Towards A Formal Theory of On Chip Communications in the ACL2 Logic
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1 (c) Julien Schmaltz, ACL2 2006, San José August p. 1/37 Towards A Formal Theory of On Chip Communications in the ACL2 Logic Julien Schmaltz Saarland University - Computer Science Department Saarbrücken, Germany Dominique Borrione TIMA Laboratory - VDS Group Grenoble, France
2 (c) Julien Schmaltz, ACL2 2006, San José August p. 2/37 A Motivation Example ecall Automatic emergency call system A phone call is automatically emitted when car sensors detect an accident Navigation Interface ecall Interface FlexRay Bus Phone Interface Sensors Interface
3 (c) Julien Schmaltz, ACL2 2006, San José August p. 3/37 FlexRay Bus Basic protocol Idle units 1, to start 0 Sync edges at each byte (from 1 to 0) Deterministic scheduling Time is divided into rounds Each unit has one slot per round Navigation Interface ecall Interface FlexRay Bus Phone Interface Sensors Interface
4 (c) Julien Schmaltz, ACL2 2006, San José August p. 4/37 Verification Proof of each component Proof of their interconnection Navigation Interface ecall Interface OK OK FlexRay OK Bus OK OK Phone Interface Sensors Interface
5 (c) Julien Schmaltz, ACL2 2006, San José August p. 5/37 Global Objective One model for all architectures...?
6 (c) Julien Schmaltz, ACL2 2006, San José August p. 6/37 Contribution A functional formalism for communications: GeNoC (Generic Network on Chip) Identifies the essential constituents and their properties Formalizes the interactions between them Correctness of the system is a consequence of the essential properties of the constituents Mechanized support in ACL2 Encapsulation allows abstraction Functional instantiation generates proof obligations automatically
7 (c) Julien Schmaltz, ACL2 2006, San José August p. 7/37 Outline Communication Principles GeNoC Definition and Correctness ACL2 Theorem/Removing Quantifiers Abstraction using Encapsulation s of GeNoC
8 (c) Julien Schmaltz, ACL2 2006, San José August p. 8/37 A Unifying Model Navigation Interface Phone ecall Interface Communication Architecture Interface Sensors Interface
9 (c) Julien Schmaltz, ACL2 2006, San José August p. 8/37 A Unifying Model messages Interface frames messages Interface frames Communication Architecture frames frames Interface Interface messages messages
10 (c) Julien Schmaltz, ACL2 2006, San José August p. 9/37 Functional Modeling messages messages frames frames Scheduling Scheduling Routing Routing frames frames messages messages System = F(Routing, Scheduling,, )
11 (c) Julien Schmaltz, ACL2 2006, San José August p. 10/37 Proof Obligations messages messages PO i PO i frames frames Routing Scheduling Scheduling Routing PO r PO s frames frames messages PO i messages POi
12 (c) Julien Schmaltz, ACL2 2006, San José August p. 11/37 System Theorem messages messages PO i PO i frames frames Routing Scheduling Scheduling Routing PO r PO s frames frames messages PO i messages POi Thm messages reach their destination
13 (c) Julien Schmaltz, ACL2 2006, San José August p. 11/37 System Theorem messages messages PO i PO i frames frames Routing Scheduling Scheduling Routing PO r PO s frames frames messages PO i messages POi Thm messages reach their destination
14 (c) Julien Schmaltz, ACL2 2006, San José August p. 12/37 Outline Communication Principles GeNoC Definition and Correctness ACL2 Theorem/Removing Quantifiers Abstraction using Encapsulation s of GeNoC
15 (c) Julien Schmaltz, ACL2 2006, San José August p. 13/37 Overall Modeling Principles Function GeNoC takes the list of pending communications returns the list of results and the list of aborted communications Transactions A transaction represents a pending communication, i.e. the intention of A of ing msg to B It is a 4-tuple (id A msg B)
16 Function GeNoC Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B (id 1 A msg 1 B) (id 2 D msg 2 T) (id 3 F msg 3 E) (id 4 R msg 4 Z) Routing Aborted Missives Transactions Results (c) Julien Schmaltz, ACL2 2006, San José August p. 14/37
17 From transactions to missives Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A (id 1 A msg 1 B) (id 1 A msg 1 B) (id 2 D msg 2 T) (id 3 F msg 3 E) (id 4 R msg 4 Z) Routing Node B Aborted Missives Transactions Results (c) Julien Schmaltz, ACL2 2006, San José August p. 15/37
18 From transactions to missives Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A (id 1 A frm 1 B) (id 1 A frm 1 B) (id 2 D frm 2 T) (id 3 F frm 3 E) (id 4 R frm 4 Z) Routing Node B Aborted Missives Missives Results (c) Julien Schmaltz, ACL2 2006, San José August p. 15/37
19 Routing Algorithm (id 1 frm 1 Routes 1 ) Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B (id 1 frm 1 Routes 1 ) (id 2 frm 2 Routes 2 ) (id 3 frm 3 Routes 3 ) (id 4 frm 4 Routes 4 ) Routing Aborted Missives Travels Results (c) Julien Schmaltz, ACL2 2006, San José August p. 16/37
20 Scheduling Policy Scheduling Scheduled (id 1 frm 1 Routes 1 ) (id 3 frm 3 Routes 3 ) Interface A Interface B A Messages Frames Frames Messages B Node A Node B Routing (id 2 frm 2 Routes 2 ) (id 4 frm 4 Routes 4 ) Aborted Missives Delayed Results (c) Julien Schmaltz, ACL2 2006, San José August p. 17/37
21 Results Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B (id 2 frm 2 Routes 2 ) (id 4 frm 4 Routes 4 ) Routing (id 1 B msg 1 ) (id 3 E msg 3 ) Aborted Missives Delayed Results (c) Julien Schmaltz, ACL2 2006, San José August p. 18/37
22 Aborted Missives Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B (id 2 D frm 2 T) (id 4 R frm 4 Z) Routing (id 1 B msg 1 ) (id 3 E msg 3 ) Aborted Missives Missives Results (c) Julien Schmaltz, ACL2 2006, San José August p. 19/37
23 Aborted Missives Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B Routing (id 4 R frm 4 Z) (id 1 B msg 1 ) (id 3 E msg 3 ) (id 2 T msg 2 ) Aborted Missives Results (c) Julien Schmaltz, ACL2 2006, San José August p. 19/37
24 Correctness Criterion Scheduling Interface A Interface B A Messages Frames Frames Messages B Node A Node B (id 1 A msg 1 B) (id 2 D msg 2 T) (id 3 F msg 3 E) (id 4 R msg 4 Z) Routing (id 1 B msg 1 ) (id 3 E msg 3 ) (id 2 T msg 2 ) (id 4 R frm 4 Z) Aborted Missives Transactions Results (c) Julien Schmaltz, ACL2 2006, San José August p. 20/37
25 (c) Julien Schmaltz, ACL2 2006, San José August p. 21/37 Termination Function GeNoC is a recursive function and must be proved to terminate because: it is a prerequisite for mechanized reasoning (here ACL2) it is necessary to ensure liveness To ensure the termination, we associate to every node a finite number of attempts. At every recursive call of GeNoC, every node with a pending transaction consumes one attempt.
26 (c) Julien Schmaltz, ACL2 2006, San José August p. 22/37 Formal Definition From a list of transactions, T, the set of nodes NodeSet and a list of attempt numbers att, function GeNoC produces: The list R of results The list A for aborted missives GeNoC : D T GenNodeSet AttLst D R D M (T, NodeSet, att) (R, A)
27 (c) Julien Schmaltz, ACL2 2006, San José August p. 23/37 Correctness Criterion res R,!trans T, { Id R (res) = Id T (trans) Msg R (res) = Msg T (trans) Dest R (res) = Dest T (trans) For any result res, there exists a unique transaction trans such that trans and res have the same identifier, message, and destination.
28 (c) Julien Schmaltz, ACL2 2006, San José August p. 23/37 Correctness Criterion res R,!trans T, { Id R (res) = Id T (trans) Msg R (res) = Msg T (trans) Dest R (res) = Dest T (trans) Typical formula scheme Always check for Id equality In ACL2, the idea is filtering according to Id s
29 (c) Julien Schmaltz, ACL2 2006, San José August p. 24/37 Outline Communication Principles GeNoC Definition and Correctness ACL2 Theorem/Removing Quantifiers Abstraction using Encapsulation s of GeNoC
30 (c) Julien Schmaltz, ACL2 2006, San José August p. 25/37 ACL2 Correctness Predicate (defun genoc-thm (R T /R ids ) (and (equal (R-msgs R) (T-msgs T /R ids )) (equal (R-dests R) (T-dests T /R ids )))) T /R ids = T filtered according to the ids of R Check that the messages and the destinations of T /R ids and R are equal.
31 (c) Julien Schmaltz, ACL2 2006, San José August p. 26/37 ACL2 Theorem (defthm GeNoC-is-correct (mv-let (R A) (GeNoC T NodeSet att) (declare (ignore A)) (implies (T lstp T ) (GeNoC-thm R (filters T (R-ids R))))))
32 Proof Obligations Interfaces The composition is an identity Routing (id A frm B) (id frm Routes) Missive/Travel matching Same frame and identifier Routes effectively go from the correct origin to the correct destination Scheduling Mutual exclusion between Scheduled and Delayed No addition of new identifiers Preserve frames and route correctness (c) Julien Schmaltz, ACL2 2006, San José August p. 27/37
33 (c) Julien Schmaltz, ACL2 2006, San José August p. 28/37 Proof of the theorem Routing correctness + preserved by scheduling right destination No modification on frames every result is obtained by Interfaces correctness received message = sent message Mutual exclusion between Scheduled and Delayed + no new identifiers cut the proof in two parts
34 (c) Julien Schmaltz, ACL2 2006, San José August p. 29/37 Outline Communication Principles GeNoC Definition and Correctness ACL2 Theorem/Removing Quantifiers Abstraction using Encapsulation s of GeNoC
35 (c) Julien Schmaltz, ACL2 2006, San José August p. 30/37 Encapsulation: Interfaces Function builds a frame from a message: (( ) ) Function recovers a message from a frame: (( ) ) Their composition is an identity: (defthm InterfaceCorrectness ;; (msg) = msg (equal ( ( msg)) msg)) Some additional constraints
36 (c) Julien Schmaltz, ACL2 2006, San José August p. 31/37 Interfaces Encapsulate Event (encapsulate ((( ) ) (( ) )) ;; local witnesses (local (defun (msg) msg)) (local (defun (frm) frm)) ;; proof obligations (defthm InterfaceCorrectness (equal ( ( msg)) msg)) (defthm -nil (not ( nil))) (defthm -not-nil (implies msg ( msg))))
37 (c) Julien Schmaltz, ACL2 2006, San José August p. 32/37 Checking Compliance (defthm check-instance-interface t ;; we prove true :rule-classes nil ;; no rule :hints (("GOAL" ;; we use InterfaceCorrectness ;; with flexray for ;; and flexray for :use (:functional-instance InterfaceCorrectness ( flexray ) ( flexray )))))
38 (c) Julien Schmaltz, ACL2 2006, San José August p. 33/37 Outline Communication Principles GeNoC Definition and Correctness ACL2 Theorem/Removing Quantifiers Abstraction using Encapsulation s of GeNoC
39 (c) Julien Schmaltz, ACL2 2006, San José August p. 34/37 s of GeNoC OSI Layer 1 - Bi-Φ-M OSI Layer 2 - Ethernet Scheduling Scheduling on networks - Circuit switching - Packet switching Bus arbitration - AMBA AHB arbiter Interface A Interface B A Messages Frames Frames Messages B Node A Node B Routing Deterministic routing - Octagon - XY algorithm Adaptive routing - Double Y channel
40 (c) Julien Schmaltz, ACL2 2006, San José August p. 35/37 Conclusion A generic model: GeNoC Identifies the essential constituents and their properties Formalizes the global property as a consequence of proof obligations Its expression in ACL lines, 71 functions and 119 theorems One fourth is dedicated to the modules Abstraction using encapsulation Automatic generation of proof obligations using functional instantiation
41 Future Work Master/Slave protocols Deadlocks (structural and protocol level) Adding queues and channels wormhole routing in Hermes (TIMA, Grenoble, France) Verified Distributed Stacks Verisoft Stack (O.S., compiler, assembly, gates) Interconnected Stacks through a time triggered FlexRay bus Show that FlexRay matches GeNoC!... (c) Julien Schmaltz, ACL2 2006, San José August p. 36/37
42 THANK YOU!! (c) Julien Schmaltz, ACL2 2006, San José August p. 37/37
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