Recursive Object Research Articles

Asking the right questions to elicit product requirements

Eliciting precise and comprehensive product requirements from customers is of critical importance for the success of product development. In this paper, a generic process is proposed for eliciting product requirements by asking questions based on linguistic analysis. The linguistic analysis transforms a text into a graphic language called recursive object model (ROM). Two types of questions are asked in the process. One type of question, generated according to the topological structure of the ROM diagram, is domain-independent whereas the other relies on the domain of product development. A generic template is developed for generating the questions and for determining the sequence in which those questions are asked. The answers to the questions can be sought on the internet, in text books, the dictionary, the designer's own knowledge and experience, the customers and other partners involved in the product development, and/or nature itself. The generation of new questions may be based on the answers that are obtained. A software prototype is developed to support the proposed process. A case study of a rivet-setting tool design is used to illustrate the process of generating questions.

Recursive object model (ROM)—Modelling of linguistic information in engineering design

Throughout the engineering design process, the design problem and design solutions may be represented by natural language, sketches, technical drawings, and process diagrams. Due to its ambiguity and flexibility, natural language processing has not been well integrated into the tools and methods assisting the design process. This paper proposes a new graphic language, called recursive object model (ROM), to represent natural language used in engineering, which are mainly composed by statements. The ROM uses only five basic symbols to represent object, compound object, constraint relationship, predicate relationship and connection relationship. Those five elements are derived mathematically and are proven sufficient for technical English through enumeration. Three case studies addressing different aspects of design are used to demonstrate the usefulness of the ROM.

Multi-policy improvement in stochastic optimization with forward recursive function criteria

Iwamoto recently established a formal transformation via an invariant imbedding to construct a controlled Markov chain that can be solved in a backward manner, as in backward induction for finite-horizon Markov decision processes (MDPs), for a given controlled Markov chain with non-additive forward recursive objective function criterion. Chang et al. presented formal methods, called “parallel rollout” and “policy switching,” of combining given multiple policies in MDPs and showed that the policies generated by both methods improve all of the policies that the methods combine. This brief paper extends the methods of parallel rollout and policy switching for forward recursive objective function criteria and shows that the similar property holds as in MDPs. We further discuss how to implement these methods via simulation.

Semantics and logic of object calculi

The main contribution of this paper is a formal characterization of recursive object specifications and their existence based on a denotational untyped semantics of the object calculus. Existence is not guaranteed but can be shown employing Pitts’ results on relational properties of domains. The semantics can be used to analyse and verify Abadi and Leino's object logic but it also suggests extensions. For example, specifications of methods may not only refer to fields but also to methods of objects in the store. This can be achieved without compromising the existence theorem. An informal logic of predomains is in use intentionally in order to avoid any commitment to a particular syntax of specification logic.

Type Inference for Variant Object Types

Existing type systems for object calculi are based on invariant subtyping. Subtyping invariance is required for soundness of static typing in the presence of method overrides, but it is often in the way of the expressive power of the type system. Flexibility of static typing can be recovered in different ways: in first-order systems by the adoption of object types with variance annotations, in second-order systems by resorting to Self types. Type inference is known to be P-complete for first-order systems of finite and recursive object types, and NP-complete for a restricted version of Self types. The complexity of type inference for systems with variance annotations is yet unknown. This paper presents a new object type system based on the notion of Split types, a form of object types where every method is assigned two types, namely, an update type and a select type. The subtyping relation that arises for Split types is variant and, as a result, subtyping can be performed both in width and in depth. The new type system generalizes all the existing first-order type systems for objects, including systems based on variance annotations. Interestingly, the additional expressive power does not affect the complexity of the type inference problem, as we show by presenting an O(n3) inference algorithm.

Matching for the lambda calculus of objects

A relation between recursive object types, called matching, has been proposed [8] to provide an adequate typing of inheritance in class-based languages. This paper investigates the role of this relation in the design of a type system for the Lambda Calculus of Objects [15]. A new type system for this calculus is defined that uses implicit matchbounded quantification over type variables instead of implicit quantification over row schemes — as in [15] — to capture MyType polymorphic types for methods. An operational semantics is defined for the untyped calculus and type soundness for the new system is proved as a corollary of a subject reduction property. A formal analysis of the relative expressive power of the two systems is also carried out, that explains how the row schemes of [15] can be understood in terms of matching, and shows that the new system is as powerful as the original one on derivations of typing judgements for closed objects.

On subtyping and matching

A relation between recursive object types, called matching , has been proposed as a generalization of subtyping. Unlike subtyping, matching does not support subsumption, but it does support inheritance of binary methods. We argue that matching is a good idea, but that it should not be regarded as a form of F-bounded subtyping (as was originally intended). We show that a new interpretation of matching as higher-order subtyping has better properties. Matching turns out to be a third-order construction, possibly the only one to have been proposed for general use in programming.

Inductive, coinductive, and pointed types

An extension of the simply-typed lambda calculus is presented which contains both well-structured inductive and coinductive types, and which also identifies a class of types for which general recursion is possible. The motivations for this work are certain natural constructions in category theory, in particular the notion of an algebraically bounded functor, due to Freyd. We propose that this is a particularly elegant core language in which to work with recursive objects, since the potential for general recursion is contained in a single operator which interacts well with the facilities for bounded iteration and coiteration.

Representation and realistic rendering of natural phenomena with cyclic CSG graphs

A method for ray tracing recursive objects defined by parametric rewriting systems using constructive solid geometry (CSG) as the underlying method of object representation is introduced. Thus, the formal languages of our rewriting systems are subsets of the infinite set of CSG expressions. Instead of deriving such expressions to build up large CSG trees, we translate the systems into cyclic CSG graphs, which can be used directly as an object representation for ray tracing. For this purpose the CSG concept is extended by three new nodes. Selection nodes join all the rules for one grammar symbol, control flow by selecting proper rules, and are end-points of cyclic edges. Transformation nodes map the rays in affine space. Calculation nodes evaluate a finite set of arithmetic expressions to modify global parameters, which effect flow control and transformations. The CSG graphs introduced here are a very compact data structure, much like the describing data set. This property meets our intention to avoid both restrictions of the complexity of the scenes by computer memory and the approximation accuracy of objects.

Intelligent knowledge based expert inventory control system for computer integrated manufacturing

Abstract The paper discusses the framework and development of an expert inventory management system for integrative manufacturing planning. The system developed with an artificial intelligent language provides a linkage between management and computer-integrated manufacturing(CIM), has the following major elements: data base to represent a hierarchical tree using recursive objects on different levels; knowledge base containing heuristic rules; goal oriented interaction; and backtracking interface procedures. Potential benefits of the system includes: better manufacturing planning, reduced inventory levels and production lead times, and consistent inventory control records.

Existence of Optimal Solutions for Control and Variational Problems with Recursive Objectives

Carlson has formulated an open question as to the precise connections between conditions on the recursive objective functions for an optimal control model used by Carlson (J. Optim. Theory Appl.66 (1990), 311-336) and a variational model for optimal growth in Becker et al. (J. Econ. Theory47 (1989), 76-100). A complete answer to his question is provided by the introduction of a new lower closure result.

A recursive object algebra based on aggregation abstraction for manipulating complex objects

We present an object algebra for manipulating complex objects in object-oriented database systems. All operators are recursively defined. Unlike most of the existing query languages, the design of this object algebra is based on aggregation abstraction. It allows to take complex objects collectively as a unit of high level queries and enables complex objects to be accessed at all levels of aggregation hierarchies without resorting to any kind of path expressions. Features of aggregation abstraction, such as acyclicity of aggregation hierarchies and aggregation inheritance, have played important roles in such a development. We also formally described the output type of each operator in order to support dynamic classification of query results in the IsA type/class semi-lattice. The algebraic-equivalence rewriting rules for query optimization of this algebra are developed, too.

Recursive utility and optimal capital accumulation II: sensitivity and duality theory

Summary. This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we nd the value function is dierentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sucient for an optimum. This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where the planner’s preferences are represented by a recursive objective functional. Time preference is exible. A previous paper (Becker, Boyd and Sung, 1989) established the existence of optimal paths by choice of an appropriate topology. In this paper, we combine the same topology with a controllability condition to demonstrate the sensitivity of the optimal path with respect to changes in the initial endowment of capital, and changes in the planner’s rate of time preference. Under convexity and an interiority condition, we nd the value function is dierentiable, and derive a multiplier equation for the

Recursive utility and optimal capital accumulation. I. Existence

This paper demonstrates existence of optimal capital accumulation paths when the planner's preferences are represented by a recursive objective functional. Time preference is flexible. We employ a general multiple capital good reduced-form model. Existence of optimal paths is addressed via the classical Weierstrass theorem. The topology is uniform convergence of capital stocks on compact subsets, which is equivalent to weak convergence of investment flows under our maintained hypotheses. An improved version of a lemma due to Varaiya proves compactness of the feasible set. A monotonicity argument is combined with a powerful theorem of Cesari to demonstrate upper semicontinuity.

Recursive objects in all finite types

Recursive objects in all finite types

Combinatory recursive objects of all finite types

Combinatory recursive objects of all finite types