Mechanized%20Proof%20%20

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Mechanized Proof System Verification
Andrew Ireland Julian Richardson
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EPSRC Grants

• Parallelising compilation of Standard ML
• through prototype instrumentation and
• transformation GR/L42889.

• Computational modelling of mathematical
• reasoning GR/M45030 (Edinburgh Heriot Watt).

• Automatic guidance for the formal verification
• of high integrity Ada GR/R24081.

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Critical Systems
Safety
Mission
Security
High Integrity Software
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Mathematical Proof
A proof tells us where to concentrate our doubts.
Kline, 1988

• Build it right first time

• Reduce maintenance costs

• Scalability

• Usability

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Mechanized Proof
Proof Planning
A technique for mechanizing proof
construction based upon high-level proof
patterns.
Benefits

• Increased automation

• High-level interaction

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Proof Planning
Goal
Proof Planner
Methods Critics
User
Proof Checker
Tactic
Proof
Theory
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Automatic Proof Patching

• Conjecture generalization

• Lemma discovery

• Induction rule selection

• Case analysis

• Inductive invariant discovery

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Praxis Critical Systems

• Internationally leading within the sector.

• Aerospace, Defence, Transportation,
• Finance, Energy and Utilities.

• Boeing, Lockheed-Martin, CAA, FAA,
• DERA, Westinghouse Signals, Mondex.

• SPARK High Integrity Ada subset.

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EPSRC Research Grant
Code
SPARK Examiner
Proof Planner
User
User
Proof
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Conclusion
The time is now ripe to test the proofautomation
capabilities of proof planningon industrial
strength problems. SPARKis the ideal vehicle
given its commercialsuccess within the critical
systems sector.
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Proof Planning
Goal
Proof Checker
User
Tactic
Proof
Theory
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Proof Planning
Goal
Proof Planner
Proof Checker
Tactic
Proof
Theory
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Proof Planning
Goal
Proof Checker
Methods Critics
Tactic
Proof
Theory
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EPSRC Research Grant
Code
SPARK Examiner
User
Proof
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EPSRC Research Grant
Code
SPARK Examiner
Proof Planner
User
Proof