CSPCommunicating Sequential Processes

Prabhaker Mateti

CSP Overview

• Models distributed computing– primitives: send/receive only– no shared variables (across outer processes)

• Idealistic send/receive– no buffering– sending a value from one process and the

receiving of that value in another process appears externally as one event

CSP Synchronous Message Passing

• Send !– ex: R ! (x*y + c)– to process R send the value of expression x*y + c– sender names the receiving process R– waits until receiver R is ready to receive

• Receive ?– ex: S ? v– receiver names the sender process S– names the receptacle v

• a variable declared to be a compatible type

– waits until sender S is ready to send• Deadlock is possible

G1 S1 [] G2 S2 [] ...[] Gn Sn

• Gi must not have sends• Gi can include at the tail a receive• Example: val > 0; Y?P() Q– Suppose val = 0. The above input is not

attempted.– Suppose val > 0, but Y is not ready to send. Then,

we are not committed to perform this input.– Suppose val > 0, and Y is ready to send. Then, we

perform this input, and execute Q.

Additional CSP NotationNotation Comments

:= assignment

C1; C2 Sequential composition: C2 after C1

C1 || C2 Simult parallel; not C1; C2 or C2;C1

C2 || C1 Same as C1 || C2

if G1 S1 [] G2 S2 [] ...[] Gn Sn fi If statement; Hoare used [ …]; [] is fat bar

do G1 S1 [] G2 S2 [] ...[] Gn Sn od Loop; Hoare used *[ … ]

Multiple Gi can be true; non-determinism

Skip Do-nothing (no-op) statement

; Also used to end declarations

Small Set of Integers

• Design a server that can provide the abstraction of a Small Set of Integers

• Make it as distributed as possible• Make it as symmetric as possible• Simplifying Assumptions– Finite, say 100 integers– any/all integers can be elements– query “have you got x” replied with Boolean– request “insert x”, no replies

• if duplicate, no problem• if ran out of room, problem … but silently discard

Small Set of Integers: Design

• An array S of 102 processes• S(i: 1..100)– each process holds an integer or is empty-handed– S(i) has an integer implies• S(i-1) also has an integer• integer of S(i-1) < integer of S(i)

• S(101) is a sink• S(0) is the “receptionist”

Small Set of IntegersS(i: 1 .. 100) :: do n: integer; S(i-1)?has(n) S(0)!false [] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!insert(n); n := m [] m = n skip [] m > n S(i+1)!insert(m)

fiod od

Small Set of Integers: S(i)do n: integer; S(i-1)?has(n) S(0)!false[] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n :=

m [] m = n skip [] m > n S(i+1)!insert(m)

fiod

od

• Each S(i) starts out empty handed

• Any has(whatever) is replied with false.

• The first inserted value is saved in n

• After the first insert, the process spends its life in the second loop.

• Note: we have no breaks or exits.

Small Set of Integers: has(m)do n: integer; S(i-1)?has(n) S(0)!false[] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m ≤ n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n :=

m [] m = n skip [] m > n S(i+1)!insert(m)

fiod

od

• processes are arranged in a “row”– 0 index at left, 101 at right

• S(i-1)?has(m) (black color) implies– S(i) is not empty handed– S(i-1) does not have m

• n is the number S(i) is holding• elements are sorted from l-to-r

• m = n: we have it• m < n: no one else has m either

• reply to the receptionist S(0)

Small Set of Integers: insert(m)do n: integer; S(i-1)?has(n) S(0)!false[] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n :=

m [] m = n skip [] m > n S(i+1)!insert(m)

fiod

od

• no S(j) has m (j < i)

• Case m = n– request to insert a duplicate

element– do nothing

• Case m > n– to be inserted m is higher– ask S(i+1) to insert m

• Case m < n– the number n held by S(i) is

higher– ask neighbor S(i+1) to hold n– S(i) now holds m

Small Set of Integers: S(0) and S(101)

• S(101) is a sinkS(101) ::

do S(100)?has(m) S(0)!false[] S(100)?insert(m) skip

od

• S(0) is the “receptionist”S(0) ::

doClient ?has(n) S(1)!has(n); if (i: l.. 100) S(i)? b Client ! b fi[] Client ? insert(n) S(1)?insert(n)

od

Small Set of Integers: Questions

• Does “distributed” mean “concurrent” and/or “parallel”

• How do we delete?• Can we redesign this into a lossless set of

integers?

Matrix Multiplication

Matrix Multiplication

[ M(i: 1..3,0) ::WEST || M(0, j: 1..3) ::NORTH || M(i: 1..3,4) ::EAST || M(4, j: 1..3) ::SOUTH || M(i: 1..3, j:

1..3)::CENTER ]• Declarations omitted

for clarity

• NORTH = do true M(1, j)!0 od

• EAST = do M(i,3)?x skip od

• CENTER = do M(i, j - 1)?x

M (i, j+1)!x; M (i-1, j)?sum; M (i+1, j)!(A (i, j)*x+sum) od

Sieve of Eratosthenes

• Print all primes less than 10000– 2, 3, 5, 7, 11, 13, …

• Design– Use an array SIEVE of processes– SIEVE(i) filters multiples of i-th prime– sqrt(10000) processes are needed– SIEVE(0) and SIEVE(101)

Sieve of Eratosthenes[SIEVE(i: 1..100)::

SIEVE( i - 1)?p; print ! p;mp := p;do SIEVE(i - 1)? m

do m > mp --> mp := mp + p od;if m = mp --> skip [] m < mp --> SIEVE(i + l)!mfi

od|| SIEVE(0):: print!2; n := 3; do n < 10000 --> SIEVE(1)!n; n := n + 2 od|| SIEVE(101):: do SIEVE(100)?n --> print ! n od|| print:: do (i: 0..101) SIEVE(i)?n --> .“print-the-number” n od]

Shared Variables

• Duality: variables v. processes– Provide a “shared variable” V as a process V– User processes do:• V ! exp equiv of V := exp• V ? u equiv of u := V, u local to this process

• semaphores, by intention, are shared variables.

Semaphores in CSP

S:: val: integer; val := 0; /* or any +int */do

(i:I..100)X(i)?V() val := val + 1 II (i:l..100) val > 0; X(i)?P() val := val - 1

od• Within the loop: 100 + 100 (unnamed) processes• these 200 processes share the integer val• yet there is no mutex problem here; why?• Array X of 100 client processes can do– S!P() or S!V()

Buffered Message Passing

• CSP send/receive have no buffering == Synchronous Message Passing

• A Buffer process can be inserted between the (original) sender and (original) receiver.

• This gives a Semi Asynchronous Message Passing.– Sends do not block (until the Buffer becomes full)

Modeling Remote Proc Call

• RPC client• server ! proc5(e1, e2); server? proc5(r1, r2, r3)

• RPC Server• do …

[] client?proc4(…) …[] client?proc5(v1, v2) …

client!proc5(e3, e4, e5)[] …

od

Fairness

[ X:: Y!stop()ll Y::

c := true; do

c; X?stop() c := false

[] c n := n + 1od

]

• Will/Must this terminate?

• We (programmers) should not assume fairness in the implementation

Process Algebras

• mathematical theories of concurrency

• Events– on, off, valve.open,

valve.close, mouse?(x,y), screen!bitmap

• Primitive processes– STOP (communicates

nothing), – SKIP (represents

successful termination)

• Event Prefix: e P• Deterministic Choice• Nondeterministic

Choice• Interleaving• Interface Parallel• Hiding• www.usingcsp.com/ has

an entire book by Hoare

CSP Implementations

• Occam is based on CSP– Machine Lang of Transputer

CPU, 1990s– Andrews book, Section 10.x

• CSP in Java == JCSP Software Release at www.cs.kent.ac.uk/projects/ofa/jcsp/

• Communicating Process Architectures Conference == CPA

• CSP in Jython and Python, CPA 2009

• Limbo, Newsqueak are prog langs from Bell Labs, included in the Inferno OS, 2004

• Concurrent Event-driven Programming in occam-π for the Arduino, CPA 2011

• Experiments in Multi-core and Distributed Parallel Processing using JCSP, CPA 2011

• LUNA: Hard Real-Time, Multi-Threaded, CSP-Capable Execution Framework, CPA 2011

CSP References

• C. A. R. Hoare, ``Communicating Sequential Processes,'' Communications of the ACM, 1978, Vol. 21, No. 8, 666-677.– www.usingcsp.com/ has an entire book by Hoare.– For now, do not read it (!!)

• Andrews, Chapter on Synchronous Message Passing.

• U of Kent, CSP for Java (JCSP), www.cs.kent.ac.uk/projects/ofa/jcsp/