A Rehabilitation of Message-Passing Concurrency

Transcription

1 A Rehabilitation of Message-Passing Concurrency Frank Pfenning Carnegie Mellon University PWLConf 2018, St. Louis

2 A Paper I Love Types for Dyadic Interaction, Kohei Honda, CONCUR 1993 With some newer developments Session Types as Intuitionistic Linear Propositions, Luís Caires & Pf., CONCUR 2010 Manifest Sharing with Session Types, Stephanie Balzer & Pf., ICFP 2017

3 The Activity of Programming Every programmer, all the time, reasons Operationally (how) Logically (what) The effectiveness of a programming language depends critically on sort(a); x = A[0]; hd(sort(a)) How programs execute What they achieve Which reasoning principles connect the operational and logical meaning of a program

4 Why is Functional Programming So Effective? Functions are a universal and fundamental abstraction Intuitionistic Logic Logic Type Theory Types Simple Types (,,+,α) Computation β-reduction

5 What about Concurrency? Concurrent Separation Logic Logic Is Shared Memory a Fundamental Abstraction? Types? Computation Read/Write Shared Memory

6 What about Concurrency? Processes and Channels are a Fundamental Abstraction!? Logic Linear Logic! [Caires & Pf 10] Concurrent Type Theory? Session Types! [Honda 93] Types? π-calculus Computation Communication

7 There is Hope Previous talk! Do not communicate by sharing memory; instead, share memory by communicating. Effective Go From the language point of view: Go Goroutines (threads/processes) as a fundamental abstraction Channels (chan τ) as a fundamental abstraction Connection to logic is missing Types are not expressive enough

8 Example: A Store (Stack or Queue) Protocol Client: ins; x; recurse Provider Client s choice (external) Client: del $c : A Typed dyadic channel Client Provider: none; close. Provider s choice (internal) Provider: some; x; recurse Protocol should be expressed by a type!

9 A Simple Client, in CC0 $s : stack int main() { int n = 10; stack $s = empty(); for (int i = 0; i < n; i++) { $s.ins; send($s, i); print_stack($s); return 0; empty() $s : stack provider of $s $s : stack provider of $s main() main() main() main()

10 A Simple Provider, in CC0 stack $s elem(int x, stack $t) { switch ($s) { case ins: { $t : stack $s : stack int y = recv($s); stack $r = elem(x, $t); $s = elem(y, $r); elem(x, $t) $t : stack ins ; y case del: { elem(x, $t) $s.some; send($s, x); $s = $t; $t : stack $r : stack $s : stack elem(x, $t) elem(y, $r)

11 stack $s elem(int x, stack $t) { switch ($s) { case ins: { int y = recv($s); stack $r = elem(x, $t); $s = elem(y, $r); case del: { $s.some; send($s, x); $s = $t; Forwarding (or channel identification) is not part of the π-calculus $t : stack $s : stack elem(x, $t) $t : stack del elem(x, $t) $t : stack some ; x elem(x, $t) $s = $t : stack

12 stack $s empty() { switch ($s) { case ins: { int x = recv($s); stack $e = empty(); $s = elem(x, $e); case del: { $s.none; close($s); $s : stack empty() ins ; x empty() $e : stack $s : stack empty() elem(x, $e)

13 stack $s empty() { switch ($s) { case ins: { int x = recv($s); stack $e = empty(); $s = elem(x, $e); case del: { $s.none; close($s); $s : stack empty() del empty() none ; close

14 Summary So Far Processes provide one channel and are clients to other channels Spawning a process returns a fresh channel $c, with two endpoints New process provides $c Spawning process is client of $c Processes can terminate by forwarding Communication is bidirectional Processes send and receive labels or integers

15 Typing Channels Channel types should encode protocol of communication Provider and client must execute complementary actions External choice: Provider branches on label / Client sends label Internal choice: Provider sends label / Client branches on label Termination: Provider terminates / Client waits for termination Basic data: sending or receiving atomic values

16 Session Types, Abstractly Type Provider action Continuation <latexit sha1_base64="1u1jtsh/u4h5hig1kbeteycwfao=">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</latexit> 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sha1_base64="6wt34bj6xdtlynfm54v5dntxjmc=">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</latexit> A ::= N{` : A``2L receive some k 2 L A k {` : A``2L send some k 2 L A k A ( B receive channel c : A B A B send channel c : A B 1 terminate none 8x:.A receive v : [v/x]a 9x:.A send v : [v/x]a stack A = N{ ins : A ( stack A, del : { none : 1, some : A stack A <latexit sha1_base64="8uq0s6a0uxb6duix33+jrhacyia=">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</latexit> <latexit 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17 Types as Propositions These types are exactly the propositions of linear logic, except! An instance of the Curry-Howard correspondence Typing rules correspond to sequent calculus inference rules Programs correspond to process expressions Communication corresponds to cut reduction

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sha1_base64="0d9mwu0dzalk4qzbkf6vabvw6dg=">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</latexit> Session Typing Judgments channels used by P x 1 : A 1,...,x n : A n {z ` P :: (x : A) channel provided by P Configuration ::= (P 1 P n ) <latexit sha1_base64="qcfabh9i3zqkwt4cqzm+pljvqry=">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</latexit> <latexit sha1_base64="c2zejerfka3en4y5sz8ay639fq8=">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</latexit> <latexit sha1_base64="c2zejerfka3en4y5sz8ay639fq8=">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</latexit> <latexit sha1_base64="rwlodfw0qhp+tvdfckzjcimotai=">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</latexit> Configuration Typing channels used by Ω = :: 0 channels provided by Ω

19 Theoretical Properties Without recursive types and processes Session fidelity (Preservation) <latexit sha1_base64="+nuye4wnqklnzrkagmbpafp/fh8=">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</latexit> If = :: 0 and 7! 0 then = :: 0 Deadlock freedom Termination <latexit sha1_base64="1lyrooazg3xuh/szd+abbyaowgc=">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</latexit> If = :: 0 then poised or 7! 0 for some 0 <latexit sha1_base64="tigiv844f9f9gi5fdx7/yomkdjs=">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</latexit> If ` :: 0 then 7! 0 for 0 poised With recursion Session fidelity (Preservation) Deadlock freedom Ω is poised if all processes in Ω attempt to communicate along a channel in the external interface

20 Mode of Communication Both synchronous and asynchronous communication can be supported Asynchronous: messages still must appear in order (for session fidelity) Synchronization via polarization of the types Synchronous: messages can be coded via one-action processes Asynchronous seems to be the right default Closer to reasonable implementation Generalizes to channels with multiple endpoints

21 Session Types, in CC0 choice stack_req { <?int ;?choice stack_req> ins; <!choice stack_response> del; ; choice stack_response { < > none; <!int ;?choice stack_req> some; ;? = receive! = send ; = sequence of interaction < > session type typedef <?choice stack_req> stack;

22 Tracing the Type-Checker stack $s elem(int x, stack $t) { switch ($s) { case ins: { % $s : <?int ; stack> - $t : stack int y = recv($s); % $s : stack - $t : stack stack $r = elem(x, $t); % $s : stack - $r : stack $s = elem(y, $r); case del: { % $s : <!choice stack_response> - $s.some; % $s : <!int ; stack> - $t : stack send($s, x); % $s : stack - $t : stack $s = $t;

23 Tracing the Type-Checker stack $s empty() { switch ($s) { case ins: { % $s : <?int ; stack> -. int x = recv($s); % $s : stack -. stack $e = empty(); % $s : stack - $e : stack $s = elem(x, $e); case del: { % $s : <!stack_response> -. $s.none; % $s : < > -. close($s);

24 The Problem with Sharing #c : A Client 1 Typed shared channel If both clients can freely interact along #c Client 2 session fidelity will be violated Client 1 ins x #c : store Typed shared channel ins y Client 2

25 Linear and Shared Channels Type Provider action Continuation A ::= N{` : A``2L receive some k 2 L A k {` : A``2L send some k 2 L A k A ( B receive channel c : A B A B send channel c : A B 1 terminate none 8x:.A receive v : [v/x]a 9x:.A send v : [v/x]a #S detach from client S <latexit 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sha1_base64="g0pr4ix/ferc6gp9zcn8wjm5rt8=">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</latexit> S ::= "A accept client A!A, #"A <latexit sha1_base64="t2zuff3t2nan3q21zn9aonsskpu=">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</latexit> <latexit 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26 A Shared Queue queue A = "N{ ins : A ( #queue A, del : { none : #queue A, some : A #queue A <latexit sha1_base64="srxwwyodjuivrgqqxgx3l/1pidk=">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</latexit> <latexit sha1_base64="srxwwyodjuivrgqqxgx3l/1pidk=">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</latexit> <latexit sha1_base64="srxwwyodjuivrgqqxgx3l/1pidk=">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</latexit> <latexit sha1_base64="srxwwyodjuivrgqqxgx3l/1pidk=">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</latexit> The section describes a critical region Types must be equisynchronizing (released at the same type they are acquired to guarantee session fidelity) Certain deadlocks can now arise Sharing and critical regions are manifest in the type!

27 Why is Functional Programming So Effective? Functions are a universal and fundamental abstraction Intuitionistic Logic Logic Type Theory Types Simple Types (,,+,α) Computation β-reduction

28 What about Concurrency? Processes and Channels are a Fundamental Abstraction! Logic Linear Logic! [Caires & Pf 10] Concurrent Type Theory? Session Types! [Honda 93] Types π-calculus + fwd Computation Communication

29 Session Types at Present Scribble multiparty session types ABCD project groups.inf.ed.ac.uk/abcd/ Simon Gay, Nobuko Yoshida, Philip Wadler At CMU SILL (functional), CC0 (imperative), RSILL (time and work) Thanks to my collaborators: Coşku Acay, Stephanie Balzer, Luís Caires, William Chargin, Ankush Das, Henry DeYoung, Anna Gommerstadt, Dennis Griffith, Jan Hoffmann, Limin Jia, Jorge Pérez, Rokhini Prabhu, Klaas Pruiksma, Miguel Silva, Mário Florido, Bernardo Toninho, Max Willsey

30 A Paper I Love Types for Dyadic Interaction, Kohei Honda, CONCUR 1993 Kohei Honda,