09 November 2012

1. 09 November 2012 Dongmei Liu, Hong Zhu and Ian Bayley Applying Algebraic Specification To Cloud Computing

2. Outline • Motivation and Related works • Our Algebraic Specification Language • Case Study of IaaSGoGrid • Discussion • Conclusion and Future work

3. Motivation Encourage rigour Well-founded mathematical basis. Well-defined semantics Automating analysis • Formal Specification • Merits • Limitation • Classification of approaches • Algebraic Specification • Heterogeneous algebras • Signature • Axioms Difficult to learn and use Limited scope Limited scalability Property-Oriented Model-Oriented axiomatic algebraic

4. Motivation REST: From Research to Practice (2011, Erik Wilde) • RESTful Web Services • Identification of resources (URIs) • Manipulation of resources through representations • HTTP methods • Stateless • Cloud Computing • Open API • OCCI (Open Cloud Computing Interface) http://stage.vambenepe.com/archives/863 The OCCI Core specification The OCCI Rendering specifications The OCCI Extension specifications

5. Related Works • Description of RESTful WS • Formats for annotating the syntax and semantics • Graphic notation(UML state machine diagram) • Algebraic Specification • Algebras • Co-algebras • Extend algebraic and co-algebraic • Algebraic testing WADL hRESTS/Micro WSMO SA-REST O. Liskin,etc. Welcome to the Real World: A Notation for Modeling REST Services, IEEE Internet Computing, 2012

6. CASOCC-WS • Overall structure • Sorts, operators and/or axioms that logically belong together are grouped into a unit. <Specification> ::= {<Spec Unit>} <Spec Unit> ::= Spec <Sort Name> [<Observability>]; <Signature> [<Axioms>] End • <Sort Name> ::= <Identifier> <Observability> ::= is observable by <Operator ID> | is unobservable <Operator ID> ::= <Identifier>

7. CASOCC-WS • Example Spec BOOL is observable by eqv; Operators: Creator: true: VOID -> BOOL; false: VOID -> BOOL; Transformer: and: BOOL, BOOL -> BOOL; or: Bool, BOOL -> BOOL; eqv: BOOL, BOOL -> BOOL; not: BOOL -> BOOL; Axioms: For b: BOOL that b and true == b; b or false == b; b and b == b; b or b == b; ... End … End

8. CASOCC-WS • Signature • specify the syntactic aspect of the software entity • defines a set of typed operations • reuse • <Signature> ::= [<Imported Sorts>;] <Operations> • <Imported Sorts> ::= Sort <Imported Sort List> • <Imported Sort List> ::= <Sort Name>[, <Imported Sort List>] • <Operations> ::= Operators: • [<Creators>;][<Transformers>;][<Observers>;][<Definers>;] • <Creators> ::= Creator: <OpList> • <Transformers> ::= Transformer: <OpList> • <Observers> ::= Observer: <OpList> • <Definers> ::= Definer: <OpList> • <OpList> ::= <Operation> [; <OpList>]

9. CASOCC-WS • Operator • Function: identifier, domain and co-domain types • have more than one domain sort and more than one co-domain sort at the same time • Spec STACK; • Sort BOOL, NAT; • Operators: • Creator: • newStack: -> STACK; • Transformer: • push: STACK, NAT -> STACK; • pop: STACK -> STACK; • Observer: • isNewStack: STACK -> BOOL; • top: STACK -> NAT; • End • Spec STREAM is unobservable; • Sort NAT; • Operators: • Transformer: • next: STREAM -> STREAM, NAT; • End

10. CASOCC-WS • Operator • Function: identifier, domain and co-domain types • have more than one domain sort and more than one co-domain sort at the same time • <Operation> ::= <Operator ID> :['['<Context Sort>']'] • [<Domain Type>] -> <Co-domain Type> • <Context Sort> ::= <Sort Name> • <Domain Type> ::= <Type> | VOID • <Co-domain Type> ::= <Type> | VOID • <Type> ::= <Sort Name> [, <Type>]

11. CASOCC-WS • Axioms • specify the semantics of the operators • describing the properties that operators are required to satisfy • consists of a variable declarations block and a list of conditional equations. • <Axioms> ::= Axiom: <Axiom List> • <Axiom List> ::= <Axiom> [<Axiom List>] • <Axiom> ::= <Var Declarations> <Equations> End • <Var Declarations> ::= • For all <Var-Sort Pairs> that • <Var-Sort Pairs> ::= • <Var IDs> : <Sort Name> [, <Var-Sort Pairs>] • <Var IDs> ::= <Var ID> [, <Var IDs>] • <Var ID> ::= <Identifier>

12. CASOCC-WS For all SLR: ServerListRequest that SLR.num_items>=0; SLR.page>=0, if SLR.num_items> 0; End • Equation • conditional equation • local variable and Let… in For all s: STACK, n: NAT that isNewStack(push(s,n))== False; pop(push(s, n))== s; top(push(s, n))== n; End For all s: STACK, n: NAT that Let s1 = push(s,n) in isNewStack(s1) == False; pop(s1) == s; top(s1) == n; End End

13. CASOCC-WS • Equation • conditional equation • local variable and Let… in • <Equation> ::= [<Label>:] <Condition> [, if <Conditions>]; • | Let <Var Definitions> in <Equations> End • <Conditions> ::= <Condition> [(,|or) <Conditions>] • <Condition> ::= <Bool Term> | <Term> <Relation OP> <Term> • | "(" <Condition> ")" | "~" <Condition> • <Bool Term> ::= True | False | <Term> • <Relation OP> ::= "==" | "<>" | ">" | "<" | ">=" | "<=" | "IS“ • <Term> ::= <Var ID> | "(" <Term> ")“ | "<" <Term List> ">" • | <Operator ID> ["(" [<Parameters>] ")"] | "[" <Term> "]" • | <Term> "." <Term> | <Term> "#" <Term> • | <numeric_expression> | <string_expression> • | <literal_expression> | NULL

14. CASOCC-WS • Modular • software entity: abstract data type, class, component, WS • Algebraic and co-algebraic Op: [s] s1, … , sn s'1, … , s'k • Kinds of operators • Creator • Transformer • Observer • Conditional equations • Relation Operation • Let … in …

15. Case Study: GoGird • GoGrid • world's largest pure-play Infrastructure-as-a-Service provider specializing in Cloud infrastructure solutions • API • a REST-like query interface

16. Case Study: GoGrid • Overall Structure of the Specification • First, for each object, specifying the requests and responses of the operations, defining their structures and the constraints on the values of the elements. • Then, specify the semantics of the operators on the type of objects by defining the relationships between the requests and the responses.

17. Case Study: GoGrid Spec Server; Sort Option, IP, ServerImage; Operators: Observer: id: Server -> long; name: Server -> string; description: Server -> string; ip: Server -> IP; image: Server -> ServerImage; ram: Server -> Option; state: Server -> Option; type: Server -> Option; os: Server -> Option; isSandbox: Server -> boolean; datacenter: Server -> Option; Axiom: For all SO: Server that SO.id <> null; End End • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec ListofServer; Sort Server; Operators: Observer: items: ListofServer,int -> Server; length: ListofServer -> int; End

18. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec CommonParameter; Operators: Observer: api_key: CommonParameter -> string; sig: CommonParameter -> string; v: CommonParameter -> string; format: CommonParameter -> string; Axiom: For all CP: CommonParameter that CP.api_key<> NULL; CP.sig<> NULL; CP.v<> NULL; End End

19. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec ServerListRequest; Sort CommonParameter, ListofString; Operators: Observer: para: ServerListRequest -> CommonParameter; num_items: ServerListRequest -> int; page: ServerListRequest -> int; server_type: ServerListRequest -> string; isSandbox: ServerListRequest -> boolean; datacenter: ServerListRequest -> ListofString; timestamp: ServerListRequest -> int; Axiom: For all SLR: ServerListRequest that SLR.num_items>=0; SLR.page>=0, if SLR.num_items > 0; End End

20. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec ListResSummary; Operators: Observer: total: ListResSummary -> int; start: ListResSummary -> int; returned: ListResSummary -> int; numpages: ListResSummary -> int; Axiom: For all LRS: ListResSummary that LRS.total>= 0; LRS.start >= 0; LRS.returned >= 0; LRS.numpages>= 0; End End

21. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec ServerListResponse; Sort ListResSummary, ListofServer, ListofString; Operators: Observer: status: ServerListResponse -> string; request_method: ServerListResponse -> string; summary: ServerListResponse -> ListResSummary; objects: ServerListResponse -> ListofServer; statusCode: ServerListResponse -> int; Axiom: For all SLR: ServerListResponse that SLR.request_method== "/grid/server/list"; End For all SLR:ServerListResponse, i,j:int that SLR.objects.items(i).id <> SLR.objects.items(j).id, if status == "success", i <> j, 0 <= i, i <= SLR.summary.returned, 0 <= j, j <= SLR.summary.returned; End ... End

22. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Spec ServerGrid; Sort CommonParameter, Server, ListofServer, … ListofString, ServerListRequest, ListResSummary, ServerListResponse, …; Operators: Observer: clockTime: ServerGrid -> int; sharedSecret: ServerGrid, string -> string; List: [ServerGrid] ServerListRequest-> ServerListResponse; Get: [ServerGrid] ServerGetRequest-> ServerGetResponse; Transformer: Add: [ServerGrid] ServerAddRequest-> ServerAddResponse; Delete: [ServerGrid] ServerDeleteRequest-> ServerDeleteResponse; Edit: [ServerGrid] ServerEditRequest-> ServerEditResponse; Power: [ServerGrid] ServerPowerRequest -> ServerPowerResponse; End

23. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Axiom <Authentication>: For all G:ServerGrid, X:ServerListRequest that Let key = X.para.api_key, sig_Re= MD5(key, G.sharedSecret(key), X.timeStamp) in G.List(X).statusCode == 403, If X.para.sig <> sig_Re or abs(X.timeStamp - G.clockTime) > 600; End End

24. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Axiom <List-XOp>: For all G: ServerGrid, X: ServerListRequest, X1: ServerXOpRequest that [G.List(X)].XOp(X1) == G.XOp(X1); End

25. Case Study: GoGrid • The Specification of Server • Objects and Collections • Requests and Responses • Semantics of the Operations Axiom <Add-List>: For all G: ServerGrid, X1: ServerAddRequest, X2: ServerListRequest that [G.Add(X1)].List(X2).objects == insert(G.List(X2).objects, G.Add(X1).objects), If X2.num_items == 0, X2.server_type == NULL, X2.isSandbox == NULL, X2.datacenter == NULL, G.Add(X1).statusCode == 200, G.List(X2).statusCode == 200; End

26. Case Study: GoGrid • Results

27. Parser Tool • JavaCC(Compiler Compiler) • parser generator for use with Java applications • a tool that reads a grammar specification and converts it to a Java program that can recognize matches to the grammar. • generates top-down parsers, which limits it to the LL(k) <numeric_expression> ::= <Term> <Arithmetic OP> <Term> <numeric_expression> ::= <numeric_p> [ (*|/) <numeric_p> ] <numeric_p> ::= <numeric_v> [ (+|-) <numeric_v> ] <numeric_v>] ::= <integer_literal> | <float_literal> | ( <Term> )

28. Parser Tool • JavaCC(Compiler Compiler)

29. Parser Tool • JavaCC(Compiler Compiler)

30. Parser Tool • JavaCC(Compiler Compiler)

31. Parser Tool • JavaCC(Compiler Compiler)

32. Parser Tool • GUI

33. Discussion • Improving Document Preciseness • Detecting Incompleteness • Checking Consistency • Reducing Redundancy • Understandability of Document

34. Conclusion • apply the CASOCC-WS specification language to cloud computing interface with a case study on GoGrid System • demonstrate that CASOCC-WS can be used for RESTful WS • detect non-trivial errors including ambiguity, inconsistency and incompleteness • demonstrate that algebraic specifications can be easy to understand

35. Further work • More case study for cloud computing, OCCI • Extend the algebraic specification language • Combine Ontology to describe RESTful WS • Develop a tool to support automated testing of a cloud computing interface

36. Thanks Questions?