## Observational Specifications and the Indistinguishability Assumption (1995)

Venue: | Theoretical Computer Science |

Citations: | 17 - 0 self |

### BibTeX

@ARTICLE{Bernot95observationalspecifications,

author = {Gilles Bernot and Michel Bidoit and Teodor Knapik},

title = {Observational Specifications and the Indistinguishability Assumption},

journal = {Theoretical Computer Science},

year = {1995},

volume = {139},

pages = {275--314}

}

### Years of Citing Articles

### OpenURL

### Abstract

To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the specification. A software is then declared correct if it corresponds to some algebra of this class. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. Based on this notion we provide an institution for observational specifications. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence. We define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. We assume th...

### Citations

487 |
Institutions: abstract model theory for speci and programming
- Goguen, Burstall
- 1990
(Show Context)
Citation Context ...lgebras which are of the form hA; =i where A is an algebra (in the usual sense) equipped with an equivalence relation =. We discuss the conditions which make our formalism provide an institution [8], =-=[9]-=-. A first obvious condition is to attach the observations to some institution component. Since the observations act on the semantics of a specification in the same way as the axioms, we believe that t... |

69 |
Universal realization, persistent interconnection and implementation of abstract modules
- Goguen, Meseguer
- 1982
(Show Context)
Citation Context ...ed by "") or not. Then the crucial point is to define the "" relation, according to the Indistinguishability Assumption. Obviously, such a relation does not coincide with "=&q=-=uot;. Unlike in [16], [17] or [10]-=- but similarly to [1] and [5] we want to consider more general observations than sort observation since sort observation does not provide the satisfactory expressive power (as shown in [2]). Unfortuna... |

47 |
Context induction: a proof principle for behavioural abstractions, in: A. Miola (Ed
- Hennicker
(Show Context)
Citation Context ... relation on the carriers of an algebra in order to relax the satisfaction relation. Usually this is done using the concept of observable contexts. Since this concept was only defined for sort ([10], =-=[12]-=-, [16]) or signature 1 ([1], [5]) observations, we should start by defining it in the situation when we observe an arbitrary set of terms. In the most usual framework one considers a set of observable... |

44 |
Final algebra semantics and data type extensions
- Wand
- 1979
(Show Context)
Citation Context ...o our Indistinguishability Assumption, we do not consider that two elements can either be indistinguishable, distinguishable or incomparable. Our point of view is close to final semantics ([3], [13], =-=[20]-=-): we consider indistinguishable these pairs of elements, for which we do not observe the contrary. This is stated in the undermentioned definition. For a while assume already defined the notion of ob... |

39 |
and Andrzej Tarlecki. Toward formal development of programs from algebraic specifications
- Sannella
- 1988
(Show Context)
Citation Context ...hould correspond to the correct realization of a specification SP, is usually defined in the following way: Beh[SP; Obs] = fB 2 Alg[Sig[SP]] j 9 A 2 Alg[SP]; A j Obs Bg (1:i) Based on this notion, in =-=[19]-=- Sannella and Tarlecki have developed an institution independent formalism. Even if very general, in our opinion, these approaches do not provide a satisfactory observational semantics. It turns out t... |

36 |
Behavioural validity of conditional equations in abstract data types, in: Contributions to General Algebra 3, Teubner
- Reichel
- 1985
(Show Context)
Citation Context ...in the loose framework (which is one of the topics of further research). Moreover, one might think that our indistinguishability relation would coincide with the Reichel's I-indistinguishability (see =-=[17]-=-) when we restrict our approach to sort observation and the Reichel's one to total algebras. This is not true, since we use multicontexts from MC \Sigma (A) instead of MC \Sigma . Consequently, in our... |

29 |
Initial behaviour semantics for algebraic speci
- Nivela, Orejas
- 1988
(Show Context)
Citation Context ...le (i.e. related by "") or not. Then the crucial point is to define the "" relation, according to the Indistinguishability Assumption. Obviously, such a relation does not coincide =-=with "=". Unlike in [16]-=-, [17] or [10] but similarly to [1] and [5] we want to consider more general observations than sort observation since sort observation does not provide the satisfactory expressive power (as shown in [... |

23 |
Final data types and their specification
- Kamin
- 1983
(Show Context)
Citation Context ...ding to our Indistinguishability Assumption, we do not consider that two elements can either be indistinguishable, distinguishable or incomparable. Our point of view is close to final semantics ([3], =-=[13]-=-, [20]): we consider indistinguishable these pairs of elements, for which we do not observe the contrary. This is stated in the undermentioned definition. For a while assume already defined the notion... |

21 |
Proving the correctness of algebraically specified software: Modularity and observability issues
- Bernot, Bidoit
- 1991
(Show Context)
Citation Context ... the crucial point is to define the "" relation, according to the Indistinguishability Assumption. Obviously, such a relation does not coincide with "=". Unlike in [16], [17] or [1=-=0] but similarly to [1]-=- and [5] we want to consider more general observations than sort observation since sort observation does not provide the satisfactory expressive power (as shown in [2]). Unfortunately, an indistinguis... |

21 |
Initial and final algebra semantics for data type specifications: two characterization theorems
- Bergstra, Tucker
- 1983
(Show Context)
Citation Context ...according to our Indistinguishability Assumption, we do not consider that two elements can either be indistinguishable, distinguishable or incomparable. Our point of view is close to final semantics (=-=[3]-=-, [13], [20]): we consider indistinguishable these pairs of elements, for which we do not observe the contrary. This is stated in the undermentioned definition. For a while assume already defined the ... |

14 |
The stratified loose approach: a generalization of initial and loose semantics
- Bidoit
- 1988
(Show Context)
Citation Context ...tics extends to an observational stratified loose semantics without additional assumptions. For instance, the next theorem shows that our approach fulfills the requirement of "reusing by restrict=-=ion" [4]-=-. Theorem 9.5 Let oe : \Sigma ! \Sigma 0 be a signature morphism. For all observational specifications OSP = h\Sigma; \Theta; Wi and OSP 0 = h\Sigma 0 ; \Theta 0 ; W 0 i such that oe(\Theta) ` \Theta ... |

12 |
Orejas, New concepts for amalgamation and extension in the framework of specification logics
- Baldamus, F
- 1993
(Show Context)
Citation Context ...phisms and these observations which preserve 10.2. Consequently our approach could motivate more liberal formalizations than institutions of the notion of "logical system" as e.g. specificat=-=ion logic [6]-=- or pre-institutions [18]. Since the satisfaction condition holds only for some signature morphisms, in order to define an institution in our framework, one could forget some problematic arrows of Sig... |

5 | Behavioural approaches to algebraic specifications: a comparative study - Bernot, Bidoit, et al. - 1994 |

3 |
Diepen N.W.P. Implementation of Modular Algebraic Specifications
- van
- 1988
(Show Context)
Citation Context ...cial point is to define the "" relation, according to the Indistinguishability Assumption. Obviously, such a relation does not coincide with "=". Unlike in [16], [17] or [10] but s=-=imilarly to [1] and [5]-=- we want to consider more general observations than sort observation since sort observation does not provide the satisfactory expressive power (as shown in [2]). Unfortunately, an indistinguishability... |

1 |
Observational Logic for Algebraic Specification: an Approach with Observational Satisfaction Relation and Formulae as Observations. Laboratoire de l'Informatique de l'Ecole Normale Sup'erieure
- Knapik
- 1992
(Show Context)
Citation Context ...n, while formula observation is the most powerful. The reason is that it is hard to define an indistinguishability relation w.r.t. formula or atom observation and requires a more elaborated framework =-=[14]-=-. In our opinion this is due to the fact that formula and atom observations have no direct meaning at the (imple2 menting) software level. On the contrary, observing some chosen terms may be viewed at... |

1 | Thatte S.R. Generalization of Final Algebra Semantics by Relativization - Moss |

1 |
A soft stairway to institutions, Talk at the 8
- Salibra, Scollo
- 1991
(Show Context)
Citation Context ... that a 0 6 oe(W) b 0 . 2 We can conclude from the above that in our approach, the satisfaction condition does not hold in general. Only the if part of Property 10.1 holds. Consequently, according to =-=[18]-=-, our approach defines a reduction-preserving pre-institution. The converse part of 10.1 holds only for these signature morphisms and these observations which preserve 10.2. Consequently our approach ... |