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Verification of cache-coherence protocols with TLA+. Homayoon Akhiani, Damien Doligez, Paul Harter, Leslie Lamport, Joshua Scheid, Mark Tuttle, Yuan Yu Compaq Computer Corporation. TLA+. A formal specification language based on set theory, first-order logic, temporal logic

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verification of cache coherence protocols with tla

Verification of cache-coherence protocols with TLA+

Homayoon Akhiani, Damien Doligez, Paul Harter,

Leslie Lamport, Joshua Scheid, Mark Tuttle, Yuan Yu

Compaq Computer Corporation

Compaq Computer Corporation

slide2
TLA+
  • A formal specification language based on set theory, first-order logic, temporal logic
  • Hierarchical style clarifies written
    • specifications: becomes
    • proofs: becomes
  • Engineers find reading easy, writing not too hard

<1>1.

<2>1. CASE

<2>2. CASE

<2>3. QED

Compaq Computer Corporation

used tla to demonstrate formal methods to engineering
Used TLA+ to demonstrate formal methods to engineering
  • Analyzed cache-coherence protocols for
    • EV6: Alpha 21264 processor
    • EV7: Alpha 21364 processor
  • Built TLC, a model-checker for TLA+
  • Analyzed proposals for industry standards
    • PCI-X, …

Compaq Computer Corporation

cache coherence protocols
Cache coherence protocols

cache

cache

processor

processor

memory

x=2

cachex=1

cachex=2

processor

processor

Alpha memory model defines ordering of reads and writes to x.

Cache coherence protocol enforces the Alpha memory model.

Goal: prove the cache coherence protocol is correct.

Compaq Computer Corporation

ev6 cache coherence in three easy steps two man years
EV6 cache coherence in “three easy steps”+“two-man years”

Model Alpha memory model.(200 lines)

Prove implementation

(550 lines, 2 months, informal)

Model abstract protocol.(500 lines)

Prove implementation

(5500 lines, 4+ months, incomplete)

Model complete protocol.(2000 lines, 3 months)

Compaq Computer Corporation

step 1 alpha memory model
Step 1: Alpha memory model

We specified the Alpha memory memory model:

  • The official specification is an informal description of the allowed sequences of reads and writes.
  • We needed a precise, state-based specification.
  • We specified a slightly simplified memory model.

Compare the specifications:

  • Official, English specification: 12 pages
  • Logical, precise specification: 200 lines

Compaq Computer Corporation

step 2 model abstract protocol
Step 2: Model abstract protocol

protocol = abstract protocol + implementation junk

Surprisingly,

  • abstract protocol’s correctness was far from obvious
  • we discovered a bug… in the memory model

Proved hardest part of correctness:

  • 35-line invariant based on 300 lines of definitions
  • 550-line proof, cases nested 10 levels deep

Compaq Computer Corporation

step 3 model complete protocol
Step 3: Model complete protocol

Obstacle 1: find a single, complete description

  • English documents: 20 documents, 4-inch stack
  • Lisp simulator: crucial to understanding some details

Obstacle 2: algorithm complexity

  • 60 different kinds of messages
  • 15 “quarks” could combine to model all 60 messages

Protocol: 9 man-months, 1900 lines of TLA+

Partial proof: 7 man-months, 1000-line invariant

Compaq Computer Corporation

results one bug
Results: one bug
  • Quite unexpected to find only one bug!
  • Heavy simulation had found the easy bugs
  • Demonstrating our bug requires
    • four processors
    • two memory locations
    • fifteen messages
  • Hand proof appears essential to finding this bug:
    • extensive simulation did not find it
    • state space too large for exhaustive model checking

Compaq Computer Corporation

lessons learned
Lessons learned
  • The designers had no trouble reading our spec.
  • The level of rigorous analysis resulting even from a partial proof delighted the designers
  • The demonstration convinced engineers to consider doing the same thing on their own...
  • The basic methodology worked as expected
  • Tools, even simple tools, are essential…

Compaq Computer Corporation

tlc model checker

Check for

Invariant false

Deadlock

TLC model checker

State machine in

rich subset of TLA+

(Initial, NextState)

Configuration file

making state machine

finite

Minimal state trace

from an initial state

to a bad state

Invariant

Compaq Computer Corporation

tlc implementation
TLC implementation
  • Require no changes to TLA+ specifications
    • use the richness of TLA+, no primitive language
    • use configuration files instead
  • Interpret specifications, don’t compile them
    • better user interaction possible
  • Use explicit state representation, not BDDs
    • BDD encoding of TLA+ formulas difficult
    • use canonical state representation + fingerprinting
    • use efficient disk-based state set and queue implem.

Compaq Computer Corporation

tlc status
TLC status
  • 20,000 lines of Java
  • Compaq internal distribution available now
  • Performance is good, sometimes slow: threaded and distributed implementations now exist.
  • Liveness checking/livelock detection coming
  • Coverage analysis is desired: What does lack of an error mean: a correct spec or a buggy spec?

Compaq Computer Corporation

ev7 cache coherence
EV7 cache coherence
  • First intense application of TLC model checker
  • First TLA+ specification written by engineers
  • Specification is 1800 lines
  • Specification accepted by TLC w/o modification
  • State space reduced 50% by adding 15 lines to remove a lot of symmetry in state space

Compaq Computer Corporation

results
Results
  • 73 bugs found (90% found by TLC):
    • 37 minor: typos, type errors, etc
    • 12 bugs: wrong message/wrong state
    • 14 missing cases
    • 7 spurious cases (dead code)
    • 3 miscellaneous (1 TLA+, 1 MC, 1 spec design)
  • War story: Find bug B by hand; find bug B’ like B by simulation; find bug B’’ in bug-fix for B; find “???” written in original documentation!

Compaq Computer Corporation

lessons learned16
Lessons learned
  • Learning TLA+ is not a major task, but writing good specifications still requires experience
  • EV6 verification was
    • humbling: only one error actually found
    • encouraging: the basic method works as expected
  • EV7 verification was very satisfying:
    • TLA+ specifications can be written by engineers
    • TLC can handle industrial-sized specifications
  • Formal specification belongs in design process…

Compaq Computer Corporation