An Efficient and Parallel Abstract Interpreter in Scala - - PowerPoint PPT Presentation

Universit´ e Libre de Bruxelles Computer Science Department MEMO-F524 Masters thesis

An Efficient and Parallel Abstract Interpreter in Scala — Presentation —

Olivier Pirson — opi@opimedia.be

• rcid.org/0000-0001-6296-9659

November 27, 2017

https://bitbucket.org/OPiMedia/efficient-parallel-abstract-interpreter-in-scala

Vrije Universiteit Brussel Promotors Coen De Roover Wolfgang De Meuter Advisor Quentin Stievenart

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

1 Abstract interpretation for static analysis 2 Concrete vs abstract interpretation 3 Parallelism 4 Next steps 5 References

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

How do better than testing?

“The first moral of the story is that program testing can be used very effectively to show the presence of bugs but never to show their absence.” (Dijkstra, 1971–1973)

Figure: First “flight” of Ariane 5 in 1996.

Investigation of Ariane failure: first large-scale example of static analysis by abstract interpretation.

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Static analysis

Static analysis of program: analysis made without executing program. Goal? Prove some properties of program (like correctness, or some properties use to transform and optimize program). Or in the opposite, find bugs. Problem! Undecidable problem (we know that by Rice’s theorem).

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Static analysis by abstract interpretation

Abstract interpretation: approximation technique to perform static analysis. Based on mathematical notion of partially ordered sets (in particular lattice). Difficulty! Find good abstractions: enough precise to prove desired property, and enough approximate to be decidable (and with doable complexity).

Figure: Ren´ e Magritte, Le Calcul Mental. 1940. An Efficient and Parallel Abstract Interpreter in Scala — Presentation 5 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Example of abstraction

{. . . , −3, −2, −1, 0, 1, 2, 3, . . .} abstracted by sign = {⊥, +, 0, −, ⊤} ⊤ −

• +

⊥

Figure: Hasse diagram of the complete lattice of signs.

top ⊤ = {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} + = {1, 2, 3, . . .}

• 0 = {0}

− = {−1, −2, −3, . . .} bottom ⊥ = ∅ May be good abstraction for multiplication operations. With additions, directly loss of precision.

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

1 Abstract interpretation for static analysis 2 Concrete vs abstract interpretation 3 Parallelism 4 Next steps 5 References

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Concrete interpretation

Trace: concrete interpretation with small-step semantics, for one instance. e s0 s1 s2 s3 s4 · · · injection function concrete transition function Program is executed by interpreter, described by an Abstract Machine (AM). One execution is for one instance on this program. e is for one expression, i.e. a program. si are states during this execution.

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Abstract interpretation

Trace: concrete interpretation with small-step semantics, for one instance. e s0 s1 s2 s3 s4 · · ·

• s0
• s1
• s2
• s3
• s4
• s3′

injection function

• injection

function abstraction function α abstract transition function Abstracting Abstract Machine (AAM). 2 over-approximations: Finite state space. Abstract transition function returns all directly reachable states. State graph: abstract interpretation, for all instances. “The abstract simulates the concrete” (Might)

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Concrete interpretation

Correct program Incorrect program

Figure: Patrick Cousot. Abstract Interpretation in a Nutshell. An Efficient and Parallel Abstract Interpreter in Scala — Presentation 10 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Abstract interpretation

Correct program Incorrect program

Figure: Patrick Cousot. Abstract Interpretation in a Nutshell.

Correct abstract interpretation Incorrect abstract interpretation

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Abstract interpretation

Correct abstract interpretation Incorrect abstract interpretation

Figure: Patrick Cousot. Abstract Interpretation in a Nutshell.

Summary of difficulties: Decidability? Soundness vs completeness? Good complexity vs precision? = ⇒ Parallelism

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

1 Abstract interpretation for static analysis 2 Concrete vs abstract interpretation 3 Parallelism 4 Next steps 5 References

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Goal of the thesis: parallelism to improve speed

Parallelism to keep good precision and improve speed. I will parallelize Scala-AM, implemented by Quentin Stievenart. Target language: Scheme (“simple” but “general”).

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Actor model

Actor, like an object, isolated entity with its own encapsulated data and

• behaviour. With some fundamental differences.

Entirely private. No shared mutable state (so no data race). Communication by immutable asynchronous messages (sent and received sequentially). Each actor has a mailbox (a queue). Capability to create other actors.

Figure: Richard Doyle. Using Akka and Scala to Render a Mandelbrot Set. 2014. http://blog.scottlogic.com/2014/08/15/using-akka-and-scala-to-render-a-mandelbrot-set.html An Efficient and Parallel Abstract Interpreter in Scala — Presentation 15 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Akka toolkit

Akka: toolkit for Scala (and also Java). Concurrent and distributed (use many cores or several computers without modification). Reduced overhead. Light implementation of actors (in 1 GiB memory, possibility of millions actors, instead thousands of threads).

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Sequential worklist strategy

• s
• s
• s
• s
• s

worklist

Figure: K. Dewey, V. Kashyap, B. Hardekopf. A parallel abstract interpreter for JavaScript. 2015. An Efficient and Parallel Abstract Interpreter in Scala — Presentation 17 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Naive worklist parallel strategy

• s
• s
• s
• s
• s

worklist merge

Figure: K. Dewey, V. Kashyap, B. Hardekopf. A parallel abstract interpreter for JavaScript. 2015. An Efficient and Parallel Abstract Interpreter in Scala — Presentation 18 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Naive worklist parallel strategy

Redundant computations. Synchronization at the merge step. Article test on few real JavaScript programs. Results show that this adaptation of the sequential algorithm is not optimal.

Figure: L. Andersen, M. Might. Multi-core Parallelization of Abstracted. 2013.

I am curious about the results of this algorithm with the lot of little Scheme programs with Scala-AM.

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Better, per-context parallel strategy

Authors introduce a per-context parallel strategy. The main idea is to separate these two parts: state exploration control of state space by some merging operations. The intuitive idea is to parallelize “functions” instead basic “blocks”.

Figure: K. Dewey, V. Kashyap, B. Hardekopf. A parallel abstract interpreter for JavaScript. 2015. An Efficient and Parallel Abstract Interpreter in Scala — Presentation 20 / 24

An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

1 Abstract interpretation for static analysis 2 Concrete vs abstract interpretation 3 Parallelism 4 Next steps 5 References

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

Next steps

A lot of work! Become more comfortable with actors paradigm and Akka. Implement the naive parallel algorithm, and experiment. Implement better parallel algorithms. Evaluate all of them and identify problematic parts. Read more. . . .

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

1 Abstract interpretation for static analysis 2 Concrete vs abstract interpretation 3 Parallelism 4 Next steps 5 References

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An Efficient and Parallel Abstract Interpreter in Scala — Presentation Abstract interpretation for static analysis Concrete vs abstract interpretation Parallelism Next steps References

References

Thank you! Questions time. . .

• L. Andersen, M. Might. Multi-core Parallelization of Abstracted

Abstract Machines. 2013. Patrick Cousot. Abstract Interpretation in a Nutshell.

• K. Dewey, V. Kashyap, B. Hardekopf. A parallel abstract

interpreter for JavaScript. 2015. Matthew Might. Tutorial: Small-step CFA. 2011. Quentin Sti´

• evenart. Static Analysis of Concurrency Constructs

in Higher-Order Programs. 2014.

• D. Van Horn, M. Might. Abstracting Abstract Machines. 2010.

Document, L

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T EX sources, and complete references on Bitbucket:

https://

Olivier Pirson. An Efficient and Parallel Abstract Interpreter in Scala — Preparatory Work. 2017.

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