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19
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
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Cited by 26 (5 self)
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this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
Objects and classes in Algollike languages
 Information and Computation
, 2002
"... Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and ..."
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Cited by 22 (5 self)
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Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and classes. An important idea that comes to light is that classes are abstract data types, whose theory corresponds to that of existential types. Equational and Hoarelike reasoning methods, and relational parametricity provide powerful formal tools for reasoning about Algollike objectoriented programs. 1
A Unifying Approach to Dataindependence
, 2000
"... A concurrent system is dataindependent with respect to a data type when the only operation it can perform on values of that type is equality testing. The system can also assign, input, nondeterministically choose, and output such values. Based on this intuitive definition, syntactic restrictions wh ..."
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Cited by 20 (7 self)
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A concurrent system is dataindependent with respect to a data type when the only operation it can perform on values of that type is equality testing. The system can also assign, input, nondeterministically choose, and output such values. Based on this intuitive definition, syntactic restrictions which ensure dataindependence have been formulated for a variety of different formalisms. However, it is difficult to see how these are related. We present the first semantic definition of dataindependence which allows equality testing, and its extension which allows constant symbols and predicate symbols. Both are special cases of a definition of when a family of labelled transition systems is parametric. This provides a unified approach to dataindependence and its extensions. The paper also contains two theorems which, given a system and a specification which are dataindependent, enable the verification for all instantiations of the data types (and of the constant symbols and the predicate symbols, in the case of the extension) to be reduced to the verification for a finite number of finite instantiations. We illustrate the applicability of the approach to particular formalisms by a programming language similar to UNITY.
Enriched Lawvere Theories
"... We define the notion of enriched Lawvere theory, for enrichment over a monoidal biclosed category V that is locally finitely presentable as a closed category. We prove that the category of enriched Lawvere theories is equivalent to the category of finitary monads on V. Morever, the Vcategory of mod ..."
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Cited by 16 (0 self)
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We define the notion of enriched Lawvere theory, for enrichment over a monoidal biclosed category V that is locally finitely presentable as a closed category. We prove that the category of enriched Lawvere theories is equivalent to the category of finitary monads on V. Morever, the Vcategory of models of a Lawvere Vtheory is equivalent to the Vcategory of algebras for the corresponding Vmonad. This all extends routinely to local presentability with respect to any regular cardinal. We finally consider the special case where V is Cat, and explain how the correspondence extends to pseudo maps of algebras.
Constructive Data Refinement in Typed Lambda Calculus
, 2000
"... . A new treatment of data refinement in typed lambda calculus is proposed, based on prelogical relations [HS99] rather than logical relations as in [Ten94], and incorporating a constructive element. Constructive data refinement is shown to have desirable properties, and a substantial example of ..."
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. A new treatment of data refinement in typed lambda calculus is proposed, based on prelogical relations [HS99] rather than logical relations as in [Ten94], and incorporating a constructive element. Constructive data refinement is shown to have desirable properties, and a substantial example of refinement is presented. 1 Introduction Various treatments of data refinement in the context of typed lambda calculus, beginning with Tennent's in [Ten94], have used logical relations to formalize the intuitive notion of refinement. This work has its roots in [Hoa72], which proposes that the correctness of a concrete version of an abstract program be verified using an invariant on the domain of concrete values together with a function mapping concrete values (that satisfy the invariant) to abstract values. In algebraic terms, what is required is a homomorphism from a subalgebra of the concrete algebra to the abstract algebra. A strictly more general method is to take a homomorphic relatio...
Specification Refinement with System F
 In Proc. CSL'99, volume 1683 of LNCS
, 1999
"... . Essential concepts of algebraic specification refinement are translated into a typetheoretic setting involving System F and Reynolds' relational parametricity assertion as expressed in Plotkin and Abadi's logic for parametric polymorphism. At first order, the typetheoretic setting ..."
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Cited by 6 (3 self)
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. Essential concepts of algebraic specification refinement are translated into a typetheoretic setting involving System F and Reynolds' relational parametricity assertion as expressed in Plotkin and Abadi's logic for parametric polymorphism. At first order, the typetheoretic setting provides a canonical picture of algebraic specification refinement. At higher order, the typetheoretic setting allows future generalisation of the principles of algebraic specification refinement to higher order and polymorphism. We show the equivalence of the acquired typetheoretic notion of specification refinement with that from algebraic specification. To do this, a generic algebraicspecification strategy for behavioural refinement proofs is mirrored in the typetheoretic setting. 1 Introduction This paper aims to express in type theory certain essential concepts of algebraic specification refinement. The benefit to algebraic specification is that inherently firstorder concepts are tra...
A Theory of Program Refinement
, 1998
"... We give a canonical program refinement calculus based on the lambda calculus and classical firstorder predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is t ..."
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Cited by 6 (1 self)
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We give a canonical program refinement calculus based on the lambda calculus and classical firstorder predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is that it should be possible to induce a refinement calculus in a generic manner from a programming language and a program logic. For concreteness, we adopt the simplytyped lambda calculus augmented with primitive recursion as a paradigmatic typed functional programming language, and use classical firstorder logic as a simple program logic. A key feature is the construction of the refinement calculus in a modular fashion, as the combination of two orthogonal extensions to the underlying programming language (in this case, the simplytyped lambda calculus). The crucial observation is that a refinement calculus is given by extending a programming language to allow indeterminate expressions (or ‘stubs’) involving the construction ‘some program x such that P ’. Factoring this into ‘some x...’
Logical Relations and Data Abstraction
 Proc. Computer Science Logic, CSL 2000, Fischbachau. Springer LNCS 1862
, 1996
"... We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suita ..."
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Cited by 4 (1 self)
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We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suitable logical relation. This allows us to introduce new types and operations of any order on those types, and to impose equations between terms of any order. Implementations are required to respect these equations up to a general form of contextual equivalence, and two implementations are equivalent if they produce the same contextual equivalence on terms of the enlarged language. Logical relations are introduced abstractly, soundness is almost automatic, but completeness is more difficult, achieved using a variant of Jung and Tiuryn's logical relations of varying arity. The results are expressed and proved categorically.
A higherorder simulation relation for System F
 Proc. 3rd Intl. Conf. on Foundations of Software Science and Computation Structures. ETAPS 2000
, 2000
"... The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. Thi ..."
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The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. This paper generalises this notion to abstract data types whose signatures contain higherorder and polymorphic functions. At higher order, the tight connection in the logic between the existence of a simulation relation and observational equivalence ostensibly breaks down. We show that an alternative notion of simulation relation is suitable. This also gives a simulation relation in the logic that composes at higher order, thus giving a syntactic logical counterpart to recent advances on the semantic level.
Axiomatics for Data Refinement in Call By Value Programming Languages
"... We give a systematic category theoretic axiomatics for modelling data refinement in call by value programming languages. Our leading examples of call by value languages are extensions of the computational calculus, such as FPC and languages for modelling nondeterminism, and extensions of the first ..."
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We give a systematic category theoretic axiomatics for modelling data refinement in call by value programming languages. Our leading examples of call by value languages are extensions of the computational calculus, such as FPC and languages for modelling nondeterminism, and extensions of the first order fragment of the computational calculus, such as a CPS language. We give a category theoretic account of the basic setting, then show how to model contexts, then arbitrary type and term constructors, then signatures, and finally data refinement. This extends and clarifies Kinoshita and Power's work on lax logical relations for call by value languages.