## Semantics of architectural specifications in Casl (2001)

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Venue: | Proc. 4th Intl. Conf. Fundamental Approaches to Software Engineering FASE’01, Springer LNCS 2029 |

Citations: | 8 - 6 self |

### BibTeX

@INPROCEEDINGS{Schröder01semanticsof,

author = {Lutz Schröder and Till Mossakowski and Andrzej Tarlecki and Bartek Klin and Piotr Hoffman},

title = {Semantics of architectural specifications in Casl},

booktitle = {Proc. 4th Intl. Conf. Fundamental Approaches to Software Engineering FASE’01, Springer LNCS 2029},

year = {2001},

pages = {253--268},

publisher = {Springer}

}

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### Abstract

Abstract. We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with modeltheoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model functor has amalgamation, which makes it possible to express the amalgamability conditions in the semantic rules in static terms. Using these concepts, we develop the semantics at various levels in an institution-independent fashion.

### Citations

986 | Categories for the Working Mathematician - Lane - 1971 |

515 |
Institutions: Abstract model theory for specification and programming
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...three steps of the semantics are in fact independent of the details of the underlying Casl logical system: we present them in the framework of an arbitrary logical system formalized as an institution =-=[GB92]-=-. As a result, the factorization properties to which we reduce the amalgamation conditions are still relatively abstract. A calculus for checking these factorization properties in the case of the spec... |

383 |
ML for the Working Programmer
- Paulson
- 1996
(Show Context)
Citation Context ...lity conditions’ are typically expected to be at least partially discharged by some static analysis — similarly to the sharing requirements present in some programming languages (cf. e.g. Standard ML =-=[Pau96]-=-). Of course, the basic static analysis given here is not suited for this purpose, since no information is stored about dependencies between units. This will be taken care of in the second level of th... |

322 | LARCH: Languages and Tools for formal specification - GUTTAG, HORNING - 1993 |

266 |
Abstract and Concrete Categories
- Adámek, Herrlich, et al.
(Show Context)
Citation Context ...ly on the notion of institution [GB92]. An institution I consists of a category Sign of signatures, a model functor Mod : Sign op → CAT, where CAT denotes the quasicategory of categories and functors =-=[AHS90]-=-, and further components which formalize sentences and satisfaction. In this context, we need only the model functor. For a signature Σ, Mod(Σ) is referred to as the category of models for Σ, and for ... |

155 |
Fundamentals of Algebraic Specification 1: Equations and Initial Semantics
- Ehrig, Mahr
- 1985
(Show Context)
Citation Context ...components in the intersection of their signatures, they can be unambiguously put together to form a model of the union of their signatures. Many standard logical systems (like multisorted equational =-=[EM85]-=- and first-order logic [MT93] with the respective standard notions of model) admit amalgamation, so quite often this property is taken for granted in work on specification formalisms (cf. e.g. [ST88])... |

149 |
Putting theories together to make specifications
- BURSTALL, GOGUEN
- 1977
(Show Context)
Citation Context ...y algebraic specification languages (see e.g. [Wir86,EM85,GHG + 93,CoFI96,SW99]) is the provision of operations for building large specifications in a structured fashion from smaller and simpler ones =-=[BG77]-=-. For the quite different purpose of describing the modular structure of software systems under development [SST92], architectural specifications have been introduced as a comparatively novel feature ... |

145 | Toward formal development of programs from algebraic specifications: Implementations revisited
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ...r building large specifications in a structured fashion from smaller and simpler ones [BG77]. For the quite different purpose of describing the modular structure of software systems under development =-=[SST92]-=-, architectural specifications have been introduced as a comparatively novel feature in the algebraic specification language Casl recently developed by the CoFI group [CoF,CoF99a,Mos99]. The main idea... |

94 | Specifications in an arbitrary institution
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ... [EM85] and first-order logic [MT93] with the respective standard notions of model) admit amalgamation, so quite often this property is taken for granted in work on specification formalisms (cf. e.g. =-=[ST88]-=-). However, the expected amalgamation property fails to hold for the logical system underlying Casl. We develop a three-step semantics that circumvents this problem. The first step is a purely model-t... |

55 | Moving between logical systems
- Tarlecki
- 1996
(Show Context)
Citation Context ...stitution SubP CF OL, i.e. Mode ◦ Φ op and Mod are naturally isomorphic. One can build an institution around enrCASLsign and define an institution representation of SubP CF OL therein in the sense of =-=[Tar96]-=-. At any rate, we shall use terms like ‘amalgamable’ w.r.t. Mode. The details of the definitions and full proofs will be presented separately [SMT + ]; the basic concepts are outlined below. As sugges... |

51 |
Using category theory to design implicit conversions and generic operators
- Reynolds
- 1980
(Show Context)
Citation Context ...xample, the step from CASLsign to enrCASLsign chiefly consists in replacing the preorder on the sorts by a sort category (category sorted algebras, although without a view on amalgamation, go back to =-=[Rey80]-=-). The fact that all embeddings are actually interpreted as injective maps is reflected by the requirement that all morphisms in the sort category are monomorphisms. There is an elegant way to handle ... |

51 | Structured Algebraic specifications: A kernel language - Wirsing - 1983 |

41 | The Common Framework Initiative for algebraic specification and development, electronic archives, notes and documents accessible from http://www.brics.dk/Projects/CoFI - CoFI |

35 | Relating CASL with other specification languages: the institution level - Mossakowski |

34 | Fundamentals of algebraic speci 1 - Ehrig, Mahr - 1985 |

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

14 |
Specification in an arbitrary institution with symbols
- Mossakowski
- 2000
(Show Context)
Citation Context ...sink (have a common target signature and are jointly epi); we thus slightly generalize the amalgamation operation of Casl here, again avoiding the need to present the details of signature unions (cf. =-=[Mos00]-=-). Imports as used in Example 1 can be regarded as syntactical sugar for a parametrized unit which is instantiated only once. 2 Institutions and Amalgamation The semantic considerations ahead rely on ... |

11 | Casl: A guided tour of its design - Mosses - 1999 |

11 | Architectural specifications in CASL
- Bidoit, Sannella, et al.
- 1999
(Show Context)
Citation Context ... be used as building blocks for models of more complex specifications, e.g. by amalgamating units or by applying parametrized units. Architectural specifications have been introduced and motivated in =-=[BST99]-=-. The aim of the present paper is to outline the semantics of architectural specifications at various levels. We use a simple subset of Casl architectural specifications, which is expressive enough to... |

11 | Checking amalgamability conditions for Casl architectural specifications - Klin, Hoffman, et al. - 2001 |

7 | Putting theories together to make speci cations - Burstall, Goguen - 1977 |

7 | Specification languages - Sannella - 1999 |

6 | Relating CASL with other speci languages: the institution level - Mossakowski - 2002 |

5 | Speci in an arbitrary institution with symbols - Mossakowski - 2000 |

4 |
An implementation of static semantics for architectural specifications
- Klin
- 2000
(Show Context)
Citation Context ...However, decision procedures can be developed for important special cases; for instance, orders (rather than preorders) of sorts admit deciding the amalgamability conditions by a polynomial algorithm =-=[Kli00]-=-. For the general case, it seems that an approximative algorithm that restricts the length of ‘cells’ involved in the proofs will suffice in practically relevant cases. The technique for the extended ... |

3 |
Verifying architectural specifications
- Hoffman
- 2001
(Show Context)
Citation Context ...levant as soon as we discuss further issues of verification in architectural specifications (represented here by the remaining fitting condition in the semantics of unit applications). As proposed in =-=[Hof00]-=-, formal proof obligations can be extracted from such conditions using colimits of specification diagrams, but only if the underlying institution has the amalgamation property. The technique proposed ... |

2 | Catalogue of existing frameworks - CoFI - 1996 |

1 | Architectural speci in Casl - Bidoit, Sannella, et al. - 1999 |

1 | Semantics of architectural speci (in Polish - Homan - 2000 |

1 | Amalgamation via enriched signatures - Schröder, Mossakowski, et al. |