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

2. Outline  Motivation and Related works  Our Algebraic Specification Language  Case Study of IaaS GoGrid  Discussion  Conclusion and Future work

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

4. Motivation  RESTful Web Services  Identification of resources (URIs)  Manipulation of resources through representations  HTTP methods  Stateless  Cloud Computing  Open API  OCCI (Open Cloud Computing Interface) REST: From Research to Practice (2011, Erik Wilde) http://stage.vambenepe.com/arc hives/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 Spec ification  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. ::= { } ::= Spec [ ]; [ ] End ::= { } ::= Spec [ ]; [ ] End ::= is observable by | is unobservable ::= is observable by | is unobservable ::=

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 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 ::= [ ;] ::= Sort ::= [, ] ::= Operators: [ ;][ ;][ ;][ ;] ::= Creator: ::= Transformer: ::= Observer: ::= Definer: ::= [; ] ::= Sort ::= [, ] ::= Operators: [ ;][ ;][ ;][ ;] ::= Creator: ::= Transformer: ::= Observer: ::= Definer: ::= [; ]

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 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 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 ::= :['[' ']'] [ ] -> ::= ::= | VOID ::= [, ] ::= :['[' ']'] [ ] -> ::= ::= | VOID ::= [, ]

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. ::= Axiom: ::= [ ] ::= End ::= For all that ::= : [, ] ::= [, ] ::= ::= Axiom: ::= [ ] ::= End ::= For all that ::= : [, ] ::= [, ] ::=

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

13. CASOCC-WS  Equation  conditional equation  local variable and Let… in ::= [ :] [, if ]; | Let in End ::= [(,|or) ] ::= | | "(" ")" | "~" ::= True | False | ::= "==" | "<>" | ">" | " =" | "<=" | "IS“ ::= | "(" ")“ | " ">" | ["(" [ ] ")"] | "[" "]" | "." | "#" | | | | NULL ::= [ :] [, if ]; | Let in End ::= [(,|or) ] ::= | | "(" ")" | "~" ::= True | False | ::= "==" | "<>" | ">" | " =" | "<=" | "IS“ ::= | "(" ")“ | " ">" | ["(" [ ] ")"] | "[" "]" | "." | "#" | | | | NULL

14. CASOCC-WS

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 ObjectListGetAddDeleteEditOther Ops ServerYes Power Server imageYes Save, Restore Load BalancerYes JobYes IPYes PasswordYes Billing Yes OptionYes

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  The Specification of Server  Objects and Collections  Requests and Responses  Semantics of the Operations 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 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

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

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

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 : 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

24. Case Study: GoGrid  The Specification of Server  Objects and Collections  Requests and Responses  Semantics of the Operations Axiom : 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 : 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) ::= ::= [ (*|/) ] ::= [ (+|-) ] ] ::= | | ( )

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?