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Abstract Model Specification

Abstract Model Specification. Tarang Garg Srikumar Nagaraj. Abstract Model Specification. Explicitly describes behavior in terms of a model using well-defined types (viz. set, sequences, relations, functions) & defines operations by showing effects on model Specification includes

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Abstract Model Specification

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  1. Abstract Model Specification Tarang Garg Srikumar Nagaraj

  2. Abstract Model Specification • Explicitly describes behavior in terms of a model using well-defined types (viz. set, sequences, relations, functions) & defines operations by showing effects on model • Specification includes • type - syntax of object being specified • model - underlying structure • invariant - properties of modeled object • pre/post conditions – semantics of operations

  3. Notation • Is used to test the results • Independent of program code • Mathematical Data model • Represent both static and dynamic aspects of a system

  4. Features( Z-notation) • Decompose specification into small pieces (Schemas) • Schemas are used to describe both static and dynamic aspects of a system • Data Refinement • Direct Refinement • You can ignore details in order to focus on the aspects of the problem you are interested in

  5. Schema Static Aspect • The state can occupy. • The invariant relationships that are maintained as the system moves from state to state

  6. Schema(cont.) Dynamic Aspect • The operations that are possible • The relationship between their inputs and outputs. • The change of state that happen.

  7. Notation - Example Name Some variables are declared. Relationship between the values of the variables Init Birthday Book Birthday Book Known = 

  8. Example Birthday book known: NAME birthday: NAME DATE Known : dom birthday Add Birthday Birthday Book name?: NAME date?: DATE name? known birthday’ = birthday { name? date}

  9. Example(cont.) Find Birthday Birthday book name?: NAME date? : DATE name? Known date != birthday(name?)

  10. Race condition We have not handled the condition when user tries to add a birthday, which is already known to the system, or tries to find the birthday of someone not known. Handle this by adding an extra result! To each operation. Result := of| already_known | not_known Success Result! : REPORT Result! = ok

  11. Operators (Conjunction of the two predicate parts) – any common variables of the two schemas are merged V (the effect of the schema operator is to make a schema in which the predicate part is the result of joining the predicate parts of its two arguments with the logical connective V).

  12. Logical Conjunction Operator The conjunction operator  of the schema calculus allows us to combine this description with our previous description of AddBirthday AddBirthday  Success This describes an operation which, for correct input, both acts as described by AddBirthday and produces the result ok.

  13. Logical Disjunction operator AlreadyKnown BirthdayBook name? : NAME result?: REPORT This declaration specifies that if error occurs, the state of the system should not change. Robust version of AddBirthday can be RAddBirthday  (AddBirthday  Success) V Alreadyknown Name?  known Result! = already_known

  14. Use of Operators RAdd Birthday Birthday Book name?: NAME date?: DATE result!: REPORT (name?  known  birthday’= birthday  {name? Date?}  result!= ok) V (name?  known  birthday’ = birthday  result != already_known)

  15. From specification to design Data Refinement “ to describe the concrete data structures which the program will use to represent the abstract data in the specification, and to derive description of the operation in terms of the concrete data structures” Direct Refinement: method to go directly from abstract specification to program in one step

  16. Data Refinement Data Structures: Two arrays : names [1…] of NAME dates [1…] of DATES names’ = names{i v} ; names[i] := v the right side of this equation is a function which takes the same value as names everywhere except at the argument i, where it takes the value ‘v’.

  17. Example(Data and Direct Refinement) FindBirthday1 BirthdayBook1 name?:NAME date?:DATE i : 1.. hwm name?=names(i)  date! = dates(i) Procedure FindBirthday(name: NAME; var date : DATE); var i: INTEGER; begin i:=1; while names[i]  name do i := i+1; dates := dates[i] end;

  18. Advantages • The flexibility to model a specification which can directly lead to the code. • Easy to understand • A large class of structural models can be described in Z without higher – order features, and can thus be analyzed efficiently. • Independent Conditions can be added later

  19. Chemical Abstract Model CHAM: for architectural description and analysis. Software Systems chemicals (whose reactions are controlled by explicitly stated rules). Where floating molecules can only interact according to a stated set of reaction rules.

  20. Features(CHAM) - Modular specification • Chemical reactions • Molecules (components) • Reactions (Connectors) • Solutions (States of CHAM) • This is used in areas where intended architecture will tend to be large, complex, and assembled from existing components. • Architectural elements: Processing elements, data elements, and connecting elements.

  21. Alloy: A Lightweight Object Modeling Notation

  22. Introduction • Alloy • Is a modeling notation that describes structural properties • Has a declaration syntax compatible with graphical object models • Has a “set-based” formula syntax • Is based on “Z”

  23. Example File System contents ! ! Object DirEntry Name name Parent (~children) ! entries Dir File Root!

  24. Example (File System) model FileSystem { domain {Object, DirEntry, fixed Name} state { partition File, Dir: static Object Root: fixed Dir! entries: Dir! -> DirEntry name: DirEntry -> static Name! contents: DirEntry -> static Object! parent (~children) : Object -> Dir } def parent {all o | o.parent = o.~contents.~entries} inv UniqueNames {all d | all e1, e2: d.entries | e1.name = e2.name -> e1 = e2} inv Parents { no Root.parent all d: Dir – Root | one d.parent} inv Acyclic {no d | d in d.+parent} inv Reachable {Object in Root.*children} cond TwoDeep {some Root.children.children} assert FileHasEntry {all o | sole o.parent} assert AtMostOneParent {all o | sole o.parent} op NewDirEntries (d: Dir, es: DirEntry’) { no es & DirEntry d.entries’ = d.entries + es all x: Dir – d | x.entries’ = x.entries } op Create (d: Dir!, o: Object’!, n: Name) { n! in d.entries.name some e: DirEntry’ | NewDirEntries (d, e) && e.contents’ = o && e.name’ = n} assert EntriesCreated {all d: Dir, e: DirEntry’ | NewDirEntries (d, e) -> DirEntry’ = DirEntry + e} assert CreateWorks {all d, o, n | Create (d, o, n) -> o n d.children’} }

  25. Example (File System) • Structure of the model • Domain paragraph • State paragraph • Definition paragraph • Invariants • Condition • Assertions • Operations • Assertions

  26. Analysis • Alloy supports two kinds of analysis • Simulation: Consistency of an invariant or operation is demonstrated by generating a state or transition. • Checking: A consequence of a specification is tested by attempting to generate a counterexample. • Together they enable an incremental process of specification.

  27. Based On Z • Alloy is based on Z because: • Simple and intuitive semantics (based on sets). • Well suited for object oriented modeling. • Data structures are built from concrete mathematical structures.

  28. Features • Automatic analysis • Theorem proving is deep & automatic. • Easier to read and write. Plain ASCII notation. • Relational operators are powerful. • Incorporates mutability notions from informal notations.

  29. Design Faults • Omission of the let construct & relational operators • No integers • No distinction between attributes and relations

  30. Formalizing Style to Understand Descriptions of Software Architecture

  31. Introduction • Software architecture describes a software system • Architectural descriptions are informal & diagrammatic • Represented by boxes & lines • For one system they may mean filters & pipes • For another system boxes  abstract data types or objects & lines  procedure calls

  32. Introduction • Different graphical conventions used to describe more than one kind of component or connection type in a single system • Generalized meanings to architectural descriptions

  33. How is it done? • Formalize abstract syntax for architectures • For a given style: • Define the semantic model • Discuss concrete syntax for easing syntactic descriptions in a given style • Define the mapping from abstract syntax into semantic model • Make explicit the constraints on the syntax

  34. How is it done? • Demonstrate analysis within & between formally defined architectural styles

  35. Abstract Syntax of Software Architectures • Component: • Relationship between component & it’s environment is defined as a collection of interaction points or ports: • [PORT, COMPDESC] Component ports : P PORT description : COMPDESC

  36. Abstract Syntax of Software Architectures • Connectors: • Connector has an interface that consists of a set of roles: • [ROLE, CONNDESC] Connector roles : P ROLE description : CONNDESC

  37. Abstract Syntax of Software Architectures • Instances of components & connectors are identified by naming elements from the syntactic class [COMPNAME, CONNNAME] PortInst == COMPNAME x PORT RoleInst == CONNNAME x ROLE

  38. Step 1 (Define Semantic Model) Filter Alphabet : DATAPORT P DATAPORT States : P STATE Inputs, outputs : P DATAPORT Start : STATE Transitions : (STATE x (DATAPORT seq DATA)) (STATE x (DATAPORT seq DATA)) Inputs n outputs = o Dom alphabet = inputs u outputs Start e states • s1, s2 : STATE ; ps1, ps2 : DATAPORT seq DATA • ((s1, ps1), (s2, ps2)) e transitions • s1 e states L s2 e states • L dom ps1 = inputs L dom ps2 = outputs • L ( i : inputs • ran (ps1(i))  alphabet(i)) • L ( o : outputs • ran (ps2(o))  alphabet(o))

  39. Step 1 (Define Semantic Model) Pipe source, sink : DATAPORT alphabet : P DATA source = sink

  40. Step 2 Define Concrete Syntax FilterDescriptions : P COMPDESC PipeDescription : P CONNDESC

  41. Step 3 • Mapping from Abstract Syntax to Semantic Model PFComp : Connector P Pipe •  c : Connector ; p1, p2 : Pipe | p1  PFComp (c ) • p2  PFComp (c )  p1.alphabet = p2.alphabet

  42. Step 4 • Highlight the constraints in the syntax LegalPFComponent Component Description  FilterDescriptions

  43. Advantages • Provides a templates for formalizing new architectural styles in a uniform way • Provides uniform criteria for demonstrating that the notational constraints on a style are sufficient to provide meanings for all described systems • Makes possible a unified semantic base through which different stylistic interpretations can be compared

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