Let's try to understand (part of) Iris Willem Penninckx The Paper - - PowerPoint PPT Presentation

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Let's try to understand (part of) Iris Willem Penninckx The Paper - - PowerPoint PPT Presentation

Aug 20, 2022 383 likes •653 views

Let's try to understand (part of) Iris Willem Penninckx The Paper Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent Reasoning Ralf Jung, David Swasey, Filip Sieczkowski, Kasper Svendsen, Aaron Turon, Lars Birkedal, and Derek

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Let's try to understand (part of) Iris

Willem Penninckx

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The Paper

Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent Reasoning Ralf Jung, David Swasey, Filip Sieczkowski, Kasper Svendsen, Aaron Turon, Lars Birkedal, and Derek Dreyer

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DISCLAIMER

I'm not an expert

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Concurrency is about shared state

Situation Shared state Verify this Shared memory Memory No secret

  • verwrites,

Counter only increases Message- passing Network Protocol Input/output Filesystems, Humans, ... Protocol

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How to verify when there's concurrency?

“Monoids and invariants are all you need”

– Iris

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Invariant: assertion about shared state

Atomic operation 1 Atomic operation 2 Atomic operation 3 Atomic operation 4 Thread 1: Assertion holds

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Set “error” element Name of the monoid Commutative binary operator

(Iris-style) Monoid

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“Case study”: Verification + concurrency + heap

Proglang: v = malloc() v1 = !v2 v1 := v2 v1 = v2

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Invariant, e.g.: GLOBAL physical state is h

Attempt #1

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v1 = malloc() v1 := 7 Thread 1:

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“partial knowledge” in monoid

Set

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“partial knowledge” in monoid

Global knowledge Local partial knowledge

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“partial knowledge” in monoid

Global knowledge Local partial knowledge No global knowledge

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“partial knowledge” in monoid

Global knowledge Local partial knowledge No global knowledge g = h

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“partial knowledge” in monoid

Exercise: what does this mean?

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Exercise: what is the neutral element? Note: in paper composition Is just pointwise (so (\eps, l1) . (\eps l2) is not always \bot)

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v1 = malloc() Thread 1: v1 := 7

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v1 = malloc() Thread 1: v1 := 7 Combined: = = Link with physical? Know in physical state!

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Let's prove

v1 := 7 Our invariant holds

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Strategy

  • Open invariant
  • Combine thread's ghost state with invar's

–

  • Do physical update

–

  • Do ghost update
  • Split thread's ghost state and invar's
  • Close invariant

Know in physical state!

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frame v1 := 7 Need to update ghost state to close invar

  • Phys. Upd
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??? Allowed if “does not harm other threads”

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No: other thread might have e.g.

“Does not harm other threads”

Yes: cell update

? ?

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Increase-only counter

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Wrapping up

  • Monoids
  • Physical assertion
  • Ghost assertion
  • Invariants
  • Teaser Episode 3
  • Can I model I/O in Iris? (Willem)
  • Logical Atomicity (Amin)