Formally proving facts in the refinement algebra
Download
1 / 11

Formally proving facts in the refinement algebra - PowerPoint PPT Presentation


  • 117 Views
  • Uploaded on

Formally proving facts in the refinement algebra. Vlad Shcherbina Ilya Maryassov Alexander Kogtenkov Alexander Myltsev Pavel Shapkin Sergey Paramonov Mentor: Sir Tony Hoare. Project motivation. Educational (get some experience with interactive theorem provers )

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Formally proving facts in the refinement algebra' - jesus


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Formally proving facts in the refinement algebra l.jpg

Formally proving facts in the refinement algebra

VladShcherbina

IlyaMaryassov

Alexander Kogtenkov

Alexander Myltsev

PavelShapkin

Sergey Paramonov

Mentor: Sir Tony Hoare


Project motivation l.jpg
Project motivation

  • Educational (get some experience with interactive theorem provers)

  • Relevant to the school

    • provers are used in verification

    • the theory itself can be used in principle to reason about programs and specifications

  • It’s always nice to be absolutely sure

(almost:)


Theory l.jpg
Theory

  • Concise

    • one binary relation

    • few operations

    • few axioms

  • Formal reasoning is unaccustomed

  • Intuition could be deceptive


Interactive theorem provers l.jpg
Interactive theorem provers

  • Most proof steps are automated, but sometimes user intervention is required

    • to introduce useful lemma

    • to apply some nontrivial substitution

      ...

  • LCF-style (proof is correct by construction)


Thanks l.jpg
Thanks

  • to Thomas Thümand Oliver Schwarz for introduction to Coq

  • to John Wickersonfor introduction to Isabelle


Slide6 l.jpg
Coq

  • First order (for our purposes) intuitionistic logic

  • In the form of natural deduction

  • Proofs are constructed “backwards”

  • Proofs are spells, that are hard to comprehend without running Coq.


Example l.jpg
Example

  • Refinement relation ⊑ is partial

  • Binary operations ; and |

  • (definition) Milner transition: p -q-> r <=> (q; r) ⊑ p

  • Exchange law: (p | p’) ; (q| q’) ⊑ (p ; q) | (p’;q’)

    • Parallel rule for Milner transition:p -q-> r & p’ –q’-> r’ => => p|p’ –(q|q’)-> r|r’


Coq demo time l.jpg

Coq demo time

(***********)

(* v *)

(* <O___,, *)

(* \VV/ *)

(* // *)

(* *)

(***********)


Statistics l.jpg
Statistics

  • ~30 theorems

  • ~500 lines of Coq definitions and proofs

  • 5-60 minutes per proof (given the proof plan)

  • 2 inaccuracies found


Slide10 l.jpg

(************)

(* ???? *)

(* ?? ?? *)

(* ?? *)

(* ?? *)

(* *)

(* ?? *)

(************)

(***********)

(* v *)

(* <O___,, *)

(* \VV/ *)

(* // *)

(* *)

(***********)

https://github.com/

Vlad-Shcherbina/

TheoryOfRefinement


ad