## Logical Foundations of CafeOBJ (0)

Venue: | Theoretical Computer Science |

Citations: | 10 - 1 self |

### BibTeX

@ARTICLE{Diaconescu_logicalfoundations,

author = {Razvan Diaconescu and Kokichi Futatsugi},

title = {Logical Foundations of CafeOBJ},

journal = {Theoretical Computer Science},

year = {},

volume = {285},

pages = {289--318}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. Then we focus on the actual logical foundations of the language at two different levels: basic specification and structured specification, including also the definition of the CafeOBJ institution. We survey some novel or more classical theoretical concepts supporting the logical foundations of CafeOBJ together with pointing to the main results but without giving proofs and without discussing all mathematical details. Novel theoretical concepts include the coherent hidden algebra formalism and its combination with rewriting logic, and Grothendieck (or fibred) institutions. However for proofs and for some of the mathematical details not discussed here we give pointers to relevant publications. ...

### Citations

476 |
Institutions: Abstract model theory for specication and programming
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...y be added in the future. 3 Module System. The principles of the CafeOBJ module system are inherited from OBJ which builds on ideas first realized in the language Clear [1], most notably institutions =-=[1-=-9, 15]. CafeOBJ module system features several kinds of imports, sharing for multiple imports, parameterised programming allowing multiple parameters, views for parameter instantiation, integrat... |

474 |
Categories for the working mathematician
- MacLane
- 1998
(Show Context)
Citation Context ...ral algebra can be found in [18, 26, 34] for the many-sorted version, and in [25, 20] for the order-sorted version. For category theory we generally use the same notations and terminology as Mac Lane =-=[31], except t-=-hat composition is denoted by ";" and written in the diagrammatic order. The application of functions (functors) to arguments may be written either normally using parentheses, or else in dia... |

473 |
Conditional rewriting logic as a unified model of concurrency
- Meseguer
- 1992
(Show Context)
Citation Context ... equations in proving strict equalities. Rewriting Logic Specification. Rewriting logic specification in CafeOBJ is based on a simplified version of Meseguer 's rewriting logic (abbreviated as `RWL') =-=[32]-=- specification framework for concurrent systems which gives a non-trivial extension of traditional algebraic specification towards concurrency. RWL incorporates many different models of concurrency in... |

273 |
An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types
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- 1978
(Show Context)
Citation Context ...logy and Notations This work assumes some familiarity with basic general algebra (in its many-sorted and order-sorted form) and category theory. Relevant background in general algebra can be found in =-=[18, 26, 34]-=- for the many-sorted version, and in [25, 20] for the order-sorted version. For category theory we generally use the same notations and terminology as Mac Lane [31], except that composition is denoted... |

208 | Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations
- Goguen
- 1992
(Show Context)
Citation Context ...the language revise the OBJ view on importation modes and parameters [12]. Type System and Partiality. CafeOBJ has a type system that allows subtypes based on order sorted algebra (abbreviated `OSA') =-=[25, 20]-=-. This provides a mathematically rigorous form of runtime type checking and error handling, giving CafeOBJ a syntactic flexibility comparable to that of untyped languages, while preserving all the adv... |

161 |
The semantics of Clear, a specification language
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- 1980
(Show Context)
Citation Context ...urther and new methodologies may be added in the future. 3 Module System. The principles of the CafeOBJ module system are inherited from OBJ which builds on ideas first realized in the language Clear [1], most notably institutions [19, 15]. CafeOBJ module system features several kinds of imports, sharing for multiple imports, parameterised programming allowing multiple parameters, views for... |

142 | Membership algebra as a logical framework for equational specification - Meseguer - 1997 |

111 | A hidden agenda
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- 1997
(Show Context)
Citation Context ...empotence, and combinations between all these. This feature is reflected at the execution level by term rewriting modulo such equational theories. Behavioural Specification. Behavioural specification =-=[21, 22, 13, 29]-=- provides a novel generalisation of ordinary algebraic specification. Behavioural specification characterises how objects (and systems) behave, not how they are implemented. This new form of abstracti... |

102 |
et a!. Principles of OBJ2
- Futatsugi
(Show Context)
Citation Context ... Romanian Academy. 2 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, JAPAN Preprint submitted to Elsevier Preprint 26 February 2000 Equational Specification and Programming. This is inherited from OBJ =-=[27, 17]-=- and constitutes the basis of the language, the other features being somehow built on top of it. As with OBJ, CafeOBJ is executables(by term rewriting), which gives an elegant declarative way of funct... |

100 | EQLOG: equality, types and generic modules for logic programming - Goguen, Meseguer |

99 |
Unifying functional, object-oriented and relational programming with logical semantics
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- 1987
(Show Context)
Citation Context ...perations is given by MEL. Logical semantics. CafeOBJ is a declarative language with firm mathematical and logical foundations in the same way as other OBJ-family languages (OBJ, Eqlog [23, 4], FOOPS =-=[24]-=-, Maude [32]) are. The mathematical semantics of CafeOBJ is based on state-of-theart algebraic specification concepts and results, and is strongly based on category theory and the theory of institutio... |

85 | Logical support for modularisation
- Diaconescu, Goguen, et al.
- 1991
(Show Context)
Citation Context ...y be added in the future. 3 Module System. The principles of the CafeOBJ module system are inherited from OBJ which builds on ideas first realized in the language Clear [1], most notably institutions =-=[1-=-9, 15]. CafeOBJ module system features several kinds of imports, sharing for multiple imports, parameterised programming allowing multiple parameters, views for parameter instantiation, integrat... |

85 | Towards an algebraic semantics for the object paradigm
- GOGUEN, DIACONESCU
- 1994
(Show Context)
Citation Context ...empotence, and combinations between all these. This feature is reflected at the execution level by term rewriting modulo such equational theories. Behavioural Specification. Behavioural specification =-=[21, 22, 13, 29]-=- provides a novel generalisation of ordinary algebraic specification. Behavioural specification characterises how objects (and systems) behave, not how they are implemented. This new form of abstracti... |

52 | Observational logic
- Hennicker, Bidoit
- 1999
(Show Context)
Citation Context ...empotence, and combinations between all these. This feature is reflected at the execution level by term rewriting modulo such equational theories. Behavioural Specification. Behavioural specification =-=[21, 22, 13, 29]-=- provides a novel generalisation of ordinary algebraic specification. Behavioural specification characterises how objects (and systems) behave, not how they are implemented. This new form of abstracti... |

33 |
Theorem Proving and Algebra
- Goguen
- 1994
(Show Context)
Citation Context ...logy and Notations This work assumes some familiarity with basic general algebra (in its many-sorted and order-sorted form) and category theory. Relevant background in general algebra can be found in =-=[18, 26, 34]-=- for the many-sorted version, and in [25, 20] for the order-sorted version. For category theory we generally use the same notations and terminology as Mac Lane [31], except that composition is denoted... |

32 | and Răzvan Diaconescu. An Oxford survey of order sorted algebra - Goguen - 1994 |

26 | Extra theory morphisms for institutions: logical semantics for multi-paradigm languages
- Diaconescu
- 1998
(Show Context)
Citation Context ...aude [32]) are. The mathematical semantics of CafeOBJ is based on state-of-theart algebraic specification concepts and results, and is strongly based on category theory and the theory of institutions =-=[19, 11, 9, 15]. The foll-=-owing are the principles governing the logical and mathematical foundations of CafeOBJ: P1. there is an underlying logic 6 in which all basic constructs and features of 6 Here "logic" should... |

25 | Grothendieck institutions
- Diaconescu
- 1994
(Show Context)
Citation Context ...aude [32]) are. The mathematical semantics of CafeOBJ is based on state-of-theart algebraic specification concepts and results, and is strongly based on category theory and the theory of institutions =-=[19, 11, 9, 15]. The foll-=-owing are the principles governing the logical and mathematical foundations of CafeOBJ: P1. there is an underlying logic 6 in which all basic constructs and features of 6 Here "logic" should... |

24 | Category-based semantics for equational and constraint logic programming
- Diaconescu
- 1994
(Show Context)
Citation Context ... with partial operations is given by MEL. Logical semantics. CafeOBJ is a declarative language with firm mathematical and logical foundations in the same way as other OBJ-family languages (OBJ, Eqlog =-=[23, 4]-=-, FOOPS [24], Maude [32]) are. The mathematical semantics of CafeOBJ is based on state-of-theart algebraic specification concepts and results, and is strongly based on category theory and the theory o... |

23 |
Emil Căzănescu and Grigore Ros¸u. Weak inclusion systems
- Virgil
- 1997
(Show Context)
Citation Context ...ng the imported and the importing modules. Inclusion systems where first defined by [15] for the institution-independent study of structuring specifications. Weak inclusion systems were introduced in =-=[3]-=-, and 22 they constitute a simplification of the original definition of inclusion systems of [15]. We recall the definition of inclusion systems: Definition 34 hI ; Ei is a weak inclusion system for a... |

13 | Completeness of category-based equational deduction
- Diaconescu
- 1995
(Show Context)
Citation Context ...rous treatment of such conditions can be achieved within the so-called constraint logic [10], which can however be regarded as a special case of an abstract categorical form of plain equational logic =-=[5, 4, 10]-=-. 10 Equational attributes such as associativity (A), commutativity (C), identity (I), or idempotence (Z) are just special cases of strict equations. However, the behavioural part of HOSRWL has anothe... |

9 | Foundations of behavioural specification in rewriting logic
- Diaconescu
- 1996
(Show Context)
Citation Context ...this can be directly specified by the user. CafeOBJ does not directly implement final semantics, however final models play an important role for the loose semantics of behavioural specifications (see =-=[13, 8]-=-). Initial model semantics applies only to non-behavioural specification, and is supported by the following result: 7 Theorem 1 Let T be a theory in either MSA, OSA, RWL, or OSRWL. Then the initial mo... |

8 | Component-based algebraic specification and verification
- Diaconescu, Futatsugi, et al.
- 1999
(Show Context)
Citation Context ...hodologies, especially the object-oriented ones emerging from the behavioural specification paradigm. This includes refining the existing object composition methodology based on projection operations =-=[30, 14, 12]-=- but also the development of new methodologies and careful identification of the application domains most suitable to certain specification and verification methodologies. The development of CafeOBJ h... |

7 | Category-based constraint logic - Diaconescu |

5 |
Kokichi Futatsugi, and Razvan Diaconescu. Component-based algebraic specification: - behavioural specification for component-based software engineering
- Iida
- 1999
(Show Context)
Citation Context ...ation by several methodologies. 5 CafeOBJ currently highlights a methodology for concurrent object composition which features high reusability not only of specification code but also of verifications =-=[12, 30]-=-. Behavioural specification in CafeOBJ may also be effectively used as an object-oriented (state-oriented) alternative for classical data-oriented specifications. Experiments seem to indicate that an ... |

4 |
Completeness of semantic paramodulation: a category-based approach
- Diaconescu
- 1996
(Show Context)
Citation Context ...he case of rewriting logic the relationship between the proof calculus and rewriting is very intimate, but for equational logic the completeness of rewriting can be found, among other many places, in =-=[18, 7]-=-. Notice that hidden logics of the CafeOBJ cube do not admit a complete (finitary) proof calculus. However, advanced proof techniques support the verification process in the case of behavioural specif... |

2 | Behavioural rewriting logic: semantic foundations and proof theory
- Diaconescu
- 1996
(Show Context)
Citation Context ...port the verification process in the case of behavioural specifications, most notably the hidden coinduction method (see [22] for the original definition, [12, 13] for its realization in CafeOBJ, and =-=[6]-=- for the details for the case of proving behavioural transitions). 12 Meaning that z is in the subterm determined by the operation. 16 3 The CafeOBJ Institution In this section we define the CafeOBJ i... |

1 |
Categories fibrees et descente. In Rev etements etales et groupe fondamental, S eminaire de G eom etrie Alg ebraique du Bois-Marie 1960/61, Expos e VI
- Grothendieck
- 1971
(Show Context)
Citation Context ...ich is a Grothendieck construction on the CafeOBJ cube. The Grothendieck construction for institutions was first introduced by [11] and generalises the famous Grothendieck construction for categories =-=[28]-=-. The essence of this Grothendieck construction is that it constructs a `disjoint sum' of all institutions of the CafeOBJ cube, also introducing theory morphisms across the institution embeddings of t... |