CML Theorem Prover Simon Foster 2nd Review Brussels, 21 November, - - PowerPoint PPT Presentation

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CML Theorem Prover Simon Foster 2nd Review Brussels, 21 November, 2013 Deliverable: D33.2 (m24) www.compass-research.eu Theorem Prover Usage CML specifications to be verified by the COMPASS tool type-checking alone is insufficient to

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www.compass-research.eu

CML Theorem Prover

Simon Foster

2nd Review Brussels, 21 November, 2013

Deliverable: D33.2 (m24)

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Theorem Prover Usage

CML specifications to be verified by the COMPASS tool
type-checking alone is insufficient to ensure correctness
further proof obligations need to be satisfied

“does this function input satisfy the pre-condition?” “has variable x been assigned at this point?” “does my loop terminate?”

answering this requires use of a theorem prover
mechanically provides proof or counterexamples of these

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Approach

Proof Tools

Interactive: Isabelle, Coq, PVS, Agda, ACL2
Automated: E, Prover9, SPASS, Vampire, Z3
Bespoke: KeY, Rodin, Boogie

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Our Approach

creating a theorem prover from scratch an onerous task
embed CML semantics (D23.4) into off-the-shelf tool
adapt and make use of existing native proof facilities
our tool of choice: Isabelle/HOL

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Isabelle/HOL

proof assistant for Higher Order Logic
the Eclipse of the theorem proving world

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Automated Proof blast: automated classical deduction sledgehammer: integration of automated theorem proving nitpick: counterexample generator Dependable Technology Over twenty years of development Significant library of formal proofs (cf. AFP) Secure – proofs are constructed against a small logical core

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Mechanised Theory Library

Isabelle/UTP: mechanised semantic proof framework for CML
> 250 algebraic laws of programming mechanised
standard first-order predicate theory
imperative programming (relations)

– algebraic theories: Relation Algebra, Kleene Algebra, Complete Lattices

correctness: refinement, Hoare logic, wp calculus
designs: P ⊢ Q, basis for SoS contractual obligations
systems of systems: reactive processes, CSP, CML actions

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Integration with COMPASS tool

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SLIDE 7

Theorem Prover Demo Video

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Theorem Prover Conclusions

Main Achievements

substantial theory library mechanised in Isabelle/UTP
theoretical underpinnings of CML made applicable
automated proof tactics for discharging conjectures
highly extensible – supports a variety of semantic theories

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Future Work

link to CML proof obligation generator underway
future basis for SoS verification through SysML translation
Formal underpinnings for CML contracts through refinement