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A Behavioral Notion of Subtyping
 ACM Transactions on Programming Languages and Systems
, 1994
"... The use of hierarchy is an important component of objectoriented design. Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding of ..."
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Cited by 505 (13 self)
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of how subtypes and supertypes are related. This paper takes the position that the relationship should ensure that any property proved about supertype objects also holds for its subtype objects. It presents two ways of defining the subtype relation, each of which meets this criterion, and each of which
The Subtype Relation  A Practical Overview
, 1994
"... The subtype relation plays an important role in the Object Oriented Paradigm. Although its informal definition is straightforward and clearly suggests its design applications, people seem not to fully understand its use. With this paper we do not intend to reevaluate the definition but, taking a pr ..."
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The subtype relation plays an important role in the Object Oriented Paradigm. Although its informal definition is straightforward and clearly suggests its design applications, people seem not to fully understand its use. With this paper we do not intend to reevaluate the definition but, taking a
Behavioural Subtyping Relations for ObjectOriented Formalisms
 AMAST 2000: International Conference on Algebraic Methodology And Software Technology
, 2000
"... . In this paper we investigate the objectoriented notion of subtyping in the context of behavioural formalisms. Subtyping in OOformalisms is closely related to the concept of inheritance. The central issue in the choice of subtyping relations among classes is the principle of substitutability: ..."
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Cited by 25 (8 self)
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. In this paper we investigate the objectoriented notion of subtyping in the context of behavioural formalisms. Subtyping in OOformalisms is closely related to the concept of inheritance. The central issue in the choice of subtyping relations among classes is the principle of substitutability
Subtyping recursive types
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1993
"... We investigate the interactions of subtyping and recursive types, in a simply typed λcalculus. The two fundamental questions here are whether two (recursive) types are in the subtype relation, and whether a term has a type. To address the first question, we relate various definitions of type equiva ..."
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Cited by 319 (9 self)
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We investigate the interactions of subtyping and recursive types, in a simply typed λcalculus. The two fundamental questions here are whether two (recursive) types are in the subtype relation, and whether a term has a type. To address the first question, we relate various definitions of type
Practical Verification of Component Substitutability Using Subtype Relation
"... The flexibility which components provide for assembling applications makes them an appealing solution to many engineering problems. Its darker side is the need to exercise much greater care when replacing and upgrading components within deployed applications, to ensure their stability. Formally stro ..."
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Cited by 4 (1 self)
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strong methods for substitutability checks are therefore desirable but so far, not many are practically used. This paper presents a method of checking component substitutability based on subtyping relation. It uses a representation of the subtype evaluation on different levels of the component type
On SubtypingRelation Completeness, with an Application to IsoRecursive Types
"... Wellknown techniques exist for proving the soundness of subtyping relations with respect to type safety. However, completeness has not been treated with widely applicable techniques, as far as we’re aware. This paper develops some techniques for stating and proving that a subtyping relation is comp ..."
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Wellknown techniques exist for proving the soundness of subtyping relations with respect to type safety. However, completeness has not been treated with widely applicable techniques, as far as we’re aware. This paper develops some techniques for stating and proving that a subtyping relation
Flexible Subtyping Relations for ComponentOriented Formalisms
, 2002
"... this paper is that of substitutability: given a system containing a component A,wewantto able to tell if we can "safely" replace component A by a new component B. By "safely", we mean that weneedto preserve some set of properties for the new resulting system. So wetackle the pro ..."
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the problem by first modelling the system and its components with a component/objectoriented language, and then by checking whether component B ' model satisfies some set of properties ("type") we might be interested in. For this, we may define an appropriate notion of subtyping by saying
A Decision Procedure for the Subtype Relation on Intersection Types with Bounded Variables
, 1989
"... We introduce an extension of the intersection type discipline in which types may contain variables with upper and lower bounds, present an algorithm for deciding the subtype relation in the extended system, and prove that the algorithm is correct. This work was supported in part by the Office of Nav ..."
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Cited by 6 (3 self)
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We introduce an extension of the intersection type discipline in which types may contain variables with upper and lower bounds, present an algorithm for deciding the subtype relation in the extended system, and prove that the algorithm is correct. This work was supported in part by the Office
A Pragmatic Behavior Subtyping Relation Based on Both States and Actions
, 2000
"... Abstract. A behavior preserving relation between Petrinet systems is introduced in this paper, basing on the observability of both places and transitions, which is important in modeling the dynamic behavior of concurrent objectoriented systems with Petri nets. Each group of closely related attribu ..."
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and to dispel the interference among groups, thus relieving the problem of inheritance anomaly by the possibility of dividing the synchronization code into independent parts. For a formal definition of this behavior subtyping relation, Elementary Net systems, with both Selements and Telements labeled
A Calculus for Overload Functions with Subtyping

, 1992
"... We present a simple extension of typed calculus where functions can be overloaded by putting different "branches of code" together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The cru ..."
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Cited by 146 (24 self)
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. The crucial feature of the present approach is that the branch selection depends on the "runtime type" of the argument, which may differ from its compiletime type, because of the existence of a subtyping relation among types. Hence overloading cannot be eliminated by a static analysis of code
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