Engineering Static Analyzers with Soufflésouffle-lang.org/pdf/SoufflePLDITutorial.pdf•Graph...

EngineeringStaticAnalyzerswithSoufflé

BernhardScholzTheUniversityofSydney,Australia

HerbertJordanUniversityofInnsbruck,Austria

Pavle SuboticUniversityCollegeLondon,UK

AlexanderJordanOracleLabs,Brisbane

Agenda

• SouffléOverviewasaTool

• BriefIntroductiontoDatalog

• SouffléasaLanguage

• Use-Cases:StaticProgramAnalysis

Soufflé:OverviewBernhardScholz

TheUniversityofSydney

StaticProgramAnalysisTools

• Lot’sofapplicationsforstaticprogramanalysis• Bugfinding,compileroptimisation,programcomprehension

• Fullyfunctionalanalysisforreallanguagesisexpensive!• State-of-the-arttools

• DevelopedinlanguageslikeC++/MLOCs• Testing• Fine-Tuning:scalabilityvs.precisionvs.efforttodevelop

• Needtorapidlydevelopstaticprogramanalysistools• Deepdesignspaceexplorations

Datalog asDSLforStaticProgramAnalysis

• Datalog instaticprogramanalysis• Reps’94,Engler’96,…

• Datalog isrestrictedHorn-Logic• Declarativeprogrammingforrecursiverelations• Finiteconstantset• Noback-trackingforevaluation/fast• Extensional/Intensional database

• Extractor• Syntactictranslationtologicalrelations

• Datalog Engine• ExtensionalDatabase/Facts:inputrelations• Intensional Database/Rules:programanalysisspecification

InputProgram

InputRelations

Result

ProgramAnalysis

Extractor

DatalogEngine

SecurityAnalysisinDatalog

• Vulnerablestatementmustbeprotectedinthecode• SafeandUnsaferegionsintheCFGExample: Security Analysis in Java

void m(int i, int j){

s: while (i < j){

l1: protect();

l2: i++;

}

l3: vulnerable();

}

s `1

`3 `2

// I/O relations

E(s:Node,d:Node) input

P(node:Node) input

I(node:Node) output

// Security Analysis

I("s").

I(y) :- I(x), E(x,y), !P(y).

Security Analysis

Security sensitive methods, e.g., vulnerable()

Permission checks prior to security sensitive method, e.g., protect()

Check that on all path protect() is invoked

Datalog specification: concise security check with rules & facts

B.Scholz, H.Jordan, P. Subotic, T.Westmann (Oracle) July 7, 2016 6 / 1

s

l3

l1

l2

Source: CFG: Datalog Program:Unsafe(”s”).Unsafe(y) :-Unsafe(x), Edge(x, y), !Protect(y).

Violation(x) :-Vulnerable(x),Unsafe(x).

WhyisDatalog noteverywhere?Performance Gap: C++ vs. Datalog

On graph with 100 vertices connected by 100K randomly edges

C++: 2 sec, 34 MB

us i ng Tuple = s td : : a r r ay<i n t ,2>;us i ng Re l a t i o n = s td : : s e t<Tuple>;R e l a t i o n edge , t c ;edge = someSource ( ) ;t c = edge ;auto d e l t a = tc ;wh i l e ( ! d e l t a . empty ( ) ) {

Re l a t i o n nDe l ta ;f o r ( const auto& t1 : d e l t a ) {

auto a = edge . l ower bound ({ t1 [ 1 ] , 0} ) ;auto b = edge . upper bound ({ t1 [ 1 ]+1 ,0} ) ;f o r ( auto i t = a ; i t != b ; ++i t ) {

auto& t2 = ⇤ i t ;Tuple t r ({ t1 [ 0 ] , t2 [ 1 ]} ) ;i f ( ! c o n t a i n s ( tc , t r ) )

nDe l ta . i n s e r t ( t r ) ;}

}t c . i n s e r t ( nDe l ta . beg i n ( ) , nDe l ta . end ( ) ) ;d e l t a . swap ( nDe l ta ) ;

}}

µZ Datalog: 340 sec, 1667 MB

path (X,Y) :� edge (X,Y ) .path (X, Z) :� path (X,Y) ,

edge (Y, Z ) .


Performance Gap: C++ vs. Datalog


C++: 2 sec, 34 MB







}}



edge (Y, Z ) .




C++: 2 sec, 34 MB







}}



edge (Y, Z ) .


WhytheGap?

- Generalevaluationalgorithms- ExistingenginesfocusonDBapps

Whatcanwedo?

:ANewDatalog SynthesisTool

• NewParadigmforEvaluatingDatalog Programs• Toachievesimilarperformancetohand-writtenC++code

• Assumptions• Rulesdonotchangeinstaticprogramanalysistools• Facts(=inputprogramrepresentation)maychange• Executedonlargemulti-coreshared-memorymachines

• Solution:• SynthesiswithFutamura projections• Applypartialspecializationtechniques• Synthesisinstages

• Eachstageopensarenewopportunitiesforoptimisations

HowdoesSouffléwork?

FactExtractor

SOUFFLÉ

Inputs Facts

Spec Result

AST

RAM

C++ ANALYZER

Spec

Facts

Result

Standalonetoolasbinaryorlibrary

Futamura Projections

• Specialization • Specialization• Hierarchy

Copyright©2014Oracleand/oritsaffiliates.Allrightsreserved.|

Futamura Projection

Interpreter'

Program'

Input' Output'

Interpreter' Program'

Output'

Mix'

Specialized'Program'

Compiler'

Source'Language'

Target'Program'Input'

(a) Interpretation (b) Futamura Projection


OracleConfidenGal–Restricted 10

FutamuraProjecGon

Specializations

Declarative to Imperative

Level 1: Semi-Naıve evaluation + Datalog rules =) RAM

Level 2: RAM evaluator + RAM operations =) templetized C++

Level 3: C++ compiler + template code =) program

Professor Yoshihiko Futamura


DatalogSpecialization

RAMSpecialization

C++Specialization



C++: 2 sec, 34 MB







}}



edge (Y, Z ) .


Third Stage: RAM to C++

Meta-Programming in C++

Translates RAM to C++ with templates

Relation type determines underlying data-structure for indexesUse Tries for relations with 1-2 attributesUse B-Tries for relations with 2 or more attributes

Avoid virtual-dispatch for basic data-structureTemplates are used for ”static” dispatch

Highly optimized for parallel execution (optimistic locking, ...)

Tool Time [s] Memory [MB]Sou✏e / B-tree (sequential) 1.26 25.6Sou✏e / B-tree (parallel) 0.42 26.3Sou✏e / Trie (sequential) 0.38 3.5Sou✏e / Trie (parallel) 0.12 4.5

Table: Data structure evaluation tools for random-graph connectivity problem.B.Scholz, H.Jordan, P. Subotic, T.Westmann (Oracle) July 7, 2016 20 / 1

Soufflé'sPerformance

• Example

• PerformanceNumbers

• Vs.Hand-crafted:2s/34MM

USECASEA:SecurityInOpenJDK7

OpenJDK7:7MLOC,1.4Mvariables,350Kheapobjects,160Kmethods,590Kinvocations,

1Gtuples

Soufflé–c

Points-to.dlSecurityAnalysisX.dl

AnalyzerXJDKXbuildY Results

USECASEB:AWSVPCNetworks

~10-100KInstances,90%staticrules,10%dynamicrules

ExternalTool JavaInterface

Soufflécompiler

SouffléInterpreter 10%

90%

Analysis+Data

Results

USECASEC:StaticParallelC/C++CodeAnalysisFramework

parallel

C++parallel

C++parallel

C++

Fron

tend

Backen

d

IR exe

Optimizer

Analysis Transformation

Insieme CompilerFramework

Souffle

Insieme’s DatalogAnalysisFramework

pointsto escape …

IR

FactExtractor

ResultExtractor

InputFacts

OutputFacts

AnalysisResults

Insieme’s Datalog basedAnalysis Module

USECASED:SecurityInSmartContracts

USECASEE:Points-ToAnalysis

• JavaPoints-ToAnalysisinDatalog• BuildsmemoryabstractionsforJavaprograms• Feature-Rich:varioustypesofpoints-tocontexts• Efficientimplementation

• Pipeline• SOOTforextractingsemanticrelations• Parameterizable analysis

• RecentlyportedtoSoufflé• SOAP’17

x

y

z

a

b

f

Variables

HeapObjects

vP

hP

ABriefIntroductiontoDatalog

AdaptedfromKifer/Bernstein/Lewis/Roehm

Datalog

• Datalog islogic-based querylanguage• Easytouserelationalprogramminglanguage• Recursive queries• AdaptsProlog-stylesyntax

• Basedonfirst-orderlogic• Decidablefragmentoflogic• FiniteUniverse• Nofunctors

RecentlyNewInterestinDatalog

• OriginalResearchisfromthe1980’sand’90s• cf.systemCoral,LDL++

• Datalog fordeclarativequeryingrecursivestructures• E.g.graphsornetworks

• Newapplicationscanbenefitfromthis• DataIntegration• ProgramAnalysis• DeclarativeNetworking• Security• Graphdatabases• …

• Cf.Huang,Green,Loo:“Datalog andEmergingApplications:AnInteractiveTutorial” SIGMOD2011.

BasicSyntaxofDatalog

• ThreetypesofHornClauses• Factfact.

• Rule:head:- body.

• Query:?- body.

• BuildingblocksforclausesarePredicates• ABooleanfunctiontakingafixednumberofargs• Apredicatefollowedbyitsargumentsiscalledanatom

ʻHappyDrinkerʼ Example:Facts

• Predicatesexample:frequents(Drinker,Bar)likes(Drinker,Beer)sells(Bar,Beer,Price)

• Factsexample:frequents(“jon”,“the_rose”).likes(“jon”,“vb”).sells(“the_rose”,“vb”,5).

• Queryexample:?- sells(Bar,Beer,Price).

BasicRuleStructureofDatalog

• Definearelationperson thatlistsallnamesofpersonsfromlikes relationperson(P):– likes(P, _).

• DefinearelationcheapBars containingthenamesofallbarssellingcheap“loewenbrau”beer(costinglessthan$4).

cheapBars(B,P):– sells(B,“loewenbrau”,P),P<4.• RetrievethecostofLoewenbraeu atthe“ueberbar”

?- cheapBars(“ueberbar”,P).• TofindthebarnameandbeerpricesofallbarsincheapBars thatsell“loewenbrau”forlessthan$4

?- cheapBars(B,P),P <4

happy(D) :- frequents(D,Bar) ,likes(D,Beer),sells(Bar,Beer,P)

AnatomyofaRule

Body(read ‘,’ as AND)

HeadRead thissymbol “if”

n The rule is a query asking for “happy” drinkers --- those that frequent a bar that serves a beer that they like.

n Variable bindings as equivalence constraintsn Variables must be grounded, i.e., show up in Atoms in Body.

AtomsinBody

• Anatom isapredicate,orrelationnamewithvariablesorconstantsasarguments.

• Theheadofaruleisanatom;thebodyistheconjunctionofoneormoreatoms

• Example:sells(Bar,Beer,P)

The predicate= name of arelation

Arguments arevariables

RuleInterpretation

happy(D) :- frequents(D,Bar) ANDlikes(D,Beer) AND sells(Bar,Beer,P)

Distinguishedvariable

Nondistinguishedvariables

Interpretation: drinker D is happy if there exist aBar, a Beer, and a price P such that D frequentsthe Bar, likes the Beer, and the bar sells the beerat price P.

NegatedAtoms

• WemayputNOTinfrontofanatomtonegateitsmeaning.• Example:expensiveBars(B,P):– sells(B,_,P),!cheapBars(B,P).

• Circularnegateddefinitions(direct/indirect)arenotpermitted.• Example: A(X):- !A(X).<=nogood.

Datalog Program

• ADatalog program isacollectionoffacts,rules,andaquery.• Inaprogram,predicatescanbeeither

• EDB =ExtensionalDatabase =setofgroundfacts,e.g.,predicateswhoserelationsarestoredinadatabase.

• IDB =Intensional Database =relationsdefined&computedbyrules.

• Twomajortypesofevaluationstrategies• Top-Down,i.e.,fromthegoaltothefacts.• Bottom-Up,i.e.,fromthefactstothegoal.

References

• Abiteboul/Hull/Vianu:FoundationsofDatabases(ebook)• Chapter12-15

• Kifer/Bernstein/Lewis:DatabaseSystems:AnApplication-OrientedApproach,IntroductoryVersion (2ndedition)

• Chapter13.6• Ramakrishnan/Gehrke:DatabaseManagementSystems (3rdedition- the‘Cow’book)

• Chapter24• Garcia-Molina/Ullman/Widom:DatabaseSystems:TheCompleteBook (1stedition)

• Chapter10

Soufflé:TheLanguageBernhardScholz


Soufflé:Extensions

• Datalog• Lackofastandard• Everyimplementationhasitsownlanguage

• Soufflé• Syntaxinspiredbybddbddb andmuZ/z3• Formulti-coreserverswithlargememory

• largescalecomputinginmind

• SouffléLanguage• MakesDatalog Turing-Equivalent(arithmeticfunctors)• Softwareengineeringfeaturesforlarge-scalelogic-orientedprogramming

• Performance• Ruleandrelationmanagementviacomponents

Agenda

1. Firstexample2. Relationdeclaration3. Typesystemforattributes4. Arithmeticexpressions5. Aggregation6. Records7. Components8. Performance/Profilingfacilities

Installation

• Supportedsystem• UNIX:Debian,FreeBSD,MACOSX,Win10subsystem,etc.

• Releasesareissuedregularly• http://github.com/souffle-lang/souffle/releases

• CurrentreleaseV1.1• AsaDebian Package• AsaMACOSXPackage

• Fromsourcecode• http://github.com/souffle-lang/souffle/

InvocationofSoufflé

• Invocationofsoufflé:souffle <flags><program>.dl• Evaluateinputprogram<program>.dl

• Setinputfactdirectorywithflag–F<dir>• Specifiestheinputdirectoryforrelations(default:current)

• Setoutputdirectorywithflag–D<dir>• Specifiestheoutputdirectoryforrelations(default:current)• If<dir> is”-”;outputiswrittentostdout.

TransitiveClosureExample

• Typethefollowinginfilereachable.dl.decl edge(n:symbol,m:symbol)edge(“a”,“b”)./*factsofedge*/edge(“b”,“c”).edge(“c”,”b”).edge(”c”,”d”)..decl reachable(n:symbol,m:symbol).outputreachable//outputrelationreachablereachable(x,y):- edge(x,y).//baserulereachable(x,z):- edge(x,y),reachable(y,z).//inductiverule• Evaluate:souffle -D- reachable.dl

Exercise

• Extendcodefrompreviousslide• AddanewrelationSCC(x,y)• RulesforSCC

• Ifnodexreachesnodeyandnodeyreachesnodex,then(x,y)isinSCC

• Checkwhetheranodeiscyclic• Checkwhetherthegraphisacyclic• Omittheflag“-D-”

• Whereistheoutput?

SameGenerationExample• Givenatree,findwhobelongstothesamegeneration.decl Parent(n:symbol,m:symbol)Parent("d","b").Parent("e","b").Parent("f","c").Parent("g","c").Parent("b","a"). Parent("c","a")..decl Person(n:symbol)Person(x):- Parent(x,_).Person(x):- Parent(_,x)..decl SameGeneration (n:symbol,m:symbol)SameGeneration(x,x):- Person(x).SameGeneration(x,y):- Parent(x,p),SameGeneration(p,q),Parent(y,q)..outputSameGeneration

b

gd fe

c

a

Data-FlowAnalysisExample• DFA determines static properties of programs • DFA is a unified theory; provides information for global analysis• DFA based on control flow graph, and node properties • Example: Reaching Definition

• Assignment of variable can directly affect the value at another point• Unambiguous definition dof variable v

• Definition reaches a statement u if all paths from d to u does not contain any unambiguous definition of v

• Note that functions can have side-effects to variables

d: v = <expression>;

d2: v=…

…v…d1 : v=…

Example: Reaching Definition

• Unambiguous definitions d1 and d2 of variable v

• Might reach d1 node B3?

• Might reach d2 node B3?

• Paths and effects of basic blocks influence solution

• Forward problem

start

end

B1

B4

B2 B3

38

d2: v=…

…v…d1 : v=…

Example: Reaching Definition.decl Edge(n:symbol,m:symbol)Edge("start","b1").Edge("b1","b2").Edge("b1","b3").Edge("b2","b4").Edge("b3","b4").Edge("b4","b1").Edge("b4",”end")..decl GenDef(n:symbol,n:symbol)GenDef("b2","d1").GenDef("b4","d2")..decl KillDef(n:symbol,n:symbol)KillDef("b4","d1").KillDef("b2","d2")..decl Reachable(n:symbol,n:symbol)Reachable(u,d):- GenDef(u,d).Reachable(v,d):- Edge(u,v),Reachable(u,d),!KillDef(u,d)..outputReachable

start

end

B1

B4

B2 B3

39

Soufflé’sInput:Remarks&C-Preprocessor

• Souffléusestwotypesofcomments(likeinC++)• Example://thisisaremark/*thisisaremarkaswell*/

• CpreprocessorprocessesSoufflé’sinput• Includes,macrodefinition,conditionalblocks

• Example:#include“myprog.dl”#defineMYPLUS(a,b)(a+b)

DeclarationsofRelations

• Relationsmustbedeclaredbeforebeingused:

.decl edge(a:symbol,b:symbol)

.decl reachable(a:symbol,b:symbol)

.outputreachable

edge(“a”,”b”).edge(“b”,”c”).edge(“b”,”c”).edge(“c”,”d”).reachable(a,b):- edge(a,b).reachable(a,c):- reachable(a,b),edge(b,c).

Type

I/ODirectives

• Inputdirective• Readfromatab-separatedfile<relation-name>.facts• Stillmayhaverules/factsinthesourcecode• Example:.input<relation-name>

• Outputdirective• Factsarewrittentofile<relation-name>.csv(orstdout)• Example:.output<relation-name>

• Printsizeofarelation• Example:.printsize <relation-name>

Exercise:RelationQualifier

.decl A(n:symbol)

.inputA

.decl B(n:symbol)B(n):- A(n).

.decl C(n:symbol)

.outputCC(n):- B(n).

.decl D(n:symbol)

.printsize DD(n):- C(n).

• ReadfromfileA.facts facts

• CopyfactsfromAtoB

• CopyfactsfromBtoCandoutputittofileC.csv

• CopyfactsfromCtoDandoutputthenumberoffactsonstdout

NoGoalsinSoufflé

• SouffléhasnotraditionalDatalog goals• Goalsaresimulatedbyoutputdirectives• Advantage

• severalindependentgoalsbyoneevaluation• Soufflé’slanguagewasdesignedfortoolintegration

• ManydesigndecisiontakenfromBDDBDDB/Z3• Currentstate:

• interactiveprocessingviasqlite3/db only• Future:

• ProvenanceandqueryprocessorforcomputedIDBs(comingsoon)

MoreInfoaboutI/ODirectives

• Relationscanbeloadedfrom/storedto• ArbitraryCSVfiles(changedelimiters/columns/filenames/etc.)• Compressedtextfiles• SQLITE3databases

• Thefeaturesarecontrolledviaalistofparameters• Example:.decl A(a:number,b:number).outputA(IO=sqlite,dbname="path/to/sqlite3db")

• Documentation:http://souffle-lang.org/docs/io/

• Ruleswithmultipleheadspermitted• Syntacticsugartominimizecodingeffort• Example:.decl A(x:number)A(1).A(2).A(3)..decl B(x:number).decl C(x:number)

B(x),C(x):- A(x)..outputB,C

RuleswithMultiple-Heads

.decl A(x:number)A(1).A(2).A(3)..decl B(x:number)B(x):- A(x)..decl C(x:number)C(x):- A(x)..outputB,C

Equivalent

DisjunctionsinRuleBodies

• Disjunctioninbodiespermitted• Syntacticsugartoshortencode• Example:.decl edge(x:number,y:number)edge(1,2).edge(2,3)..decl path(x:number,y:number)path(x,y):-edge(x,y);edge(x,q),path(q,y)..outputpath

Equivalent

.decl edge(x:number,y:number)edge(1,2).edge(2,3)..decl path(x:number,y:number)path(x,y):- edge(x,y).path(x,y):- edge(x,q),path(q,y)..outputpath

TypeSystem

• Soufflé'stypesystemisstatic• Definestheattributesofarelation• Typesareenforcedatcompile-time• Supportsprogrammerstouserelationscorrectly• Nodynamicchecksatruntime

• Evaluationspeedisparamount

• Typesystemreliesonthesetidea• Atypereferstoeitherasubsetofauniverseortheuniverseitself

• Elementsofsubsetsarenotdefinedexplicitly

• Subsetscanbecomposedoutofothersubsets

PrimitiveTypes

• Souffléhastwoprimitivetypes• Symboltype:symbol• Numbertype:number

• Symboltype• Universeofallstrings• Internallyrepresentedbyanordinalnumber

• E.g.,ord(“hello”)representstheordinalnumber• Symboltableusedtotranslatebetweensymbolsandnumberid

• Numbertype• Universeofallnumbers• Simplesignednumbers:setto32bit

Example:PrimitiveTypes

.decl Name(n:symbol)Name(“Hans”).Name(“Gretl”).

.decl Translate(n:symbol,o:number)Translate(x,ord(x)):- Name(x)..outputTranslate• Notethatord(x) convertsasymboltoitsordinalnumber

PrimitiveTypes

Base&UnionTypes

• Primitivetypes• Largeprojectsrequirearichtypesystems• Largeprojects:severalhundredrelations(e.g.DOOP,SecurityAnalysis)• Howtoensurethatprogrammersdon’tbindwrongattributetypes?

• Partitionnumber/symboluniverse

• Formsub-setlatticesoverbasesubsets

BaseType

• Symboltypesforattributesaredefinedby.symbol_type declarative.symbol_type City.symbol_type Town.symbol_type Village

• Define(assumingly)distinct/differentsetsofsymbolsinasymboluniverse

City Town Village

SymbolUniverse

Exercise:TypeSystem

.symbol_type City

.symbol_type Town

.symbol_type Village

.typePlace=City|Town|Village

.decl Data(c:City, t:Town,v:Village)Data(“Sydney”,”Ballina”,“Glenrowan”).

.decl Location(p:Place)outputLocation(p):- Data(p,_,_);Data(_,p,_);Data(_,_,p).• SetLocation receivesvaluesfromcellsoftypeCity,Town,andVillage.• Notethat; denotesadisjunction(i.e.,or)

LimitationsofaStaticTypeSystem

• Disjointsetpropertynotenforcedatruntime• Example:.symbol_type City.symbol_type Town.symbol_type Village.typePlace=City|Town|Village.decl Data(c:City,t:Town,v:Village)Data(“Sydney”,”Sydney”,“Sydney”).

• Element“Sydney”ismemberoftypeCity,Town,andVillage.

Base/UnionTypesforNumbers

• Numbersubsetscannotbemixedwithsymbolsubsets• Basetypeisdefinedby.number_type <name>• Example:.number_type Even.number_type Odd.typeAll=Even|Odd

NumberUniverse

Odd Even

All

Exercise:Base/UnionTypesforNumbers

.number_type Even

.number_type Odd

.typeAll=Even|Odd

.decl myEven(e:Even)myEven(2)..decl myOdd(o:Odd)myOdd(1)..decl myAll(a:All).outputmyAllmyAll(x):- myOdd(x);myEven(x).

ArithmeticExpression

• Arithmeticfunctors arepermitted• GoesbeyondpureDatalog semantics

• Variablesinfunctors mustbegrounded• Terminationmightbecomeaproblem• Example:.decl A(n:number).outputAA(1).A(x+1):- A(x),x<9.

Exercise:FibonacciNumber

• Createthefirst10numbersofseriesofFibonacciNumbers• Firsttwonumbersare1• Everynumberafterthefirsttwoisthesumofthetwoprecedingones• Example:1,1,2,3,5,8,…• Solution.decl Fib(i:number,a:number).outputFibFib(1,1).Fib(2,1).Fib(i +1,a+b):- Fib(i,a),Fib(i-1,b),i <10.

ArithmeticFunctors andConstraints

• ArithmeticFunctors• Addition:x+ y• Subtraction:x- y• Division:x/ y• Multiplication:x* y• Modulo:a% b• Power:a^ b• Counter:$• Bit-Operation:

• xband y, x bor y, xbxor y,and bnot x• Logical-Operation

• xland y, xlor y,and lnot x

• ArithmeticConstraints• Lessthan:a<b• Lessthanorequalto:a<=b• Equalto:a=b• Notequalto:a!=b• Greaterthanorequalto:a>=b• Greaterthan:a>b

NumbersinSoufflé

• Numbersindecimal,binary,andhexadecimalsystem• Example:

.decl A(x:number)A(4711).A(0b101).A(0xaffe).

• Decimal,hexadecimal,andbinarynumbersinthesourcecode• Restriction:infactfilesdecimalnumbersonly!

LogicalOperation:NumberEncoding

• NumbersaslogicalvalueslikeinC• 0representsfalse• <>0representstrue

• Usedonforlogicaloperations• xland y, xlor y,and lnot x

• Example:.decl A(x:number).outputAA(0lor 1).

TicketMachine:Counters

• Functor $• Issueanewnumbereverytimewhenthefunctor isevaluated

• Limitation• Notpermittedinrecursiverelations

• Createuniquenumbersforsymbols.decl A(x:symbol)A(“a”).A(“b”).A(“c”).A(“d”).

.decl B(x:symbol,y:number)

.outputBB(x,$):- A(x).

Exercise:CreateSuccessorRelationforaSet

• GivensetA(x:symbol)• CreateasuccessorrelationSucc(x:symbol,y:symbol)• Example:A={“a”,“b”,“c”,“d”}Succ ={(“a”,”b”),(“b”,”c”),(”c”,”d”)}

• Assumetotalordergivenbyordinalnumberofsymbols• Ordinalnumberofasymbolisobtainedbyord functor• Example:ord(“hello”)givestheordinalnumberofstring“hello”

Solution:CreateaSuccessorRelation

.decl A(x:symbol)input

.decl Less(x:symbol,y:symbol)Less(x,y):- A(x),A(y),ord(x)<ord(y).

.decl Transitive(x:symbol,y:symbol)Transitive(x,z):- Less(x,y),Less(y,z).

.decl Succ(x:symbol,y:symbol)Succ(x,y):- Less(x,y),!Transitive(x,y).

.outputLess,Transitive,Succ

Extension:ComputeFirst/LastofSuccessors

Computethefirstandthelastelementofthesuccessorrelation

.decl First(x:symbol)outputFirst(x):- A(x),!Succ(_,x).

.decl Last(x:symbol)outputLast(x):- A(x),!Succ(x,_).

StringFunctors andConstraints

• StringFunctors• Concatenation:cat(x,y)• StringLength:strlen(x)• Sub-string:substr (x,idx,len)where idx isthestartpositioncountingfrom0andlen isthelengthofthesub-stringofx.

• RetrieveOrdinalnumber:ord(x)

• StringConstraints• Substringcheck:contains(sub,str)• Matching:match(regexpr,str)

Example:StringFunctors &Constraints

.decl S(s:symbol)S(“hello”).S(“world”). S(“souffle”)..decl A(s:symbol)A(cat(x,cat(““,y))):- S(x),S(y).//stitchtwosymbolstogetherw.blank.decl B(s:symbol)B(x):- A(x),contains(“hello”,x)..decl C(s:symbol)C(x):- A(x),match (“world.*”,x)..outputA,B,C//outputdirective

AnotherStringExample

• Generateallsuffixesofastring.decl A(x:symbol)A("hello").//initialstring

A(substr(x,1,strlen(x)-1)):- //inductiveruleA(x),strlen(x)>1.

.outputA

Aggregation

• Summarizesinformationofqueries• Aggregatesonstable relationsonly(cf.negationinDatalog)

• Aggregationresultcannotbeusedforthesub-termoftheaggregatedirectlyorindirectly.

• Aggregationisafunctor• Varioustypesofaggregates

• Counting• Minimum• Maximum• Sum

Aggregation:Counting

• Countthesetsizeofitssub-goal• Syntax:count:{<sub-goal>}• Noinformationflowfromthesub-goaltotheouterscope• Example:.decl Car(name:symbol,colour:symbol)Car(“Audi”,”blue”).Car(“VW”,“red”).Car(“BMW”,“blue”).

.decl BlueCarCount(x:number)BlueCarCount(c):- c=count:{Car(_,”blue”)}..outputBlueCarCount

Aggregation:Maximum

• Findthemaximumofaset• Noinformationflowfromthesub-goaltotheouterscope,i.e.,nowitness

• Syntax:max<var>:{<sub-goal(<var>)>}• Example:.decl A(n:number)A(1).A(10).A(100)..decl MaxA(x:number)MaxA(y):- y=maxx:{A(x)}..outputMaxA

Aggregation:Minimum&Sum

• Findtheminimum/sumofasub-goal• Noinformationflowfromthesub-goaltotheouterscope

• nowitness

• Minsyntax:min<var>:{<sub-goal(<var>)>}• Sumsyntax:sum<var>:{<sub-goal(<var>)>}

Aggregation:Witnessesnot permitted!

• Witness:tuplesthatproducestheminimum/maximumofasub-goal• Example:.decl A(n:number,w:symbol)A(1,”a”).A(10,”b”).A(100,”c”)..decl MaxA(x:number,w:symbol)MaxA(y,w):- y=maxx:{A(x,w)}.<=notpermitted!!

• Witnessisboundinthemaxsub-goalandusedintheouterscope• Causessemantic/performanceissues

• Memorizingaset;whatdoesitmeanforcount/sum?• Forbiddenbythetype-checker

Records

• RelationsaretwodimensionalstructuresinDatalog• Large-scaleproblemsmayrequiremorecomplexstructure

• RecordsbreakoutoftheflatworldofDatalog• Atthepriceofperformance(i.e.extratablelookup)

• RecordsemanticssimilartoPascal/C• Nopolymorphtypesatthemoment

• RecordTypedefinition.type<name>=[<name1>:<type1>,…,<namek>:<typek>]

• Note:nooutputfacilityatthemoment

Example:Records

//Pairofnumbers.typePair=[a:number,b:number]

.decl A(p:Pair)//declareasetofpairsA([1,2]).A([3,4]).A([4,5]).

.decl Flatten(a:number,b:number)outputFlatten(a,b):- A([a,b]).

• Eachrecordtypehasahiddentyperelation• Translatestheelementsofarecordtoanumber

• Whileevaluating,ifarecorddoesnotexist,itiscreatedonthefly.• Example:.typePair=[a:number,b:number].decl A(p:Pair)A([1,2]).A([3,4]).A([4,5]).

Records:Howdoesitwork?

Ref a b

1 1 2

2 3 4

3 4 5

p

1

2

3

A Pair

References

RecursiveRecords

• Recursivelydefinedrecordspermitted• Terminationofrecursionvianil record• Example.typeIntList =[next:IntList,x:number].decl L(l:IntList)L([nil,10]).L([r1,x+10]):- L(r1),r1=[r2,x],x<30..decl Flatten(x:number)Flatten(x):- L([_,x])..outputFlatten

Ref next x

1 0 10

2 1 20

3 2 30

l

1

2

3

L IntList

nil

References

RecursiveRecords

• Semanticsistricky• Relations/setsofrecursiveelements(i.e.setofreferences)

• Monotonicallygrow

• Structuralequivalencebyidentity• Newrecordsarecreatedon-the-fly

• seamlesslyfortheprogrammer

• Closertoafunctionalprogrammingsemantics• Future:

• Polymorphismmightbepossibleattheexpenseofspeed/space

ComponentsinSoufflé

• Logicprogramshavenostructure• Amorphousmassofrules&relationdeclarations

• Createsserioussoftwareengineeringchallenges• Encapsulation:separationofconcerns• Replicationofcodefragments• Adaptionofcodefragments,etc.

• Solution:Soufflé'sComponentModel• MetasemanticsforDatalog• GeneratorforDatalog code;dissolvedatevaluationtime• SimilartoC++templates

Components(cont’d)

• Definition• Definesanewcomponenteitherfromscratchorbyinheritance• Permitted:componentdefinitionsinsidecomponentdefinitions• Syntax:.comp<name>[<params,… >]

[:<super-name>1[<params,… >],…,<super-name>k [<params,… >]]{<code>}

• Instantiation• Eachinstantiationhasitsownnameforcreatinganamespace• Typeandrelationdefinitionsinsidecomponentinheritthenamespace• Syntax:.init <name>=<name>[<params,… >]

Example:Component&NameScoping

.compmyComp {.decl A(x:number).outputAA(1).A(2).

}.init c1=myComp.init c2=myComp

.decl c1.A(x:number)

.outputc1.Ac1.A(1).c1.A(2).

.decl c2.A(x:number)output

.outputc2.Ac2.A(1).c2.A(2).

Expansionafter

instantiation

• Instantiationcreatesownnamespaceforrelationdeclarationsandtypes

Example:ComponentInheritance

.symbol_type s

.decl A(x:s,y:s)

.inputA

.compmyC {.decl B(x:s,y:s).outputBB(x,y):- A(x,y).

}.compmyCC:myC {B(x,z):- A(x,y),B(y,z).

}.init c=myCC

//outerscope:nonamespace.decl A(x:s,y:s).inputA

//namescoping//BisdeclaredinsidemyC/myCC.decl c.B(x:s,y:s).outputc.Bc.B(x,y):- A(x,y).c.B(x,z):- A(x,y),c.B(y,z).

ExpansionAfter

Instantiation

• ComponentmyCC inheritsfromcomponentmyC

OverridingRulesofSuperComponents

• Example:.compmyC {.decl A(x:number)overrideable.outputAA(1).A(x+1):-A(x),x<5.

}.compmyCC:myC {.overrideAA(5).A(x+1):-A(x),x<10.

}.init c=myCC

• Instantiationresult:.decl c.A(x:number)outputc.A(5).c.A(x+1):-c.A(x),x<10.

• Rules/factsof thederivedcomponentoverridestherulesofthesupercomponent

• Relationmustbedefinedwithqualifieroverrideable insupercomponent

• Componentthatoverwritesrulesrequires:.override<rel-name>

ComponentParameters

• Example.decl A(x:number).outputA.compcase<option>{.compone{A(1).}.comptwo{A(2).}.init c1=option

}.init c2=case<one>

• Componentone andtwo resideincomponentcasewithparameteroption

• Dependingonvalueofoption• Componentone or twoexpanded

• Conditionalexpansionofmacros

• Parametrizationofcomponents

Example:Components

• Developalibraryofcomponentsforgraphs• Thelibraryshouldcontainvariousfunctionality

• Acomponentforadirectedgraph• Acomponentforanundirectedgraph• Acomponentthatchecksforacycleinagraph• Acomponentthatcheckswhetheragraphisacyclic

• TheComponentlibraryshouldbeextendable,reuseothercomponents,etc.

Summary:Components

• Encapsulationofspecifications• Namespacesprovidedfortypes/relations• Instantiationproducesascopingnameofacomponent

• Repeatingcodefragments• Writeonce/instantiatedmultipletimes

• Components• Inheritanceofseveralsuper-components,i.e.,multipleinheritance• Hierarchiesoffunctionalities

• Parameters• Adaptcomponents/specialize

• Future:refinementofthecomponentmodel

Soufflé'sPerformanceAspect

• HowtogainfasterDatalog programs?• Compiletoachievepeakperformance• Schedulingofqueries

• Userannotationsorautomated• Findfasterqueries• Findfasterdatamodels

• Profilingisparamount• Textualandgraphicaluserinterfaceforprofilingprograms

• Practicalobservation• Onlyahandfulofruleswilldominatetheexecutiontimeofaprogram

Performance:Souffle’s CompilationFlags

• Compileandexecuteimmediately• Option–c• Example:souffle –ctest.dl

• Generatestand-aloneexecutable• Option–o<executable>• Example:souffle –otesttest.dl

• Feedback-DirectedCompilation• Option:--auto-schedule• Example:souffle --auto-scheduletest.dl

PerformanceTuning

• Soufflécomputesoptimaldata-representationsforrelations• Queryschedulingcanbemadeautomatic

• Souffléflag: --auto-schedule• Sub-optimalduetounrefinedmetricsforSelinger’s algorithm

• Forhigh-performance:• Programmerre-orderstheatomsinthebodyofarule

• Disableauto-schedulerforarulebythestrictqualifier• Syntax:<rule>..strict

• Provideyourownqueryschedule• Syntax:<rule>..plan{<#version>:(idx1,…,idxk)}

PerformanceExample

.decl Edge(x:number,y:number)Edge(1,2).Edge(500,1).Edge(i+1,i+2):- Edge(i,i+1),i <499.

.decl Path(x:number,y:number)

.printsize PathPath(x,y):- Edge(x,y).//Path(x,z):- Path(x,y),Path(y,z)..strict//Path(x,z):- Path(x,y),Edge(y,z)..strict//Path(x,z):- Edge(x,y),Path(y,z)..strict

Profiling

• ProfilingflagforSoufflé:-p<profile>• Producesaprofilelogafterexecution• Usesouffle-profile toprovideprofileinformationsouffle-profile<profile>

• Simpletext-interfaceandHTMLoutputwithJavaScript• Commands

• Help:help• Rule:rul [<id>]• Relations:rel [<id>]• Graphplotsforfixed-point:graph<id><type>

Profiling(cont’d)

• Option–jproducesHTMLfile;GraphicalRepresentationofPerformance

Additional features

Additional features

Additional features

ProgramAnalysisExamplesBernhardScholz


Points-ToAnalysis

• Flow-insensitive,inclusion-based,context-insensitive(cf.Whalley’04)

• AbstractDomain• Variables

• Local,actual/formalparameters,return-values,bases,this-variables• Heap-allocatedobjects

• Creation-siteasanabstractionfordynamicallycreatedobjects• Heap-allocatedobjecthavefields

• Relationsforcomputingpoints-toanalysis• vP(v,h):variablevmaypointtoheapobjecth• hP(h1,f,h2):fieldfofh1 maypointtoh2

Points-ToAnalysis

JavaCode Datalog Encoding

Allocations h: v=newC() vP(v,h) :- “h:v=newC()”.

Store v1.f=v2 hP(h1,f,h2):- “v1.f=v2”,vP(v1,h1),vP(v2,h2).

Load v2 =v1.f vP(v2,h2) :- “v2 =v1.f”,hP(h1,f,h2),vP(v1,h1).

Moves,Arguments v2 =v1 vP(v2,h) :- “v2 =v1”,vP(v1,h).

a:x=new Foo()

y=x;

if (cond) {z = y;

} else { b:z=new G();

z.f = y;

}

…

Points-ToExample

x

y

z

a

b

f

Variables

HeapObjects

vP

hP

Example:Points-ToinSouffle

• SimpleInputLanguagewith4statementtypesAllocation:<var> = new() Assignment:<var1>=<var2>Store:<var1>.<field> = <var2>Load:<var1>=<var2>.<field>

• Example:v1= new()v2= new()v1.f= v2v3=v1.f

Example:Extractor

• ExecuteExtractoral-extractor <input-program>

• Expectsadirectoryfactsincurrentdirectory • Exampleprogramv1 = new()v2 = v1v1.f = v2v3 = v1.f

• Producesfiles• facts/new.facts facts/assign.facts facts/load.facts facts/store.facts

Example:FactFilesEncoding

• VariableMappingtoNumbers• v1→1, v2→2, v3→3• Firstallocation:0

• GeneratedRelations:

• Exampleprogramv1 = new()v2 = v1v1.f = v2v3 = v1.f

Var Object

1 0

Var Var

2 1

new.facts assign.facts

Var Var Field

3 1 f

load.factsVar Var Field

1 f 2

store.facts

Example:Points-ToEDB• Souffle’s relationdeclarationsforfactfiles// v1 = new().decl new( var : Var, o : Obj )// v1 = v2.decl assign( trg : Var, src : Var )// v1 = v2.f.decl load( trg : Var , src : Var , field : Field )// v1.f = v2.decl store( trg : Var , field : Field, src : Var ).input new, assign, load, store

Example:Points-ToRules// v = new()pointsTo(v,o):-new(v,o).

// v = xpointsTo(v,o):-assign(v,x),pointsTo(x,o).

// v = x.fpointsTo(v,o):-load(v,x,f),pointsTo(x,t),heap(t,f,o).

// v.f = xheap(o,f,t):-store(v,f,x),pointsTo(v,o),pointsTo(x,t).

LambdaCalculusCaseStudy

• Step1:Inputlanguage• Untyped lambdacalculus

• Coregrammar:• term::=<var> //avariable,e.g.x

|\<var>.term //anabstraction(=function),e.g.“\x.x”|termterm //anapplication(=call),e.g.“ab”

• Extendedwith:• letbindingsandparenthesis support(forusability)

• IR:ASToflambdacalculusexpression

ConstructingtheAnalysis

• Step2:EncodingintoRelations• EncodingofASTinrelationalformatvialc-extractor

• Step3:SpecifyAnalysis• OnegenericDataFlow analysiscomponenthandlingparameterpassing

• Utilizingaspecializationofitselffordeterminingcontrolflowinformation

• Instantiatedfor:• Controlflow information:whichfunctioniscalledwhere(dynamicbinding)• Booleanvalue analysis:analysisresultrequestedbytheuser• Arithmeticvalue analysis:analysisresultrequestedbytheuser

• Step4:InterpretResult• theresultingtablescontain(over-approximation)valuesofBooleanandArithmeticvalueofrootterm

Example1

• Expressionsarelabeledandencodedinabs andvars,bool_lit,num_lit,root,etc.

• Applicationsencodedinapps e.g.,235means2isanapplicationwhereweapply5to3

• Wanttocomputethevalueofroot(0)

((((\x . x ) (\y . y) ) (\z . z ) ) true)01234 56 78 9

TheAnalysis• Weuseacomponentparametrizedbyvalue

.comp DataFlow<Value> {…}

• Havethreerules//thevalueofavariableisthevalueboundtoitinanapplication

_var(n,v) :- app(_,f,a), ctrl.term(f,l), abs(l,n,_), term(a,v).

//thevalueofavariableisthevalueassignedtoitterm(i,v) :- var(i,n), _var(n,v).

//thevalueofanappisthevalueofthebodyofthetargetedabsterm(i,v) :- app(i,f,_), ctrl.term(f,l), abs(l,_,b), term(b,v).

• Instantiateforeachvalueanalysis.init bool = DataFlow<Bool>bool.term(i,v) :- bool_lit(i,v).

• Starttheanalysisbool_res(v) :- root(i), bool.term(i,v).

Example2

• Noticetheimpression• Why?• Homeworkforthekeen:

• Changetheanalysistobepreciseforexample2

letfst =\x.\y.xinletid=\x.xinfst (id4)(id5)

CurrentWorkonSoufflé

• SouffléintheCloud• HowtodistributeDatalog programsintheCloud

• Provenance• Explainingresults;onlinedebugging

• QueryScheduling• Improvingschedulingperformance

• BenchmarkSuite• ForSoufflé,Z3,bddbddb,Logicblox

FutureWork

• Moredata-types• Booleandata-type• Floats/doublesmissing• Integersofvariouslength

• FunctionPredicates• In-buildAssertions

• Alongwish-list….• Refactoring• Documentations

JointheCommunity

• Newresearchprojects• plentyofideas– notenoughpersonpower

• FeatureExtensions• Refactoring• BugFixing• Documentation• Souffléongithub

• http://github.com/souffle-lang/souffle

Appendix

C++Interface/IntegrationintootherTools

• Souffle producesaC++classfromaDatalog program• C++classisaprogramonitsownright• Canbeintegratedinownprojectsseamlessly• Interfacesfor

• PopulatingEDBrelations• Runningtheevaluation• Queryingtheoutputtables

• Useofiteratorsforaccessingtuples• Examples:souffle/tests/interfaces/ofrepo

Example:C++Interface

• Example…if(SouffleProgram *prog=ProgramFactory::newInstance(”mytest")){prog->loadAll(”fact-dir”);//orinsertviaiteratorprog->run();prog->printAll();//orprintviaiteratordeleteprog;

}…

C++Interface:InputRelations

• Insertmethodforpopulatingdataif(Relation*rel =prog->getRelation(”myRel")){for(autoinput:myData){

tuplet(rel);t<<input[0]<<input[1];rel->insert(t);

}}

C++Interface:OutputRelations

• Accessoutputrelationviaiteratorif(Relation*rel=prog->getRelation(”myOutRel")){

for(auto&output:*rel){output>>cell1>>cell2;std::cout<<cell1<<"-"<<cell2<<"\n";

}}

JNIInterface

• Recentlydesigned/implementedbyP.Subotic (UCL)• CreateDatalog programviaASTobjects

• Noparsingofsourcecode

• Applications• implementaDSLinSCALA• useDatalog asabackend

• Example:• Seesouffle/interfaces/examples/Main.scala

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