Results 1  10
of
11
Observational logic
 In Algebraic Methodology and Software Technology (AMAST'98
, 1999
"... Abstract. We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are r ..."
Abstract

Cited by 53 (10 self)
 Add to MetaCart
Abstract. We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required to be compatible with the indistinguishability relation determined by the given observers. In particular, we introduce a homomorphism concept for observational algebras which adequately expresses observational relationships between algebras. Then we consider a flexible notion of observational signature morphism which guarantees the satisfaction condition of institutions w.r.t. observational satisfaction of arbitrary firstorder sentences. From the proof theoretical point of view we construct a sound and complete proof system for the observational consequence relation. Then we consider structured observational specifications and we provide a sound and complete proof system for such specifications by using a general, institutionindependent result of [6]. 1
Observer Complete Definitions are Behaviourally Coherent
 OBJ/CAFEOBJ/MAUDE AT FORMAL METHODS '99
, 1999
"... We consider observational specifications of statebased systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the nono ..."
Abstract

Cited by 34 (5 self)
 Add to MetaCart
We consider observational specifications of statebased systems which incorporate the declaration of a distinguished set of observer operations. These observers determine an indistinguishability relation for states which is called "observational equality". An important requirement for the nonobserver operations is the compatibility with the observational equality. In the CafeOBJ language (and in extended hidden algebra) this property is called "behavioural coherence". In this presentation we introduce the notion of an "observer complete definition" and we show that any (nonobserver) operation which is defined using this pattern is behaviourally coherent. We also discuss some consequences of this result for relating observational logic and extended hidden algebra semantics and for proving the correctness of observational implementations.
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 provides a ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
. 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...
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 3 (3 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. This pap ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
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.
Proof Systems for Structured Algebraic Specifications: An Overview
, 1997
"... . In this paper an overview on proof systems for structured algebraic specifications is presented. As underlying language we choose an ASLlike kernel language which includes reachability and observability operators. Three different kinds of proof systems are studied. The first two approaches are no ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
. In this paper an overview on proof systems for structured algebraic specifications is presented. As underlying language we choose an ASLlike kernel language which includes reachability and observability operators. Three different kinds of proof systems are studied. The first two approaches are noncompositional systems where the basic idea is to compute for any structured specification a flat unstructured set of axioms and rules which, combined with some standard proof systems for the underlying logic, may be used for deriving theorems of the specification. In the normal form approach of Bergstra, Hering and Klint, a flat set of axioms is constructed for each structured specification, whereas in the second approach not only individual axioms but also individual proof rules are taken into account. The drawback of the noncompositional proof systems is that they do not reflect the modular structure of specifications. Therefore we present also a structured proof system the derivations ...
Behavioural reasoning for conditional equations
 MATH. STRUCT. IN COMP. SCIENCE. IN PRINT (DOI: 10.1017/S0960129507006305
, 2007
"... The behavioral equivalence of hidden terms in an equational specification logic is not itself specifiable in general (Buss and Ro¸su 2000). But much recent work has been done on its partial specification, in particular using coinduction. In this paper we consider the more general notion of condition ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The behavioral equivalence of hidden terms in an equational specification logic is not itself specifiable in general (Buss and Ro¸su 2000). But much recent work has been done on its partial specification, in particular using coinduction. In this paper we consider the more general notion of conditional behavioral equivalence introduced by Reichel in 1984. We investigate the behavioral proof theory of a general class of equational specification logics, the hidden equational logics. Among other things we characterize the behaviorally valid conditional equations of a hidden equational logic as those conditional equations which, in a natural sense, do not increase the deductive power of the logic when they are added as new rules of inference. For a special kind of hidden equational logic (the equivalential logics) we obtain methods for proving behavioral validity that work well in practice. Those hidden equational logics whose behavioral is specifiable by a (nonhidden) equational logic are characterized in terms of a special class of equivalential logics—equivalently as those hidden equational logics that have a cobasis (Ro¸su and Goguen 2001) of a special form.
Abstraction Barriers in Equational Proof
 In Proc. of AMAST'98, volume 1548 of LNCS
, 1998
"... ion Barriers in Equational Proof Jo Erskine Hannay LFCS, Division of Informatics, University of Edinburgh, Scotland joh@dcs.ed.ac.uk Abstract. Module constructs in programming languages have protection mechanisms hindering unauthorised external access to internal operators of data types. In some c ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
ion Barriers in Equational Proof Jo Erskine Hannay LFCS, Division of Informatics, University of Edinburgh, Scotland joh@dcs.ed.ac.uk Abstract. Module constructs in programming languages have protection mechanisms hindering unauthorised external access to internal operators of data types. In some cases, granting external access to internal operators would result in serious violation of a data type's specified external properties. In order to reason consistently about specifications of such data types, it is necessary in general to incorporate a notion of protective abstraction barrier in proof strategies as well. We show how this can be done in equational calculus by simply restricting the congruence axiom, and see how the motivation for this naturally arises from FI and FRI approaches to specification refinement. 1 Introduction Many programming languages have encapsulation mechanisms that hide internal detail of data types. Besides providing abstraction from uninteresting detail, th...
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
. 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...
Relative Equational Specification and Semantics
, 1997
"... Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modula ..."
Abstract
 Add to MetaCart
Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modular hierarchical approach to proof by consistency is taken by which only toplevel equations need be considered at any level. The formalism also allows nonhomogeneous specification schemes and different proof methods at each level.