## Translating OBJ3 into CASL: the Institution Level (1998)

Venue: | In Recent Trends in Algebraic Development Techniques, Proc. 13th International Workshop, WADT '98 |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Mossakowski98translatingobj3,

author = {Till Mossakowski},

title = {Translating OBJ3 into CASL: the Institution Level},

booktitle = {In Recent Trends in Algebraic Development Techniques, Proc. 13th International Workshop, WADT '98},

year = {1998},

pages = {pages},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

We translate OBJ3 to CASL. At the level of basic specifications, we set up several institution representations between the underlying institutions. They correspond to different methodological views of OBJ3. The translations can be the basis for automated tools translating OBJ3 to CASL.

### Citations

476 |
Institutions: Abstract model theory for specication and programming
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...nd representations Any specification formalism is usually based on some notion of signature, model, sentence and satisfaction. These are the ingredients of Goguen and Burstall's notion of institution =-=[10]-=-. Definition 1. An institution I = (Sign I ; Sen I ; Mod I ; j= I ) consists of -- a category Sign I of signatures, -- a functor Sen I : Sign \Gamma! Set giving the set of sentences Sen I (\Sigma ) ov... |

208 | Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations
- Goguen
- 1992
(Show Context)
Citation Context ...erms of partial first-order logic: Definition 4. The institution SubPFOL = . Signatures The notion of subsorted signatures extends the notion of ordersorted signatures as given by Goguen and Meseguer =-=[12]-=-, by allowing not only total function symbols, but also partial function symbols and predicate symbols: A subsorted signature \Sigma = (S; TF ; PF ; P; S ) consists of a many-sorted signature (S; TF ;... |

168 |
General logics
- Meseguer
- 1989
(Show Context)
Citation Context ..., in some cases, there are more direct translations of constructs. 2 Preliminaries At the level of basic concepts, the translation of OBJ3 into CASL will be formalized as a simple map of institutions =-=[14]-=-, also called simple institution representation [22]. We therefore first introduce the notions of institution and institution representation, and then the institution underlying CASL, and finally some... |

121 | Introducing OBJ
- Goguen, Winkler, et al.
- 2000
(Show Context)
Citation Context ...ow one step towards CASL as a uniform standard is to establish translations from existing specification languages to CASL. In this work, we consider the translation of the specification language OBJ3 =-=[8]-=- into CASL. When setting up the translation, we follow the structure of the CASL language summary, which distinguishes concepts underlying the language and constructs of the language whose meaning is ... |

50 | Moving between logical systems
- Tarlecki
- 1995
(Show Context)
Citation Context ...of constructs. 2 Preliminaries At the level of basic concepts, the translation of OBJ3 into CASL will be formalized as a simple map of institutions [14], also called simple institution representation =-=[22]-=-. We therefore first introduce the notions of institution and institution representation, and then the institution underlying CASL, and finally some preliminaries for the institutions underlying OBJ3 ... |

43 | The Common Framework Initiative for algebraic specification and development, electronic archives. Notes and Documents accessible by WWW at http://www.brics.dk/Projects/CoFI - CoFI |

43 |
Order-Sorted Algebra Solves the Constructor-Selector, Multiple Representation and
- Goguen, Meseguer
- 1987
(Show Context)
Citation Context ...BJ3 is based on order-sorted algebra as developed in [12]. We here describe the institution COSASC of coherent ordersorted algebra enriched with sort constraints, as introduced by Goguen and Meseguer =-=[12, 15, 7]-=-, in some detail, since it appears that there is no complete detailed description of it in the literature 6 . Definition 5. The institution COSASC. Signatures Order signatures are triples \Sigma = (S;... |

43 | CoFI: The Common Framework Initiative for Algebraic Specification and Development
- Mosses
- 1997
(Show Context)
Citation Context ... correspond to different methodological views of OBJ3. The translations can be the basis for automated tools translating OBJ3 to CASL. 1 Introduction The goal of CoFI, the Common Framework Initiative =-=[20]-=-, is to design a family of algebraic specification languages that lead to a uniform standard in the area of algebraic specification. The Common Algebraic Specification Language (CASL) [5] is the centr... |

34 |
Operational semantics for order-sorted algebra
- Goguen, Jouannaud, et al.
(Show Context)
Citation Context ...BJ3 is based on order-sorted algebra as developed in [12]. We here describe the institution COSASC of coherent ordersorted algebra enriched with sort constraints, as introduced by Goguen and Meseguer =-=[12, 15, 7]-=-, in some detail, since it appears that there is no complete detailed description of it in the literature 6 . Definition 5. The institution COSASC. Signatures Order signatures are triples \Sigma = (S;... |

31 |
On the Existence of Free Models in Abstract Algebraic Institutions
- Tarlecki
- 1985
(Show Context)
Citation Context ...d( \Sigma ;\Gamma ). Then the unit ' M : M \Gamma! Fs\Sigma;\Gamma (M)js\Sigma;\Gamma is injective. Proof. The lemma follows from Theorem 3.5 of [12] 9 by using the diagram method for free extensions =-=[21]-=-. ut 3 The institutions underlying OBJ3 Joseph Goguen claims in [9] that the semantics of a theory (\Sigma ; \Gamma ) is neither Mod(\Sigma; \Gamma ) nor Mod(\Sigma\Omega ; \Gamma\Omega ), but rather ... |

22 | Static semantic analysis and theorem proving for Casl
- Mossakowski, Kolyang, et al.
- 1997
(Show Context)
Citation Context ... point concerns sort disambiguation of terms. Sort disambiguation in OBJ3 inserts subsort inclusions and retracts, while in CASL, only subsort injections are inserted. Note that CASL's disambiguation =-=[19]-=- corresponds to the least sort parse for regular signatures. Thus, at the construct level, the translation from OBJ3 to CASL has just to insert retracts. (It does not matter here that at the concepts ... |

20 |
Partial algebras – survey of a unifying approach towards a two-valued model theory for partial algebras. Algebra Universalis
- Burmeister
- 1982
(Show Context)
Citation Context ...ms are undefined; thus both notions of equation coincide for defined terms. A detailed description of the satisfaction relation and a proof of the satisfaction condition can be found in [6], see also =-=[1]-=-. ut Now subsorted partial first-order logic is defined in terms of partial first-order logic: Definition 4. The institution SubPFOL = . Signatures The notion of subsorted signatures extends the notio... |

19 | From total equational to partial first order logic
- Cerioli, Mossakowski, et al.
- 1999
(Show Context)
Citation Context ... We write Mw for the Cartesian product Ms 1 \Theta ::: \Theta Msn , when w = s1 :::s n . 3 Note that each term has a unique sort. We can inductively extend valuations from variables to all terms (see =-=[3]-=-): Lemma 3. Each valuation : X \Gamma! M has an extension to a S-indexed family of partial mapss# : T \Sigma (X) \Gamma!ffi M , where doms# ` T \Sigma (X) is the S-indexed set of -interpretable terms.... |

13 | Permissive subsorted partial logic in Casl
- Cerioli, Haxthausen, et al.
- 1997
(Show Context)
Citation Context ... \Gamma! Th J 0 , but sincesis simple, both formulations are equivalent using Meseguer's ff-extension. 2 2.2 The institution underlying CASL The institution underlying CASL is introduced in two steps =-=[6, 2]-=-: first, we introduce many-sorted partial first-order logic with equality (PFOL = ), and then, subsorted partial first-order logic with equality (SubPFOL = ) is described in terms of PFOL =2 . Definit... |

9 |
Remarks on remarks on many-sorted equational logic
- Goguen
(Show Context)
Citation Context ...els that mix empty and non-empty carriers. 12 We here additionally forbid models consisting only of empty carriers, but this additional restriction is not essential in any respect. It has been argued =-=[11]-=- that allowing empty carriers is necessary to get initial models and free extensions. However, Corollary 15 shows that initial models and free extensions exist if we restrict ourselves to strict signa... |

9 | Pushouts of order-sorted algebraic specifications - Haxthausen, Nickl - 1996 |

5 | Stretching first order equational logic: proofs with partiality, subtypes and retracts. Available from http://www-cse.ucsd.edu/users/ goguen/pubs
- Goguen
- 1998
(Show Context)
Citation Context ...nt of (S; ), or sort constraints t : s 7 This condition is needed to ensure that reduct functors preserve monotonicity of models (cf. [13]). In [23], this condition is missing, while the condition of =-=[9]-=- is too weak. 8 This condition is needed to ensure that the least sort parse algorithm described below is compatible with signature morphisms. 7 where t 2 T \Sigma (X) s 0 and s is a sort in the same ... |

5 | Representations, hierarchies and graphs of institutions
- Mossakowski
- 1996
(Show Context)
Citation Context ...subcategory of Mod I (\Sigma ) induced by the class of those models M satisfying \Gamma . Given institutions I and J , a simple map of institutions [14] (also called simple institution representation =-=[22, 16]-=-)s= (\Phi; ff; fi): I \Gamma! J consists of -- a functor \Phi: Sign I \Gamma! Th J 0 1 , -- a natural transformation ff: Sen I \Gamma! Sen J ffi \Phi, and -- a natural transformation fi: Mod J ffi \Ph... |

3 |
Theory and Implementation of Sort Constraints for Order Sorted Algebra
- Yan
- 1994
(Show Context)
Citation Context ...ature morphism oe: \Sigma \Gamma! \Sigma 0 consists of -- a map oe S : S \Gamma! S 0 , -- a family of maps oe TF w;s : TF w;s \Gamma! TF 0 oe S (w);oe S (s) for each w 2 S , s 2 S such that 6 Han Yan =-=[23] come-=-s closest to describing such an institution, but [23] is not publicly available. 6 -- oe S (s)s0 oe S (s 0 ) whenever sss 0 (monotonicity), -- for wsw 0 , f 2 TF w;s " TF w 0 ;s 0 , we have oe TF... |

2 |
Sublanguages of CASL
- Mossakowski
- 1997
(Show Context)
Citation Context ...ned by the context. Satisfaction Satisfaction, as well as the satisfaction condition, is inherited from PFOL = . ut We will also need some subinstitutions of SubPFOL = , which are formally defined in =-=[17]-=-. The institution SubPCondEq = is the restriction of SubPFOL = to signatures without predicate symbols and sentences that are universally quantified conditional equations. SubCondEq = is SubPCondEq = ... |

2 |
Colimits of order-sorted specifications revisited
- Mossakowski
- 1997
(Show Context)
Citation Context ...d component) have a common upper bound (local filtration). (The conjunction of regularity and local filtration is called coherence.) We further assume that each signature is strongly locally filtered =-=[18]-=-, which means that any two elements of a connected component have a least upper bound. This assumption is needed for setting up the institution representations, but it might be omitted when translatin... |