Results 1 
6 of
6
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 ..."
Abstract

Cited by 12 (7 self)
 Add to MetaCart
(Show Context)
. 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...
From Algebras and Coalgebras to Dialgebras
, 2001
"... This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras. ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras.
Behavioral institutions and refinements in generalized hidden logics
 J. Univers. Comput. Sci
, 2006
"... Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specifica ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden klogics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden klogic as well as the behavioral logic of a hidden klogic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement.
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 ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
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.
Specification Refinement with System F, The HigherOrder Case
, 2000
"... . A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setti ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
. A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setting immediately gives a natural notion of specification refinement up to observational equivalence via the notion of simulation relation. Moreover, a proof strategy for proving observational refinements formalised by Bidoit, Hennicker and Wirsing can be soundly imported into the type theory. In lifting these results to the higherorder case, we find it necessary firstly to develop an alternative simulation relation and secondly to extend the parametric PERmodel interpretation, both in such a way as to observe data type abstraction barriers more closely. 1 Introduction One framework in algebraic specification that has particular appeal and applicability is that of stepwise specification refi...
Semantic and Syntactic Approaches to Simulation Relations
, 2003
"... Simulation relations are tools for establishing the correctness of data refinement steps. In the simplytyped lambda calculus, logical relations are the standard choice for simulation relations, but they su#er from certain shortcomings; these are resolved by use of the weaker notion of prelogic ..."
Abstract
 Add to MetaCart
(Show Context)
Simulation relations are tools for establishing the correctness of data refinement steps. In the simplytyped lambda calculus, logical relations are the standard choice for simulation relations, but they su#er from certain shortcomings; these are resolved by use of the weaker notion of prelogical relations instead. Developed from a syntactic setting, abstraction barrierobserving simulation relations serve the same purpose, and also handle polymorphic operations. Meanwhile, secondorder prelogical relations directly generalise prelogical relations to polymorphic lambda calculus (System F). We compile the main refinementpertinent results of these various notions of simulation relation, and try to raise some issues for aiding their comparison and reconciliation.