Respectful Type Converters Written By: Jeannette M. Wing & John Ockerbloom Presenter: Srinivas Nutulapathi

Presentation Outline Introduction Behavioral Subtyping Respects The TOM Conversion Service Incorporating Concrete Types Applications of the Respects Relation TOM Status Summary and Future Work

Introduction Tremendous growth of the Internet and the World Wide Web gives millions of people access to vast quantities of data. Users may be able to retrieve data easily, they may not be able to interpret or display retrieved data intelligibly. Users and programs cope with this problem by converting data from one type to another.

Type Converters Type converters are applied on data objects to transform an object of one type to an object of different type. Respectful Type Converters: A converter C : A -> B respects type T if the original object of type A and the converted object of type B have the same behavior when both objects are viewed as type T object.

Example The PNG to GIF converter respects bitmap, but not pixel_map.

Behavioral Subtyping Programming language has come up with many definitions of subtype relation. Goal is to determine when this assignment x :T := E is legal. x will be used according to its “apparent” type T , with the expectation that if the program performs correctly when the actual type of x’ s objects is T, it will also work correctly if the actual type of the object denoted by x is a subtype of T.

Model of Objects, Types and Computation Assume a set of all potentially existing objects , Obj, partitioned into disjoint typed sets. Type: defines a set of values for an object and a set of methods that provide the only means to manipulate or observe that object. State: defines a value for each existing object and it is a pair of mappings, an environment and a store. State = Env x Store Env = Var -> Obj Store = Obj -> Val

A type specification implicitly defines the type’s set of objects contains information like type’s name, description of set of values over which objects of type ranges. Each of type’s methods contain its name, its signature ,i.e., the types of its arguments (in order), result, and signaled exceptions and also its behavior in terms of pre-conditions and post-conditions.

Example

Subtype Relation Abstraction Function: This function relates the different value spaces for objects of different types. Renaming Map: This defines the correspondence between the methods of two types.

Respects Fig :Two compositions of Abstraction Functions from the paper

Definition of Respects Relation Definition from the paper

The first condition in the definition requires that , from T’s view point, if m is defined for A’s values, it should be defined for B’s values and vice versa. (precondition) The second condition in the definition requires that ,if given that m is defined, then its behavior must be the same for A’s values and B’s values from T’s view point. Thus both conditions together guarantee that T cannot perceive a difference between the original A object and the converted B object; thus C respects T.

An Application :TOM Conversion Service TOM involves objects, types, and their associated metadata. The kinds of types TOM supports today are different kinds of document types (e.g., Word, PowerPoint, HTML) and packages of document types (e.g., a mail message that has an embedded postscript file, a tar file, or a zip file) The kinds of conversions TOM supports are off-the-shelf converters like postscript2pdf(i.e., Adobe Distiller), off-the-web ones like latex2html, and some home-grown ones like powerpoint2html. Users can compose available converters to produce an object of a desired target type.

TOM is a connected network of type brokers. TOM can compose converters to do conversions. TOM can tell a user when a requested conversion is unsupported or meaningless.

Part of TOMs type hierarchy The critical design decision of TOM is all objects are immutable. TOM type hierarchy is carefully designed so that each subtype either only adds new methods or changes old methods in a constrained way.

Subtype conditions that hold between types in TOM hierarchy If no changes to old methods are made then the invariants are preserved and the behavior of old methods is preserved i.e., the subtype object has more extra state information. If changes to old methods are made, then part2 of subtype definition applies: the contra/covariant rules, the exception rule, and, most importantly the precondition and post condition rules must be satisfied. In general, a subtype might both extend and constrain its supertype.

Incorporating Concrete Types Respects relation can be considered interms of concrete types too. In TOM context ,integers may be represented in terms of a 32-bit sign extension byte sequence or a two’s complement, or even ASCII strings. These are all plausible concrete representations of integers and conversions between them should respect the abstract integer type.

Extending the Definition of Respects Definiton taken from the paper

Two Other Application Of the Respects Relation Type Evolution - Respects relation helps characterize what information should be preserved when types evolve. Reuse for Interoperability – Resolving mismatches among heterogeneous components. In general for n heterogeneous components, each of which is to have the same m methods defined, if all n components are subtypes of some type T, then we need only m+(n-1) functions rather than m*n functions.

Summary Converters can be characterized into three most common kinds: Those mapping from one abstract type to another abstract type. Those mapping from a super type to a subtype or vice versa. Those mapping from a concrete type to a concrete type.

Future Work Definition of respects can be extended to accommodate mutable types. Type specifications would include a predicate called type constraints, which captures what behavior may not change from state to state. Definition of respects additionally considers the preservation of type constraints and the behavior of mutator methods.

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