fork on his right as well. When he has finished, he puts down both forks, and leaves the room. The room should keep a count of the number of philosophers in it."

The dining philosophers are famous in Computer Science because they illustrate the problem of deadlock. As Hoare explains, "The solution given above does not prevent all five philosophers from entering the room, each picking up his left fork, and starving to death because he cannot pick up his right fork."

❖ func S61_SIEVE(numPrimes int, primes chan int)

6.1 Prime Numbers: The Sieve of Eratosthenes

> "Problem: To print in ascending order all primes less than 10000. Use an array of processes, SIEVE, in which each process inputs a prime from its predecessor and prints it. The process then inputs an ascending stream of numbers from its predecessor and passes them on to its successor, suppressing any that are multiples of the original prime."

Here I ran into a problem that I suspect is with the algorithm itself. It uses one process aka goroutine per prime number. The pseudocode in the paper instantiates 101 processes, enough for the first 100 primes. However, it sends the numbers up to 10.000 to the first process, which contain the first 1229 primes. Maybe I overlooked something about how the paper's pseudo-implementation handles this, but in my Go implementation I get a deadlock after these first 100 primes.

Not wanting to spend too much time on this, I changed the function signature to accept a numPrimes parameter giving the number of primes to generate.

❖ type S43_IntSet struct { // contains filtered or unexported fields }

4.3 Data Representation: Small Set of Integers

> "Problem: To represent a set of not more than 100 integers as a process, S, which accepts two kinds of instruction from its calling process X: (1) S!insert(n), insert the integer n in the set, and (2) S!has(n); ... ; S?b, b is set true if n is in the set, and false otherwise."

Send true on res if s contains n, otherwise false.

The caller needs to pass in the result channel because otherwise we'd need to return a channel here to make the operation asynchronous. But what channel? If we make a new one every time, it's wasteful. If we have only one, we need to lock access to it, and we cannot close it, so the caller might wait indefinitely on it (although that would be an error in the client).

❖ func (s *S43_IntSet) Insert(n int, ack chan int)

Insert the number n into the set, if there is still room. Note that in Hoare's specification the client has no way of knowing whether the set is full or not, safe for testing whether the insertion worked with has().

The client can also not know when the insertion is complete. Parallel insertions and Has() queries are protected by a mutex. But there is no guarantee that the Insert() has even started to run, i.e., actually acquired the lock. To protect against seeing stale data, the client can pass in an ack channel and block on it.

4.4 Scanning a Set

> "Problem: Extend the solution to 4.3 by providing a fast method for scanning all members of the set without changing the value of the set."

The implementation below looks quite different from Hoare's. Go's channels in combination with `range` make the implementation trivial. An implementation closer to the pseudocode in the paper might return a chan int and a chan bool "noneleft" to the caller, sending a signal on noneleft after the iteration.

❖ type S45_HasQuery struct { N int Response chan bool }

❖ type S45_LeastResponse struct { Least int NoneLeft bool }

❖ type S52_Semaphore struct { // contains filtered or unexported fields }

5.2 Integer Semaphore

> "Problem: To implement an integer semaphore, S, shared among an array X(i:I..100) of client processes. Each process may increment the semaphore by S!V() or decrement it by S!P(), but the latter command must be delayed if the value of the semaphore is not positive."

This is a nice one to write using `select`. We use two channels, inc and dec, for the two operations the semaphore offers. If dec isn't possible because the semaphore is 0, the client's channel send blocks.

The number of clients, 100 in the paper, doesn't matter for the inc and dec operations since, in contrast to Hoare's pseudocode, we don't need to explicitly scan all clients in the channel receive operations. We would need to know the number if we wanted to keep track of active clients and shut down the semaphore once they are all finished. I didn't implement this, but it would be easy to do with an `activeClients int` variable and a `done` channel that decrements it.

A problem I faced initially was that I put both the inc and the dec receive operations into one select. This would require a guard on the dec receive, something like `case val > 0 && <- dec:`, but Go doesn't support that. So I would receive from dec, thereby acknowledging the operation to the caller, before knowing that the decrement was legal. The solution is obvious in retrospect: try the dec receive in a separate select, protected by a `val > 0` guard.

❖ type S62_Matrix struct { A [][]float64 WEST , SOUTH []chan float64 // contains filtered or unexported fields }

A matrix for use in example 6.2, matrix multiplication.

6.2 An Iterative Array: Matrix Multiplication

> "Problem: A square matrix A of order 3 is given. Three streams are to be input, each stream representing a column of an array IN. Three streams are to be output, each representing a column of" the product matrix IN × A."

Make a new matrix with the given values (rows, then columns). This constructor will launch the goroutines for NORTH, EAST and CENTER as described in the paper. The client can then send the values of row i of IN to WEST[i] and read column j of IN × A from SOUTH[j]. See the test for an example.

A concurrent routine for a matrix cell that's not on an edge.

A sink on the right.

A constant source of zeros from the top.