Declarative Concurrency

1. Declarative Concurrency Seif Haridi KTH Peter Van Roy UCL S. Haridi and P. Van Roy

2. Concurrency • Some programs are best written as a set of activitiy that run independently (Concurrent programs) • Concurrency is essential for interaction with the external environment • Examples includes GUI (Graphical User Interface), operating systems, (see Bounce.oza) • Also programs that are written independently but interact only when needed (Client-Server applications) • This lecture is about declarative concurrency, programs with no observable nondeterminism, the result is a function • Independent procedures that execute on their pace and may communicate through shared dataflow variables S. Haridi and P. Van Roy

3. Overview • Programming with threads • The model is augumented with threads • Programming techniques: stream commuincation, order-determining concurrency, coroutines, concurrent composition • Lazy execution • demand-driven computations, lazy streams, and list comprehensions • Soft real-time programming S. Haridi and P. Van Roy

4. The sequential model Statements are executed sequentially from a single semantic stack Semantic Stack w = a z = person(age: y) x y = 42 u Single-assignment store S. Haridi and P. Van Roy

5. The concurrent model Semantic Stack 1 Semantic Stack N Multiple semantic stacks (threads) w = a z = person(age: y) x y = 42 u Single-assignment store S. Haridi and P. Van Roy

6. Concurrent declarative model The following defines the syntax of a statement, sdenotes a statement s::= skip empty statement | x = y variable-variable binding | x = v variable-value binding | s1 s2 sequential composition | local x in s1 end declaration| proc {x y1 … yn } s1 end procedure introduction | if x then s1 else s2 end conditional | { x y1 … yn } procedure application | case x of pattern then s1 else s2 end pattern matching | threads1 end thread creation S. Haridi and P. Van Roy

7. The concurrent model ST threads1 end,E Top of Stack, Thread i Single-assignment store S. Haridi and P. Van Roy

8. The concurrent model ST Top of Stack, Thread i threads1 end,E Single-assignment store S. Haridi and P. Van Roy

9. Basic concepts • The model allows multiple statements to execute ”at the same time” ? • Imagine that these threads really execute in parallel, each has its own processor, but share the same memory • Reading and writing different variables can be done simultaneously by different threads, as well as reading the same variable • Writing the same variable is done sequentially • The above view is in fact equivalent to an interleavingexecution: a totally ordered sequence of computation steps, where threads take turn doing one or more steps in sequence S. Haridi and P. Van Roy

10. Causal order • In a sequential program all execution states are totally ordered • In a concurrent program all execution states of a given thread is totally ordered • The execution state of the concurrent program as a whole is partially ordered S. Haridi and P. Van Roy

11. Total order • In a sequential program all execution states are totally ordered sequential execution computation step S. Haridi and P. Van Roy

12. Causal order in the declarative model • In a concurrent program all execution states of a given thread is totally ordered • The execution state of the concurrent program is partially ordered thread T3 thread T2 fork a thread thread T1 computation step S. Haridi and P. Van Roy

13. Causal order in the declarative model synchonize on a dataflow variable bind a dataflow variable thread T3 x thread T2 fork a thread y thread T1 computation step S. Haridi and P. Van Roy

14. Nondeterminism • An execution is nondeterministic if there is a computation step in which there is a choice what to do next • Nondeterminism appears naturally when there are multiple concurrent states S. Haridi and P. Van Roy

15. Example of nondeterminism Thread 1 Thread 2 store x y = 5 x = 1 x = 3 time time The thread that binds x first will continue, the other thread will raise an exception S. Haridi and P. Van Roy

16. Nondeterminism • An execution is nondeterministic if there is a computation step in which there is a choice what to do next • Nondeterminism appears naturally when there are multiple concurrent states • In the concurrent declarative model when there is only one binder for each dataflow variable, the nondeterminism is not observable on the store (i.e. the store develops to the same final results) • This means for correctness we can ignore the concurrency S. Haridi and P. Van Roy

17. Scheduling • The choice of which thread to execute next and for how long is done by a part of the system called the scheduler • A thread is runnable if its next statement to execute is not blocked on a dataflow variable, otherwise the thread is suspended • A scheduler is fair if it does not starve a runnable thread • I.e. all runnable thread execute eventually • Fair scheduling make it easy to reason about programs • Otherwise some prefectly runnable program will never get its share S. Haridi and P. Van Roy

18. The semantics • In the sequential model we had: (ST ,  ) ST is a stack of semantic statements  is the single assignment store • In the concurrent model we have: • (MST ,  ) • MST is a (multi)set of stacks of semantic statements •  is the single assignment store S. Haridi and P. Van Roy

19. The initial execution state ({ [ (s,) ] }, ) statement stack store multiset S. Haridi and P. Van Roy

20. Execution (the scheduler) • At each step, one runnable semantic stack is selected from MST (the multiset of stacks), call it ST, i.e. MST = ST  MST’ • Assume the current store is , one computation step is done that transforms ST to ST’ and  to ’ • The total computation state is transformed from (MST, ) to (ST’  MST’, ’) • Which stack is selected, and how many step are tasken is the task of the scheduler, a good scheduler should be fair, i.e. each runnable ’thread’ will eventually be selected • The computation stops when there is no runnable stacks S. Haridi and P. Van Roy

21. Example of runnable thread proc {Loop P N} if N > 0 then {P} {Loop P N-1} elseskipend end thread {Loop proc {$} {Show 1} end1000} end thread {Loop proc {$} {Show 2} end 1000} end • This program will interleave the execution of two thread, one printing 1, and the other printing 2 • We assume a fair scheduler S. Haridi and P. Van Roy

22. Dataflow computation • Threads suspend of data availability in dataflow variables • The {Delay X} primitive makes the thread suspends for X milliseconds, after that the thread is runnable declare X {Browse X} local Y in thread{Delay 1000} Y = 10*10 end X = Y + 100*100 end S. Haridi and P. Van Roy

23. Illustrating Dataflow computation • Enter incrementally the values of X0 to X3 • When X0 is bound the thread will compute Y0=X0+1, and will suspend again until X1 is bound declare X0 X1 X2 X3 {Browse [X0 X1 X2 X3]} thread Y0 Y1 Y2 Y3 in {Browse [Y0 Y1 Y2 Y3]} Y0 = X0 + 1 Y1 = X1 + Y0 Y2 = X2 + Y1 Y3 = X3 + Y2 {Browse completed} end S. Haridi and P. Van Roy

24. fun {Map Xs F} case Xs of nil then nil [] X|Xr thenthread {F X} end|{Map Xr F} end end This will fork a thread for each individual element in the input list Each thread will run only in both the element X and the procedure F is known Concurrent Map S. Haridi and P. Van Roy

25. Concurrent Map Function fun{Map Xs F}case Xsof nil then nil[] X|Xr thenthread {F X} end |{Map Xr F}end end • How this really looks like: proc{Map Xs F Rs}case Xsof nil thenRs = nil[] X|Xr then R Rr inRs = R|Rrthread R = {F X}end Rr = {Map Xr F}end end S. Haridi and P. Van Roy

26. How does it work? • If we enter the following statements:declareF X Y Z{Browse thread {Map X F} end} • A thread executing Map is created. • It will suspend immediately in the case-statement because X is unbound. • If we thereafter enter the following statements:X = 1|2|Yfun {F X} X*X end • The main thread will traverse the list creating two threads for the first two arguments of the list, S. Haridi and P. Van Roy

27. How does it work? • The main thread will traverse the list creating two threads for the first two arguments of the list • thread {F 1} end, and thread {F 2} end, Y = 3|ZZ = nil • will complete the computation of the main thread and the newly created thread thread {F 3} end, resulting in the final list [1 4 9]. S. Haridi and P. Van Roy

28. Declarative programs can be easily made concurrent Just use the thread statement where concurrent is needed fun {Fib X} if X=<2 then 1 else thread {Fib X-1} end + {Fib X-2} end end Cheap concurrency and dataflow S. Haridi and P. Van Roy

29. Understanding why fun {Fib X} if X=<2 then 1 else F1 F2 in F1 = thread {Fib X-1} endF2 = {Fib X-2} F1 + F2end end Dataflow dependency S. Haridi and P. Van Roy

30. Execution of {Fib 6} F2 Fork a thread F1 F3 F4 F2 Synchronize on result F2 F5 F3 F1 F2 Running thread F1 F3 F4 F2 F6 S. Haridi and P. Van Roy

31. Fib S. Haridi and P. Van Roy

32. Streams • A stream is a sequence of message • A stream is First-in First-out channel • The producer of augments the stream with new message, and the consumer reads the messages, one by one. x5 x4 x3 x2 x1 producer consumer S. Haridi and P. Van Roy

33. Stream Communication I • The data-flow property of Oz easily enables writing threads that communicate through streams in a producer-consumer pattern. • A stream is a list that is created incrementally by one thread (the producer) and subsequently consumed by one or more threads (the consumers). • The consumers consume the same elements of the stream. S. Haridi and P. Van Roy

34. Stream Communication II • Producer, that produces incremently the elements • Transducer(s), that transforms the elements of the stream • Consumer, that accumulate the results thread 1 thread 2 thread 3 thread N producer transducer transducer consumer S. Haridi and P. Van Roy

35. Program patterns • The producer, transducers, and the consumer can, in general, be described by certain program patterns • We show the various patterns S. Haridi and P. Van Roy

36. Producer fun {Producer State} if {More State} then X = {Produce State} in X | {Producer {Transform State}} else nil end end • The definition of More, Produce, and Transform is problem dependent • State could be multiple arguments • The above definition is not a complete program ! S. Haridi and P. Van Roy

37. Example Producer fun {Generate N Limit} if N=<Limit then N|{Generate N+1 Limit} else nil end end • The State is the two arguments N and Limit • The predicate More is the condition N=<Limit • The Transform function (N,Limit)  (N+1,Limit) fun {Producer State} if {More State} then X = {Produce State} in X | {Producer {Transform State}} else nil end end S. Haridi and P. Van Roy

38. Consumer Pattern fun {Consumer State InStream} case InStream of nil then {Final State} [] X | RestInStream then NextState = {Consume X State} in {Consumer NextState RestInStream} end end • Final and Consume are problem dependent The consumer suspends until InStream is either a cons or a nil S. Haridi and P. Van Roy

39. Example Consumer fun {Sum A Xs} case Xs of X|Xr then {Sum A+X Xr} [] nil then A end end • The State is A • Final is just the identity function on State • Consume takes X and State  X + State fun {Consumer State InStream} case InStream of nil then {Final State} [] X | RestInStream then NextState = {Consume X State} in {Consumer NextState RestInStream} end end S. Haridi and P. Van Roy

40. Transducer Pattern 1 fun {Transducer State Instream} case InStream of nil then nil [] X | RestInStream then NextState#TX = {Transform X State} TX | {Consumer NextState RestInStream} end end • A transducer keeps its state in State, receives messages on InStream and sends messages on OutStream S. Haridi and P. Van Roy

41. Transducer Pattern 2 fun {Transducer State Instream} case InStream of nil then nil [] X | RestInStream then if {Test X#State} then NextState#TX = {Transform X State} TX | {Consumer NextState RestInStream}else{Consumer NextState RestInStream}end end end • A transducer keeps its state in State, receives messages on InStream and sends messages on OutStream S. Haridi and P. Van Roy

42. Example Transducer IsOdd fun {Filter Xs F} case Xs of nil then nil [] X|Xr then if {F X} then X|{Filter Xr F} else {Filter Xr F} end end end 6 5 4 3 2 1 5 3 1 Generate Filter Filter is a transducer that takes an Instream and incremently produces an Outstream that satisfies the predicate FF local Xs Ys in threadXs = {Generate 1 100} end threadYs = {Filter Xs IsOdd} end thread {Browse Ys} end end S. Haridi and P. Van Roy

43. Larger Example:The sieve of Eratosthenes • Produces prime numbers • It takes a stream 2...N, peals off 2 from the rest of the stream • Delivers the rest to the next sieve Sieve X Xs X|Zs Filter Sieve Zs Xr Ys S. Haridi and P. Van Roy

44. Sieve fun {Sieve Xs} case Xs of nil then nil [] X|Xr then Ys in thread Ys = {Filter Xr fun {$ Y} Y mod X \= 0 end} end X | {Sieve Ys} end end • The program forks a filter thread on each sieve call S. Haridi and P. Van Roy

45. Example Call local Xs Ys in thread Xs = {Generate 2 100000} end thread Ys = {Sieve Xs} end threadfor Y in Ys do {Show Y} endend end S. Haridi and P. Van Roy

46. Larger Example:The sieve of Eratosthenes • Produces prime numbers • It takes a stream 2...N, peals off 2 from the rest of the stream • Delivers the rest to the next sieve 7 | 11 |... Filter 3 Filter 5 Sieve Filter 2 S. Haridi and P. Van Roy

47. Limitation of eager stream processingStreams • The producer might be much faster than the consumer • This will produce a large intermediate stream that requires potentially unbounded memory storage x5 x4 x3 x2 x1 producer consumer S. Haridi and P. Van Roy

48. Solutions • There are three alternatives: • Play with the speed of the different threads, i.e. play with the scheduler to make the producer slower • Create a bounded buffer, say of size N, so that the producer waits automatically when the buffer is full • Use demand-driven approach, where the consumer activates the producer when it need a new element (Lazyevaluation) • The last two approaches introduce the notion of flow-control between concurrent activities (very common) S. Haridi and P. Van Roy

49. Coroutines I • Languages that do not support concurrent thread might instead support a notion called coroutining • A coroutine is a nonpreemptive thread (sequence of instructions), there is no scheduler • Switching between threads is trhe programmer’s responsibility S. Haridi and P. Van Roy

50. Coroutines II, Comparison {P ...} -- call procedure Q procedure P return Procedures: one sequence of instructions, program transfers explicitly when terminated it returns to the caller coroutine Q spawn P resume P resume Q resume Q coroutine P S. Haridi and P. Van Roy