An Automated Reasoning Perspective. Andrew Ireland. Dependable Systems Group. School of Mathematical & Computer Sciences. HeriotWatt University. Edinburgh. Setting the Scene. Inaugural lecture?.
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Safe and Secure Software SystemsAn Automated Reasoning Perspective
Andrew IrelandDependable Systems GroupSchool of Mathematical & Computer SciencesHeriotWatt UniversityEdinburghSlide2
Setting the SceneInaugural lecture?Achievements and research visionBlend of technical and big picture coupled historical perspectiveFirst things first – software and automated reasoning? Slide3
Making Stuff
a
nd How it Works’Slide4
Making Software Stuff  DataNumbers:
Lists:
…
Slide5
Making Software Stuff  DataEmpty list is represented by the constant
Nonempty list is constructed using the operator (pronounced “cons”)Example, the list even numbers [ 0, 2, 4, 6, 8 ]
is represented by0 :: (2 :: (4 :: (6 :: (8 ::
))))
Slide6
Making Software Stuff – ProgramsGluing lists together
:
Reversing a list
Slide7
Program Execution
p
rogram
d
ata
Slide8
How It Works
Slide9
A Practical Example
Slide10
Slide11
Proving Stuff Proof = Guarantee + Explanation
Proving the conjecture:Automated Reasoning: building software systems that construct proofs
Givens
Goal
All
Sylvanians
are tiny,
Coral is a
Sylvanian
Coral is tiny?
(conjecture)
t
herefore
Coral is tinySlide12
Proof as Guarantee
Givens
GoalSlide13
Proof as Guarantee
Givens
GoalSlide14
Proof as Guarantee
Givens
GoalSlide15
Proof as Guarantee
Givens
GoalSlide16
Proof as Guarantee
Givens
GoalSlide17
Proof as Guarantee
Givens
GoalSlide18
Proof as Guarantee
Givens
GoalSlide19
Proof as Guarantee
Givens
GoalSlide20
Proof as Guarantee
GoalGivensSlide21
Proof as Guarantee
GoalGivensSlide22
Proof as GuaranteeProof by Mathematical Induction – essential for reasoning about recursion, iteration, feedback loops
List induction  to prove :prove (base case)
assume
then prove
(step case)
Conjecture:
Slide23
Proof as Guarantee
Given:
Goal:
Slide24
Proof as Explanation
Given:
Goal:
Slide25
Proof as Explanation
Given
:
Goal:
Slide26
Proof as Explanation
Given
:
Goal:
Slide27
Proof as Explanation
Given
:
Goal:
Slide28
Proof as Explanation
Given
:
Goal:
Slide29
Proof as Explanation
Given
:
Goal:
Slide30
Proof as Explanation
Given
:
Goal:
Slide31
Proof as Explanation
Given
:
Goal:
Slide32
Proof as Explanation
Given
:
Goal:
Rippling = difference identification + difference reductionSlide33
Proof PlansA proof plan represents a common pattern of reasoning, e.g. ripplingProof
plan = tactic + strategyProof plans:Automate the search for proofs  via proof planningPromote strategy reuse
Guarantee
Explanation Slide34
Proof Planning
Conjecture
Theory
Method
Strategies
Tactic
[ tailored for
conjecture ]Slide35
Proof Planning
Conjecture
Theory
Method
Critic
Critics
provide
flexibility
during the search for proofs
StrategiesSlide36
Productive Use of Failure
D
Ripple
m
ethod
Missing Properties
(Lemmas)
Case Splits
Induction Rules
Conjecture
GeneralizationSlide37
Making Software Stuff Reversing a list
Reversing
a list

Faster!Slide38
.
Conjecture Generalization Critic
Given
:
Goal:
b
locked
Prooffailure Analysis:
m
atching rule, i.e.
missing universally quantified variable in conjecture, i.e.
Slide39
.
Conjecture Generalization Critic
Given
:
Goal:
p
roof planningSlide40
Conjecture Generalization Critic
Given
:
Goal:
p
roof planning
http://www.rippling.org/Slide41
Related PhD Projects
Proof planning for imperative program development
(Jamie Stark)
Reuse of proof plans
Loop invariant discovery
Program synthesis, i.e.
“... develop a program and its proof
handinhand
,
with
the proof ideas
Leading the way!”
(
Gries
, 1981)
BerthaSlide42
Related PhD Projects
Using Proof in Transformation Synthesis for Automatic Parallelisation 
EPSRC
GR/L42889 (Andrew Cook)
Verification & synthesis of performance enhancing eureka steps, e.g. transformations that facilitate the parallelization of software
Reasoning About Correctness Properties of a Coordination Programming Language
(
Gudmund
Grov
)
HUME: a novel programming language
Verification and transformation of HUME programs to improve resource usage (space and time guarantees)Slide43
Alan Turing: 19121954Slide44
Birth of the ‘Modern Computer’
Manchester’s Small Scale Experimental Machine A.K.A. “The Baby” (1948)
Turing, A. M. 1949.
“
Checking a Large Routine.”
In
Report of
a Conference on High Speed Automatic
Calculating Machines
,
Univ. Math. Lab., Cambridge, pp. 6769.
Software VerificationSlide45
And 63 Years Later …?A wealth of new logics and automated reasoning techniques Computers are faster and memory is cheap
Verification tools are typically highly integrated and automatic Significant industrial scale success stories within niche markets, e.g. Microsoft, Praxis, DRisQ, …Now it matters!Slide46
Now it Matters!Software is woven into almost all aspects of our daily lives
– from communications, entertainment and consumer electronics, to finance, defence and national infrastructureA key differentiator in commercial products is embedded software – dependability is crucial to commercial success, where software correctness is a key ingredient Cyber Security carries significant risks for economic growth and society in general – a
priority area for UK Government Software testing is not enough to guarantee safe and secure software systems – correctnessbyconstruction is called for, underpinned by a range of formal notations and automated reasoning technologiesInternational Verified Software
Initiative
–
coming
together of academia and
industry
Slide47
SPARK Programming Language
SPARK is an Ada subset that eliminates potential ambiguities and insecurities (Altran
Praxis) Expressive enough for industrial applications, but restrictive enough to support rigorous
analysis
,
i.e. correctnessbyconstruction
Applications:
e.g.
air traffic control (
iFACTS
),
avionics
(Eurofighter
Typhoon), security (
Mondex), …
Focus on exception freedom proof, e.g. proving code is free from arithmetic overflows, buffer overflows, division by
zero, ….Slide48
Consider converting 64bits of data into 16bits:
Arithmetic Overflow
Overflow ErrorSlide49
Developed
by European Space AgencyUnmanned rocket with a cargo of scientific satellites ($500 million) In 1996, just 39 seconds into its maiden flight an overflow error occurred resulting the Ariane 5 control software initiating a s
elfdestruction operation!
The Cost of Failure
Ariane
5Slide50
Verifying SPARK Code
SPARK
Examiner
SPADE
Simplifier
SPADE
Proof Checker
VCs
Cmds
UnprovenVCs
SPARK
code
Proofs
Annotations
VCs = Verification Conditions (conjectures)
Our focus was on the problems the SPARK tools failed on:
Verifying loops (iteration)
Loop invariant discovery – productive use of failure Slide51
Cmds
SPARK
Examiner
SPADE
Simplifier
SPADE
Proof Checker
Bill J. Ellis (
RA + PhD)
EPSRC Critical Systems programme
(GR/R24081
)
EPSRC RAIS Scheme
(GR/T11289
)
http://
www.macs.hw.ac.uk/nuspade
VCs
Annotations
SPADEase
SPARK
code
Proofs
UnprovenVCs
Proof Planning for SPARKSlide52
SPADEase
Unproven
VCs
Proof
Planner
Program
Analyzer
Annotations
Abstract Predicates
R >= ? and R <= ?
# assert R >= 0 and R <= I*100
subtype AR_T is Integer range 0..9;
type A_T is array (AR_T) of Integer;
...
procedure Filter(A: in A_T; R:
out Integer)is
begin
R:=0;
for I in AR_T loop
# assert R >= 0 and R <= I*100
if A(I)>=0 and A(I)<=100 then
R:=R+A(I);
end if;
end loop;
end Filter;
subtype AR_T is Integer range 0..9;
type A_T is array (AR_T) of Integer;
...
procedure Filter(A: in A_T; R:
out Integer)is
begin
R:=0;
for I in AR_T loop
if A(I)>=0 and A(I)<=100 then
R:=R+A(I);
end if;
end loop;
end Filter;Slide53
SPADEase Impact?
Peter Amey Chief Technical Officer Praxis High Integrity Systems
“… It increases the proportion of SPARKgenerated verification conditions that can be proved automatically without introducing any new opaque, blackbox processes. …”Slide54
SPADEase Impact?
“… The separation of proof planning from proof checking also acts as a talent multiplier by allowing proof experts to spend their time creating new and reusable methods and approaches rather than working on individual proofs.”
Peter Amey
Chief Technical Officer
Praxis High Integrity SystemsSlide55
Reasoning about the functional correctness of pointer programs
– proving that the code does the right thing
Separation Logic:
Adapted
the rippling proof plan
Extended work on automated invariant discovery
Ewen
Maclean,
Gudmund
Grov
(RAs),
Richard Addison
(MEng)
EPSRC funding: EP/F037597 and Platform Grant EP/J001058
www.macs.hw.ac.uk/core
Tech
Talks at
Google via
Going Beyond Exception FreedomSlide56
Beyond Code Level Analysis
Requirements
Formal Design Models
Code
Sensor:=
Brakes.Activate
;
Active:= False;
end if;
else
Alarm.Enable
;
end if;
else
if
Alarm.Enabled
then
Alarm.Disable
;
end if;
end if;
end if;
else
if
Reset.Enabled
then
Alarm.Disable
;
Brakes.Deactivate; Speed:= 0; Active:= True; end if;
end if; end Control;end ATP;
Rajiv Murali (PhD)EPSRC & BAE Systems Teresa Llano (PhD)EPSRC & BAE Systems Slide57
Reasoned Modelling
Combine common patterns of reasoning with common patterns of modelling (design)
Abstract away from lowlevel prooffailures, and automatically provide highlevel guidance to designers
Accessibility and productivity
– allow creative designers to make better use of their time
Reasoning
Modelling Slide58
Reasoned Modelling
Gudmund
Grov
, Teresa
Llano (PhD), Alison Pease
Collaboration with Edinburgh University & Imperial College:
System Design, Cognitive Modelling, AI Problem Solving
EventB (Rodin toolset) –
Bosch, Siemens, SAP, …
Funding: EPSRC
EP/F037058
,
EP/J001058, BAE Systemswww.macs.hw.ac.uk/remo
/
Reasoning
Modelling Slide59
Software System Design Environments
A Longerterm Vision
Reasoning
Modelling
Embed Reasoned
M
odelling within conventional design toolsSlide60
Knowledge TransferITI Techmedia (Scottish Enterprise)Software Integrity Engineering Programme
Ewen Maclean, Gudmund Grov, Andrew Cook (RAs)BAE Systems (Warton)A case study in reasoned modelling Teresa Llano (RA)Altran Praxis Critical Blue BAE Systems
Bill
Ellis (PhD)
Andrew Cook (PhD)
Ben
Gorry
(PhD)Slide61
Conclusion
Unsafe and insecure software can have a massive impact on economies and society in generalAutomated reasoning has an unique role to play in the development of safe and secure softwareAs the sophistication and reach of software systems increases, so will the importance of automated reasoning
As computer scientists we are challenged by a grand opportunity!Slide62
Thank You!
An Automated Reasoning Perspective Andrew Ireland Dependable Systems Group School of Mathematical amp Computer Sciences HeriotWatt University Edinburgh Setting the Scene Inaugural lecture ID: 391640 Download Presentation
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