Work Analysis with Resource-Aware Session Types

Transcription

1 Work Analysis with Resource-Aware Session Types Ankush Das Jan Hoffmann Frank Pfenning LICS, July 10,

2 Goal for this Talk Resource Analysis for Concurrent Programs Execution Time Memory Usage 2

3 Why Resource Analysis? 3

4 Why Resource Analysis? Complexity of Parallel Algorithms Çiçek et. al. (ESOP 15) 3

5 Why Resource Analysis? Complexity of Parallel Algorithms Design of Optimal Scheduling Policies Çiçek et. al. (ESOP 15) Acar et. al. (JFP 16) 3

6 Why Resource Analysis? Complexity of Parallel Algorithms Design of Optimal Scheduling Policies Çiçek et. al. (ESOP 15) Acar et. al. (JFP 16) Prevention of Side-Channel Attacks Ngo et. al. (S&P 17) 3

7 Why Resource Analysis? Complexity of Parallel Algorithms Design of Optimal Scheduling Policies Çiçek et. al. (ESOP 15) Acar et. al. (JFP 16) Prevention of Static and Side-Channel Attacks Dynamic Profiling Ngo et. al. (S&P 17) Haemmerlé et. al. (FLOPS 17) 3

8 Measures of Execution Time 4

9 Measures of Execution Time Work Sequential Complexity Execution time on one processor 4

10 Measures of Execution Time Work Sequential Complexity Execution time on one processor Span Parallel Complexity Execution time on arbitrarily many processors 4

11 Measures of Execution Time Today s talk! Work Sequential Complexity Execution time on one processor Span Parallel Complexity Execution time on arbitrarily many processors 4

12 Measures of Execution Time Today s talk! ICFP 2018 Work Sequential Complexity Execution time on one processor Span Parallel Complexity Execution time on arbitrarily many processors 4

13 Concurrent Programs are hard to analyze! 5

14 Concurrent Programs are hard to analyze! Shared Memory Read/Write Overhead 5

15 Concurrent Programs are hard to analyze! Shared Memory Communication Overhead Read/Write Overhead 5

16 Concurrent Programs are hard to analyze! Shared Memory Communication Overhead Read/Write Overhead Deadlocks 5

17 Concurrent Programs are hard to analyze! Shared Memory Communication Overhead Read/Write Overhead Deadlocks Non-Compositional 5

18 Session types can help :-) Shared Memory Communication Overhead Read/Write Overhead Deadlocks Non-Compositional 5

19 Session types can help :-) No Shared Memory Communication Overhead Deadlocks Non-Compositional 5

20 Session types can help :-) No Shared Memory Types strictly enforce communication protocols Deadlocks Non-Compositional 5

21 Session types can help :-) No Shared Memory Types strictly enforce communication protocols Deadlock Freedom Non-Compositional 5

22 Session types can help :-) No Shared Memory Types strictly enforce communication protocols Deadlock Freedom Channels abstract over 5 connected processes

23 What are Session Types? Implement message-passing concurrent programs Communication via bi-directional typed channels Curry-Howard isomorphism with intuitionistic linear logic 6

24 What are Session Types? Implement message-passing concurrent programs Communication via bi-directional typed channels Curry-Howard isomorphism with intuitionistic linear logic P Channel Q Provider Process 6 Client Process

25 What are Session Types? Implement message-passing concurrent programs Communication via bi-directional typed channels Curry-Howard isomorphism with intuitionistic linear logic bits = {b0 : bits, b1 : bits} P c : bits Channel Q Provider Process 6 Client Process

26 What are Session Types? Implement message-passing concurrent programs Communication via bi-directional typed channels Curry-Howard isomorphism with intuitionistic linear logic P bits = {b0 : bits, b1 : bits} b0/b1 c : bits Channel Q Provider Process 6 Client Process

27 Contributions 7

28 Contributions Design a type system to analyze work of session-typed programs 7

29 Contributions Design a type system to analyze work of session-typed programs based on amortized analysis can be parameterized to count different resources proved sound w.r.t. cost semantics conservative extension to standard session type system applied to all standard programs 7

30 Contributions Design a type system to analyze work of session-typed programs based on amortized analysis can be parameterized to count different resources messages exchanged proved sound w.r.t. cost semantics conservative extension to standard session type system applied to all standard programs 7

31 Contributions Design a type system to analyze work of session-typed programs based on amortized analysis can be parameterized to count different resources proved sound w.r.t. cost semantics conservative extension to standard session type system messages exchanged processes spawned applied to all standard programs 7

32 Contributions Design a type system to analyze work of session-typed programs based on amortized analysis can be parameterized to count different resources proved sound w.r.t. cost semantics conservative extension to standard session type system applied to all standard programs 7 messages exchanged processes spawned instructions executed

33 Contributions Design a type system to analyze work of session-typed programs based on amortized analysis can be parameterized to count different resources proved sound w.r.t. cost semantics conservative extension to standard session type system applied to all standard programs 7 messages exchanged processes spawned instructions executed

34 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 8

35 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 8

36 Example: Queues a b c d queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

37 Example: Queues a b c d offers choice of ins/del queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

38 Example: Queues a b c d offers choice of ins/del recv element of type A queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

39 Example: Queues a b c d ins(e) offers choice of ins/del recv element of type A queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

40 Example: Queues a b c d e ins(e) offers choice of ins/del recv element of type A queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

41 Example: Queues a b c d e ins(e) offers choice of ins/del recv element of type A behave as queue again queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

42 Example: Queues a b c d e offers choice of ins/del del queue A =&{ins : A ( queue A, del : {none : 1, some : A queue A }} 9

43 Example: Queues a b c d e offers choice of ins/del del queue A =&{ins : A ( queue A, del : {none : 1, send none if queue is empty some : A queue A }} 9

44 Example: Queues a b c d e offers choice of ins/del del queue A =&{ins : A ( queue A, del : {none : 1, terminate send none if queue is empty some : A queue A }} 9

45 Example: Queues a b c d e offers choice of ins/del del queue A =&{ins : A ( queue A, del : {none : 1, send some otherwise some : A queue A }} 9

46 Example: Queues a b c d e del offers choice of ins/del send element of type A queue A =&{ins : A ( queue A, del : {none : 1, send some otherwise some : A queue A }} 9

47 Example: Queues some(a) b c d e offers choice of ins/del send element of type A queue A =&{ins : A ( queue A, del : {none : 1, send some otherwise some : A queue A }} 9

48 Example: Queues some(a) b c d e offers choice of ins/del send element of type A behave as queue again queue A =&{ins : A ( queue A, del : {none : 1, send some otherwise some : A queue A }} 9

49 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz 10

50 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz recv ins and y 10

51 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz recv ins and y send ins and y 10

52 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz recv ins and y send ins and y recurse 10

53 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz recv ins and y send ins and y recurse send some, x 10

54 Session-typed Program x : A (element stored) elemy t : queue A tail of queue elemx s : queue A head of queue elemz recv ins and y send ins and y recurse send some, x 10 terminate

55 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 11

56 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 11

57 Cost Semantics proc(c, w, P) Process P offering along channel c and has performed work w Standard semantics extended with local work counters w for each process Total work of system is sum of local counters w w is incremented every time process P performs some work (this talk: whenever message is sent) 12

58 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 13

59 Overview proc(c, w, P) Cost Semantics Soundness Session types Theorem q w `q P :: (c : A) Type System 13

60 Type System Based on Amortized Analysis! Store potential in each process Potential can be transferred via messages Potential is consumed to perform work 14

61 Type System Based on Amortized Analysis! Store potential in each process Potential can be transferred via messages Potential is consumed to perform work `q P :: (c : A) Process P offers along channel c, acts as a client for channels in Ω and storing potential q 14

62 Concurrent Queues Count the messages! a b c d 15

63 Concurrent Queues Count the messages! a b c d ins(e) 15

64 Concurrent Queues Count the messages! ins(e) ins(e) ins(e) ins(e) a b c d e ins(e) 15

65 Concurrent Queues Count the messages! a b c d e del 15

66 Concurrent Queues Count the messages! some(a) b c d e 15

67 Concurrent Queues Count the messages! b c d e wi = Work done to process insertion = 2n (where n is the size of queue) = ins and e travel to end of queue wd = Work done to process deletion = 2 (sends back some and a ) 15

68 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} 16

69 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} Resource-Aware Session Types types augmented with potential information sender pays potential with message receiver gets potential with message 16

70 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} 17

71 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} recv 2(n+1) units 17

72 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} recv 2(n+1) units send 2n units 17

73 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} recv 2(n+1) units send 2n units cost of 2 17

74 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} recv 2(n+1) units send 2n units cost of 2 recv 2 units 17

75 Type for Queues queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} recv 2(n+1) units send 2n units cost of 2 recv 2 units 17 cost of 2

76 Rule: Sending a label c.k ; P q c : {`r` : A`}`2L `q P :: (c : A) Process P offers along channel c, acts as a client for channels in Ω and storing potential q 18

77 Rule: Sending a label c.k ; P q P p c : {`r` : A`}`2L c : A k `q P :: (c : A) Process P offers along channel c, acts as a client for channels in Ω and storing potential q 18

78 Rule: Sending a label c.k ; P q P p c : {`r` : A`}`2L c : A k `q P :: (c : A) Process P offers along channel c, acts as a client for channels in Ω and storing potential q q p + r k + 1 `p P :: (c : A k ) `q c.k :: (c : {`r` : A`}`2L ) 18

79 Features of Type System Flexible: supports counting of different resources (e.g. messages exchanged, processes spawned, etc.) by being parametric in cost model Compositional: types describe individual processes, not just whole programs Precise: potential upper bounds work accurately Conservative: strict extension of type system General: works on most standard examples Automatic: future work 19

80 Examples! 20

81 Binary Counters ctr[n] =&{inc 1 : ctr[n + 1], val 2dlog(n+1)e+2 : bits} Increment: requires one unit of potential uses amortized analysis! Value: requires logarithmic potential precise work bound 21

82 Stacks vs Queues stack A [n] =&{ins 0 : A ( stack A [n + 1], del 2 : {none : 1, some : A stack A [n 1]}} queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} Which one s more efficient? 22

83 Stacks vs Queues stack A [n] =&{ins 0 : A ( stack A [n + 1], del 2 : {none : 1, some : A stack A [n 1]}} queue A [n] =&{ins 2n : A ( queue A [n + 1], del 2 : {none : 1, some : A queue A [n 1]}} Which one s more efficient? 22

84 Contributions Type System for Work Analysis based on amortized analysis types augmented with potential information work is upper bounded by potential Flexible, Compositional, Precise, Conservative, General, Automatic 23

85 Contributions Type System for Work Analysis based on amortized analysis types augmented with potential information work is upper bounded by potential Flexible, Compositional, Precise, Conservative, General, Automatic Soundness Theorem Cost Semantics 23

86 Contributions Type System for Work Analysis based on amortized analysis types augmented with potential information work is upper bounded by potential Flexible, Compositional, Precise, Conservative, General, Automatic Soundness Theorem Cost Semantics Examples stacks, queues, binary counters efficiency comparison list examples: append, map, fold 23