A complete algebraic characterization of behavioral subtyping

Information and Computation/information and Control, 2003

Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F ! , a variant of F ! <: with this feature and with Cardelli and Wegner's kernel Fun rule for quanti ers. We de ne a typed operational semantics with subtyping and prove that it is equivalent with F ! , using logical relations to prove soundness. The typed operational semantics provides a powerful and uniform technique to study metatheoretic properties of F ! , such as Church{Rosser, subject reduction, the admissibility of structural rules, the equivalence with the algorithmic presentation of the system that performs weak-head reductions.

Electronic Notes in Theoretical Computer Science, 1998

In a previous paper we h a ve de ned a semantic preorder called operational subsumption, which compares terms according to their error generation behaviour. Here we apply this abstract framework to a concrete language, namely the Abadi-Cardelli object calculus. Unlike most semantic studies of objects, which deal with typed equalities and therefore require explicitly typed languages, we start here from a untyped world. Type inference is introduced in a second step, together with an ideal model of types and subtyping. We s h o w h o w this approach exibly accommodates for several variants, and nally propose a novel semantic interpretation of structural subtyping as embedding-projection pairs.

Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP '14, 2014

Subtyping in concurrency has been extensively studied since early 1990s as one of the most interesting issues in type theory. The correctness of subtyping relations has been usually provided as the soundness for type safety. The converse direction, the completeness, has been largely ignored in spite of its usefulness to define the greatest subtyping relation ensuring type safety. This paper formalises preciseness (i.e. both soundness and completeness) of subtyping for mobile processes and studies it for the synchronous and the asynchronous session calculi. We first prove that the well-known session subtyping, the branching-selection subtyping, is sound and complete for the synchronous calculus. Next we show that in the asynchronous calculus, this subtyping is incomplete for type-safety: that is, there exist session types T and S such that T can safely be considered as a subtype of S, but T S is not derivable by the subtyping. We then propose an asynchronous subtyping system which is sound and complete for the asynchronous calculus. The method gives a general guidance to design rigorous channel-based subtypings respecting desired safety properties.

arXiv (Cornell University), 2010

This paper presents a critical discussion of popular approaches to ensure the Liskov substitution principle in class hierarchies (e.g. Design by Contract™, specification inheritance). It will be shown that they have some deficiencies which are due to the way how effective constraints are calculated for subclass methods. A new mechanism, called client conformance, is introduced that takes the client's view on the program state into account more properly: The client's static type determines the context in which reasoning about program state is to be done. This is the context to which the runtime assertion checking (RAC) of server methods must be adapted appropriately. In a stepwise argumentation we show the improvements for RAC that can be reached following this approach in a natural way, preserving the percolation pattern mechanism: Clients will neither be confronted with unsafe or surprising executions, nor with surprising failures of server methods.

1992

Abstract We relate standard techniques for solving recursive domain equations to previous models with types interpreted as partial equivalence relations(per's) over a Dm lambda model. This motivates a particular choice of type functions, which leads to an extension of, such models to higher-order polymorphism. The resulting models provide natural interpretations for function spaces, records, recursively defined types, higher-order type functions, and bounded polymorphic types YX<: Y.

Information and Computation, 2013

Coercive subtyping is a useful and powerful framework of subtyping for type theories. The key idea of coercive subtyping is subtyping as abbreviation. In this paper, we give a new and adequate formulation of T [C], the system that extends a type theory T with coercive subtyping based on a set C of basic subtyping judgements, and show that coercive subtyping is a conservative extension and, in a more general sense, a definitional extension. We introduce an intermediate system, the star-calculus T [C] * , in which the positions that require coercion insertions are marked, and show that T [C] * is a conservative extension of T and that T [C] * is equivalent to T [C]. This makes clear what we mean by coercive subtyping being a conservative extension, on the one hand, and amends a technical problem that has led to a gap in the earlier conservativity proof, on the other. We also compare coercive subtyping with the 'ordinary' notion of subtyping-subsumptive subtyping, and show that the former is adequate for type theories with canonical objects while the latter is not. An improved implementation of coercive subtyping is done in the proof assistant Plastic.

) 1 Introduction Mitchell [Mit84][Mit91], Fuh and Mishra [FM89][FM88] studied the foundation of the now standard monomorphic subtyping. More recently, Kaes [Kae92] Smith [Smi93], Eifrig and al [EST] and Henglein [Hen96] generalized the previous type systems to polymorphic types. However, all those presentations are based on a syntactic framework. This does not mean that semantic properties of polymorphic subtyping have not been studied, but that the syntactical aspect of the type discipline plays the main role. In this paper, we study the construction of polymorphic subtyping systems from a semantic point of view rather than the syntactical one. More precisely, the construction uses abstract interpretation to derive a polymorphic subtyping system from the dynamic semantics of the language. In this framework, we identify the principal type with the greatest fixpoint of an equational system. With respect to this definition the notion of strong instance as introduced by Fuh and Mishra ...

2002

Types for proofs and programs, 1998

Coercive subtyping, as first introduced in [Luo96], offers a conceptually simple but powerful framework to understand subtyping and subset relationships in type theories with sophisticated type structures such as dependent types, induc-tive types, and type universes. A basic idea behind ...

Springer eBooks, 2016

The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in object-oriented programming languages. The soundness and the completeness, together referred to as the preciseness of subtyping, can be considered from two different points of view: denotational and operational. The former preciseness is based on the denotation of a type, which is a mathematical object describing the meaning of the type in accordance with the denotations of other expressions from the language. The latter preciseness has been recently developed with respect to type safety, i.e. the safe replacement of a term of a smaller type when a term of a bigger type is expected. The present paper shows that standard proofs of operational preciseness imply denotational preciseness and gives an overview on this subject.