26823713
Top-Down Synthesis of Divide-and-Conquer Algorithms
Abstract A top-down method is presented for the derivation of algorithms from a formal specification of a problem. This method has been implemented in a system called cypress . The synthesis process involves the top-down decomposition of the initial specification into a hierarchy of specifications for subproblems. Synthesizing programs for each of these subproblems results in the composition of a hierarchically structured program. The initial specification is allowed to be partial in that some or all of the input conditions may be missing. cypress completes the specification and produces a totally correct applicative program. Much of cypress ' knowledge comes in the form of ‘design strategies’ for various classes of algorithms. The structure of a class of divide-and-conquer algorithms is explored and provides the basis for several design strategies. Detailed derivations of mergesort and quicksort algorithms are presented.
7947888
Constructing Specification Morphisms
Specification morphisms underlie the refinement of algebraic specifications and provide the logical foundations for algorithm and data structure design. We present four techniques for formally, even mechanically, constructing specification morphisms. The first two techniques, verifying a manually constructed signature morphism and composition of specification morphisms are well-known. The remaining two techniques exploit the axioms of the source specification to help infer the translation of sort and function symbols from the source specification. The third, unskolemization, finds the translation of a function symbol by replacing occurrences of it in an axiom by an existentially quantified variable. A constructive proof of the translated axiom yields a witness to the existential that serves as the desired translation of the function symbol. The fourth technique, connections between specifications, allows the transfer of structure from one specification morphism to another. The unskolemization and connection techniques arose as abstractions from the algorithm design tactics implemented in the KIDS program transformation system (Smith (1990)). They suggest a more general approach to providing mechanized support for applying design knowledge expressed axiomatically.
44957593
Toward a Classification Approach to Design
This paper addresses the problem of how to construct refinements of specifications formally and incrementally. The key idea is to use a taxonomy of abstract design concepts, each represented by a design theory An abstract design concept is applied by constructing a specification morphism from its design theory to a requirement specification. Procedures for propagating constraints, computing colimits, and constructing specification morphisms provide computational support for this approach. Although we conjecture that classification generally applies to the incremental application of knowledge represented in a taxonomy of design theories, this paper mainly focuses on algorithm design theories and presents several examples of design by classification.
12681881
Synthesis of Constraint Algorithms
17878068
Guarded Transitions in Evolving Specifications
We represent state machines in the category of specifications, where assignment statements correspond exactly to interpretations between theories [7, 8]. However, the guards on an assignment require a special construction. In this paper we raise guards to the same level as assignments by treating each as a distinct category over a shared set of objects. A guarded assignment is represented as a pair of arrows, a guard arrow and an assignment arrow. We give a general construction for combining arrows over a factorization system, and show its specialization to the category of specifications. This construction allows us to define the fine structure of state machine morphisms with respect to guards. Guards define the flow of control in a computation, and how they may be translated under refinement is central to the formal treatment of safety, liveness, concurrency, and determinism.
206511487
Composition and refinement of behavioral specifications
This paper presents a mechanizable framework for specifying, developing, and reasoning about complex systems. The framework combines features from algebraic specifications, abstract state machines, and refinement calculus, all couched in a categorical setting. In particular, we show how to extend algebraic specifications to evolving specifications (especs) in such a way that composition and refinement operations extend to capture the dynamics of evolving, adaptive, and self-adaptive software development, while remaining efficiently computable. The framework is partially implemented in the Epoxi system.
44972038
Project CALC: Calculus as a Laboratory Course
Calculus is the study of change. The concepts of calculus enable us to model processes that change and to describe properties of these processes that remain constant in the midst of change. Now change has come to the learning of calculus -change driven by the need to respond to the revolution in technology and fueled by funds from the United States National Science Foundation. What should be changed? How and how fast? What should remain constant? In this paper we describe one answer to these questions: Project CALC, a new calculus course developed at Duke University. The key features of our approach are real-world problems, hands-on activities, discovery learning, writing and revision of writing, teamwork, and intelligent use of available tools.
16933924
Using architecture evaluation to prepare a large Web based system for evolution
This paper describes an ongoing effort to develop architecture documentation and to evaluate the architecture using the Architecture Tradeoff Analysis Method/sup SM/ (ATAM/sup SM/). The system is a large Web based application using J2EE, portal and Web services technology that is replacing a large number of legacy applications. It has very detailed documentation at the design level, but is lacking overall architecture documentation. We describe how the architecture is being documented in an iterative manner, and how sample scenarios are being developed as input for an ATAM. The package of the documentation, scenarios and ATAM will fill in important gaps in existing knowledge, and it will provide an important baseline for the system's evolution.
7534908
Building a hypertextual digital library in the humanities: a case study on London
This paper describes the creation of a new humanities digital library collection: 11,000,000 words and 10,000 images representing books, images and maps on pre-twentieth century London and its environs. The London collection contained far more dense and precise information than the materials from the Greco-Roman world on which we had previously concentrated. The London collection thus allowed us to explore new problems of data structure, manipulation, and visualization. This paper contrasts our model for how humanities digital libraries are best used with the assumptions that underlie many academic digital libraries on the one hand and more literary hypertexts on the other. Since encoding guidelines such as those from the TEI provide collection designers with far more options than any one project can realize, this paper describes what structures we used to organize the collection and why. We particularly emphasize the importance of mining historical authority lists (encyclopedias, gazetteers, etc.) and then generating automatic span-to-span links within the collection.
8267445
Explaining design plans
The paper describes a methodology for generating quality explanations from design plans. In selecting items of information for inclusion in an explanation, the methodology considers the rationales behind the strategic knowledge and object-level knowledge specified in a design plan. Rhetorical structure theory and discourse focus tracking are utilised to determine textual structure, and to maintain discourse coherence and cohesion. Using a simple system of user modelling, it is shown how the methodology flexibly includes consideration of a user's knowledge, thus resulting in more focused and convincing explanations. The methodology is used to investigate follow-up explanations, and the generation of explanations from plans which contain a misconception on the part of the designer.
27096788
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