## Global Development via Local Observational Construction Steps (2002)

### Cached

### Download Links

- [www.lsv.ens-cachan.fr]
- [ftp.dcs.ed.ac.uk]
- [www.dcs.ed.ac.uk]
- [homepages.inf.ed.ac.uk]
- DBLP

### Other Repositories/Bibliography

Citations: | 8 - 5 self |

### BibTeX

@MISC{Bidoit02globaldevelopment,

author = {Michel Bidoit and Donald Sannella and Andrzej Tarlecki},

title = {Global Development via Local Observational Construction Steps},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

The way that refinement of individual "local" components of a specification relates to development of a "global" system from a specification of requirements is explored. Observational interpretation of specifications and refinements add expressive power and flexibility while bringing in some subtle problems. The results are instantiated in the context of Casl architectural specifications.

### Citations

477 |
Institutions: Abstract model theory for specification and programming
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...ed as desired to cope with various programming features of interest by selecting the appropriate variation of algebra and signature. This flexibility has been formalized via the notion of institution =-=[GB92]-=- and related work on the theory of specifications and formal program development [ST88a,ST97,BH93]. However, rather than exploiting the full generality of institutions, to keep things simple and illus... |

412 |
Proof of correctness of data representations
- Hoare
- 1972
(Show Context)
Citation Context ...nswer has already been provided, the main references being Schoett's thesis [Sch87,Sch90] and our work on formal development in the Extended ML framework [ST89]; the general ideas go back at least to =-=[Hoa72]-=-. # This work has been partially supported by KBN grant 7T11C 002 21 and European AGILE project IST-2001-32747 (AT), CNRS--PAS Research Cooperation Programme (MB, AT), and British--Polish Research Par... |

194 |
An algebraic definition of simulation between programs
- Milner
- 1971
(Show Context)
Citation Context ...d b1 # |B|s 1 , . . . , bn # |B|sn , if (a1 , b1 ) # #s 1 , . . . , (an , bn ) # #sn then (fA(a1 , . . . , an), fB (b1 , . . . , bn)) # #s . 9 This formulation is due to [Sch87] (cf. "simulations=-=" in [Mil71] and "-=-;weak homomorphisms " in [Gin68]) and is equivalent to other standard ways of defining observational equivalence between algebras, where a special role is played by observable equalities, i.e., e... |

142 | Toward formal development of programs from algebraic specifications: Parameterisation revisited - Sannella, Sokolowski, et al. - 1992 |

121 |
Parameterized Programming
- Goguen
- 1983
(Show Context)
Citation Context ...# SP 2 #3 ### > #n ### >. SP n = EMPTY where for i = 1, . . . , n, the specifications SP i now describe the part of the system that remains to be implemented, while each # i is a parametrized program =-=[Gog84]-=- which semantically amounts to a (possibly partial) function on algebrass# i : |Alg(Sig(SP i ))| # |Alg(Sig(SP i-1 ))| which we will call a construction. Now, given specifications SP and SP # and a co... |

92 | Specifications in an arbitrary institution
- D, Tarlecki
- 1988
(Show Context)
Citation Context ...sic specifications, given by a signature and a set of axioms (sentences) over this signature; or structured specifications built over the institution we have implicitly introduced above as defined in =-=[ST88a]-=-; or structured specifications built using more advanced structuring mechanisms such as those of Casl [ABK + 03]. 3 Program Development and Refinements In this section we briefly recapitulate our view... |

67 | Universal Realization, Persistent Interconnection and Implementation of Abstract Modules - Goguen, Meseguer |

66 | On observational equivalence and algebraic specification - Sannella, Tarlecki - 1987 |

55 | Essential Concepts of Algebraic Specification and Program Development
- Sannella, Tarlecki
- 1997
(Show Context)
Citation Context ...a specification formalism and the ease of reasoning about specifications. Di#erent approaches give more or less prominence to di#erent issues. An overview that covers most of our own contributions is =-=[ST97]-=-, with some more recent work addressing the problem of how to prove correctness of refinement steps [BH98], the design of a convenient formalism for writing specifications [ABK + 03,BST02], and applic... |

53 | CASL: The Common Algebraic Specification Language - Astesiano, Bidoit, et al. - 2001 |

51 | Toward formal development of ML programs: Foundations and methodology
- Sannella, Tarlecki
- 1989
(Show Context)
Citation Context ...finements is taken into account. Part of the answer has already been provided, the main references being Schoett's thesis [Sch87,Sch90] and our work on formal development in the Extended ML framework =-=[ST89]-=-; the general ideas go back at least to [Hoa72]. # This work has been partially supported by KBN grant 7T11C 002 21 and European AGILE project IST-2001-32747 (AT), CNRS--PAS Research Cooperation Progr... |

48 |
Algebraic Theory of Automata
- Ginzburg
- 1969
(Show Context)
Citation Context ...if (a1 , b1 ) # #s 1 , . . . , (an , bn ) # #sn then (fA(a1 , . . . , an), fB (b1 , . . . , bn)) # #s . 9 This formulation is due to [Sch87] (cf. "simulations" in [Mil71] and "weak homo=-=morphisms " in [Gin68]-=-) and is equivalent to other standard ways of defining observational equivalence between algebras, where a special role is played by observable equalities, i.e., equalities between terms of observable... |

42 |
Data Abstraction and the Correctness of Modular Programming
- Schoett
- 1987
(Show Context)
Citation Context ...|A|s 1 , . . . , an # |A|sn and b1 # |B|s 1 , . . . , bn # |B|sn , if (a1 , b1 ) # #s 1 , . . . , (an , bn ) # #sn then (fA(a1 , . . . , an), fB (b1 , . . . , bn)) # #s . 9 This formulation is due to =-=[Sch87] (cf. "simulati-=-ons" in [Mil71] and "weak homomorphisms " in [Gin68]) and is equivalent to other standard ways of defining observational equivalence between algebras, where a special role is played by ... |

38 | Behavioural equivalence – a unifying concept for initial and final specifications - Reichel - 1981 |

36 | Algebraic implementation of abstract data types - Ehrig, Kreowski, et al. - 1982 |

36 |
Fundamentals of algebraic specification: Equational and initial semantics
- Ehrig, Mahr
- 1985
(Show Context)
Citation Context ...orphism " using signature pushout and amalgamation is well established in the algebraic specification tradition, going back at least to "parametrized specifications " with free functor =-=semantics, see [EM85]-=-. We will not dwell here on how particular (local) constructions are defined. Free functor semantics for parametrized specifications is one way to proceed, with the persistency requirement giving rise... |

32 | Behavioural correctness of data representations - Schoett - 1985 |

30 | Modular correctness proofs of behavioural implementations
- Bidoit, Hennicker
- 1998
(Show Context)
Citation Context ... less prominence to di#erent issues. An overview that covers most of our own contributions is [ST97], with some more recent work addressing the problem of how to prove correctness of refinement steps =-=[BH98], the desi-=-gn of a convenient formalism for writing specifications [ABK + 03,BST02], and applications to data refinement in typed #-calculus [HLST00]. A new angle that we explore here is the "global" e... |

30 | Andrzej Tarlecki, Behavioural satisfaction and equivalence in concrete model categories
- Bidoit
- 1996
(Show Context)
Citation Context ...s, like Thm. 4.3, which in turn may require a richer context of concrete institutions, with model categories equipped with concretization structure subject to a number of technical requirements as in =-=[BT96]-=-). On the other hand, to transfer the present work to the specific framework of Casl we need a precise and convincing definition of observational equivalence between Casl models (many-sorted algebras ... |

29 | Observability concepts in abstract data type specification - GIARRATANA, F, et al. - 1976 |

19 |
Algebraic preliminaries
- Sannella, Tarlecki
(Show Context)
Citation Context ...erpretationof the Boolean part of the signature.As usual, each signature morphism σ: Σ → Σ ′ determines a reduct functor σ: Alg(Σ ′ ) → Alg(Σ). This yields a functor Alg: AlgSig op → Cat. We refer to =-=[ST99]-=- for a more detailed presentation of the technicalities and for the standard notations we will use in the following. It can easilybe checked that Alg is continuous, i.e., maps colimits of algebraic si... |

14 | Parameterized specifications: parameter passing and implementation with respect to observability - Ganzinger |

13 | A general framework for modular implementations of modular systems - Bidoit, Hennicker - 1993 |

13 |
Behavioural and abstractor specifications. Science of Computer Programming 25:149–186
- Bidoit, Hennicker, et al.
- 1995
(Show Context)
Citation Context ...d (SP G ) # Abs # (#(SP )). This weaker condition turns out to be su#cient (and in fact, equivalent to (i)) if we additionally assume that the two specifications involved are behaviourally consistent =-=[BHW95]-=-, that is, closed under observational quotients. When this is not the case, then the use of this weaker condition must be paid for by a stronger version of (ii): Abs # (# # (SP # )) # Mod (# # (SP G )... |

12 | Constructive data refinement in typed lambda calculus
- Honsell, Longley, et al.
- 2000
(Show Context)
Citation Context ...oblem of how to prove correctness of refinement steps [BH98], the design of a convenient formalism for writing specifications [ABK + 03,BST02], and applications to data refinement in typed #-calculus =-=[HLST00]. A new angle that w-=-e explore here is the "global" e#ect of refining individual "local" components of a specification. This involves a well-known technique from algebraic specification, namely the use... |

12 | Checking Amalgamability Conditions for CASL Architectural Specifications - Klin, Hoffman, et al. - 2001 |

11 |
Refinement and implementation
- Ehrig, Kreowski
- 1999
(Show Context)
Citation Context ...braic specification tradition on formalizing the rather intuitive and appealing idea of program development by stepwise refinement, including [EKMP82,Gan83,GM82,Sch87,ST88b]; for a recent survey, see =-=[EK99]-=-). There are many issues that make this a di#cult problem, and some of them are rather subtle, one example being the relationship between specification structure and program structure. There are di#cu... |

11 | An algebraic de of simulation between programs - Milner - 1971 |

10 |
A.: Architectural specifications in Casl. Formal Aspects of Computing 13
- Bidoit, Sannella, et al.
- 2002
(Show Context)
Citation Context ...Research Partnership Programme (DS, AT). 2 We have another look at these issues here, in the context of the Casl specification formalism [ABK + 03] and in particular, its architectural specifications =-=[BST02]-=-. Architectural specifications, for describing the modular structure of software systems, are probably the most novel feature of Casl. We view them here as a means of making complex refinement steps, ... |

9 |
Structured theories
- Sannella, Burstall
- 1983
(Show Context)
Citation Context ...A[v] of such a conditional term p is (t k ) A[v] for the least k # 0 such that A[v] |= # k , or t A[v] if no such k # 0 exists. This allows for a further generalization of derived signature morphisms =-=[SB83]-=-, where we allow such a morphism #: # # # # to map function symbols f : s 1 . . . sn # s to conditional terms of sort s with variables {x 1 : s 1 , . . . , xn : s n }. Evidently, such a derived signat... |

9 | Speci in an arbitrary institution - Sannella, Tarlecki - 1988 |

8 | Semantics of architectural specifications in Casl - Schröder, Mossakowski, et al. - 2001 |

5 | Essential Concepts of Algebraic Speci and Program Development. Formal Aspects of Computing 9:229-269 - Sannella, Tarlecki - 1997 |

4 |
are those preserving philosophy
- functors
- 1987
(Show Context)
Citation Context ...le observationally correct constructions, even if there are strictly correct ones: that is, we may have Mod lc (SP # -#SP # ) = # even if Mod(SP # -#SP # ) #= #. This was perhaps first pointed out in =-=[Ber87]-=-, in a di#erent framework. Counterexample 5.8. Let SP 1 include a non-observable sort s with two constants a, b: s, and let SP 2 enrich SP 1 by an observable sort o, two constants c, d: o and axiom c ... |

4 |
Verifying architectural specifications. Recent Trends
- Hoffman
- 2001
(Show Context)
Citation Context ...T + 01]; a generalization of the work presented here to full architectural specifications of Casl would be tedious but rather straightforward, except perhaps for the “unguarded import” mechanism, see =-=[Hof01]-=-. Our version of architectural specifications is defined as follows. Architectural specifications: ASP ::= arch spec Dcl ∗ result T An architectural specification consists of a list of unit declaratio... |

4 | Behavioural and abstractor speci cations - Bidoit, Hennicker, et al. - 1995 |

4 | On observational equivalence and algebraic speci - Sannella, Tarlecki - 1987 |

2 | Casl: the common algebraic speci cation language, Theoret - Astesiano, Bidoit, et al. - 2002 |

2 | Fundamentals of Algebraic Speci I: Equations and Initial Semantics - Ehrig, Mahr - 1985 |

1 |
Verifying architectural specifications. Recent Trends
- Homan
- 2001
(Show Context)
Citation Context ...T + 01]; a generalization of the work presented here to full architectural specifications of Casl would be tedious but rather straightforward, except perhaps for the "unguarded import" mecha=-=nism, see [Hof01]-=-. Our version of architectural specifications is defined as follows. Architectural specifications: ASP ::= arch spec Dcl # result T An architectural specification consists of a list of unit declaratio... |

1 |
Algebraic preliminaries. In: [AKBK99], 13-30. [SMT + 01
- Sannella, Tarlecki
- 2001
(Show Context)
Citation Context ...retation of the Boolean part of the signature. As usual, each signature morphism #: # # # # determines a reduct functor # : Alg(# # ) # Alg(#). This yields a functor Alg: AlgSig op # Cat. We refer to =-=[ST99]-=- for a more detailed presentation of the technicalities and for the standard notations we will use in the following. It can easily be checked that Alg is continuous, i.e., maps colimits of algebraic s... |

1 |
functors . ..are those preserving philosophy
- Good
- 1987
(Show Context)
Citation Context ...o stable observationally correct constructions, even if there are strictly correct ones: that is, we may have Modlc(SP ι −→SP ′ )=∅even if Mod(SP ι −→SP ′ ) �= ∅.This was perhaps first pointed out in =-=[Ber87]-=-, in a different framework. Counterexample 5.8. Let SP 1 include a non-observable sort s with two constants a, b: s,andletSP2 enrich SP 1 by an observable sort o,twoconstantsc, d: o and axiom c �= d ⇐... |

1 | Architectural speci in Casl. Formal Aspects of Computing, to appear (2002). Available at http://www.lsv.ens-cachan.fr/Publis/PAPERS/BST-FAC2002. ps. Extended abstract - Bidoit, Sannella, et al. - 1999 |

1 | Parameterized speci parameter passing and implementation with respect to observability - Ganzinger - 1983 |

1 | Verifying architectural speci Recent Trends - Homan - 2001 |

1 | Constructive data re in typed lambda calculus - Honsell, Longley, et al. - 2000 |