## Foundations of Heterogeneous Specification

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Citations: | 10 - 3 self |

### BibTeX

@MISC{Mossakowski_foundationsof,

author = {Till Mossakowski},

title = {Foundations of Heterogeneous Specification},

year = {}

}

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### Abstract

We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semantics for heterogeneous specification.

### Citations

1108 | Temporal and Modal Logic
- Emerson
- 1990
(Show Context)
Citation Context ...carriers. Now M satisfies P iff M is equipped with L. Details can be found in [36, 37]. CF OL = -Ltl (actually a subinstitution of Casl-Ltl [35]) combines CF OL = with the computation tree logic CTL* =-=[17]-=- 6 . Signatures are CF OL = -signatures with – a distinguished set DS of dynamic sorts, – an injective assignment of label sorts Label ds (outside DS) to dynamic sorts ds, such that – there exists a t... |

582 |
The Theory and Practice of Concurrency
- Roscoe
- 1998
(Show Context)
Citation Context ... restricted to signature morphisms that are injective on sorts. There are several notions of model for Csp-CF OL = . We here choose the most informative one, based on labeled transition systems (LTS) =-=[38]-=-. Thus, models are CF OL = -models, possibly equipped with an LTS being labeled in the disjoint union of all carriers. On the CF OL = -part, reducts are as in CF OL = . If a model is not equipped with... |

475 |
Institutions: Abstract Model Theory for Specification and Programming
- Goguen, Burstall
- 1992
(Show Context)
Citation Context ...f translation can be used at a time. The goal of the present work is to overcome these limitations while simultaneously staying as simple as possible. 2 Institutions and Their (Co)Morphisms Following =-=[21]-=-, we formalize logics as institutions. Definition 1. An institution I = (Sign I , Sen I , Mod I , |= I ) consists of – a category Sign I of signatures, – a functor Sen I : Sign I −→ Set giving, for ea... |

177 | Using branching time temporal logic to synthesize synchronization skeletons - Emerson, Clarke - 1982 |

168 |
General logics
- Meseguer
- 1989
(Show Context)
Citation Context ...iding theorem links, which are omitted here for simplicity.sFinally, each type of morphism also comes in a simple theoroidal variant [20], meaning that signatures may be mapped to theories. Following =-=[26]-=-, the category Th of theories has as objects theories, i.e. signatures plus sets of axioms. A theory morphism is a signature morphism mapping axioms to logical consequences. Let Sig: Th −→ Sign be the... |

143 | Toward Formal Development of Programs from Algebraic Specifications
- Sannella, Tarlecki
- 1988
(Show Context)
Citation Context ...rward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi =-=[43, 46, 41]-=- x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. [19, 18]) of heterogeneity arises in the specification of reactive systems: some equational or first-order logic is used to specify... |

92 | Building specifications in an arbitrary institution
- Sanella, Tarlecki
- 1988
(Show Context)
Citation Context ...en I (Σ). ⊓⊔ The notion of institutions gains much of its importance by the fact that several languages for modularizing specifications have been developed in a completely institution independent way =-=[42, 16, 14, 22, 15, 34]-=-, one of which also has been extended to the heterogeneous case [47]. Most of their constructs can be translated into the formalism of development graphs introduced below, which hence can be seen as a... |

85 | Logical support for modularisation
- Diaconescu, Goguen, et al.
- 1991
(Show Context)
Citation Context ...en I (Σ). ⊓⊔ The notion of institutions gains much of its importance by the fact that several languages for modularizing specifications have been developed in a completely institution independent way =-=[42, 16, 14, 22, 15, 34]-=-, one of which also has been extended to the heterogeneous case [47]. Most of their constructs can be translated into the formalism of development graphs introduced below, which hence can be seen as a... |

59 | Rewriting as a unified model of concurrency - Meseguer - 1990 |

58 | Institution morphisms - Goguen, Ros¸u - 2002 |

50 | Moving between logical systems
- Tarlecki
- 1995
(Show Context)
Citation Context ...I Σ αΣ(ϕ ′ ) ⇔ βΣ(M) |= J Φ(Σ) ϕ′ The notion of institution morphism can be varied in several ways by changing the directions of the arrows or even, in the case of semi-morphisms, omitting the arrows =-=[20, 46]-=-: Sign Sen Mod morphism comorphism Sign �� �� Sign ′ Sen �� �� Sen ′ ◦ Φ Mod �� �� Mod ′ ◦ Φ forward morphism forward comorphism �� �� Sign ′ �� �� Sen ′ ◦ Φ �� �� Mod ′ ◦ Φ �� �� Sign semi morphism s... |

46 |
I borrow your logic? (transporting logical structures along maps
- Cerioli, Meseguer
(Show Context)
Citation Context ...ms, and an “x” stand for folklore knowledge or trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th =-=[3, 8, 9, 24]-=- [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g... |

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 | CoFI: The Common Framework Initiative for Algebraic Specification and Development
- Mosses
- 1997
(Show Context)
Citation Context ...en I (Σ). ⊓⊔ The notion of institutions gains much of its importance by the fact that several languages for modularizing specifications have been developed in a completely institution independent way =-=[42, 16, 14, 22, 15, 34]-=-, one of which also has been extended to the heterogeneous case [47]. Most of their constructs can be translated into the formalism of development graphs introduced below, which hence can be seen as a... |

38 |
B.: Fundamentals of Algebraic Specification 2
- Ehrig, Mahr
- 1990
(Show Context)
Citation Context |

37 | Towards an Evolutionary Formal Software Development Using Casl
- Autexier, Hutter, et al.
- 2000
(Show Context)
Citation Context ...opment graphs introduced below, which hence can be seen as a core formalism for structured and heterogeneous theorem proving. For the language Casl, such a translation has been laid out explicitly in =-=[4]-=-. Definition 2. Given an arbitrary but fixed institution I, a development graph over I is an acyclic directed graph S = 〈N , L〉. N is a set of nodes. Each node N ∈ N is a tuple (Σ N , Γ N ) such that ... |

35 | Logical systems for structured specifications
- Borzyszkowski
(Show Context)
Citation Context ...slation kinds. However, it is unclear how several kinds of translations will interact, e.g. with respect to amalgamation and interpolation properties, which are important for structured proof systems =-=[6, 32]-=-. Even if one does not use heterogeneous specifications simultaneously involving different kinds of translations, a unifying framework is highly desirable in order not to have to switch to a different... |

34 | Relating Casl with other specification languages: the institution level
- Mossakowski
(Show Context)
Citation Context ... from a particular set of operations (and possibly variables valued withsvalues from other sorts). This allows specifying inductive datatypes like lists. Details can be found in the semantics of Casl =-=[11, 31]-=-. Actually, CF OL = is a subinstitution of Casl. Casl additionally admits the use of subsorts and partiality, but we omit these here for simplicity. Csp-CF OL = (actually a subinstitution of Csp-Casl ... |

32 | W.: An Implementation-Oriented Semantics for Module Composition
- Goguen, Tracz
- 2000
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31 |
Institution morphisms. Formal Aspects of Computing 13:274–307
- Goguen, Rosu
- 2002
(Show Context)
Citation Context ...I Σ αΣ(ϕ ′ ) ⇔ βΣ(M) |= J Φ(Σ) ϕ′ The notion of institution morphism can be varied in several ways by changing the directions of the arrows or even, in the case of semi-morphisms, omitting the arrows =-=[20, 46]-=-: Sign Sen Mod morphism comorphism Sign �� �� Sign ′ Sen �� �� Sen ′ ◦ Φ Mod �� �� Mod ′ ◦ Φ forward morphism forward comorphism �� �� Sign ′ �� �� Sen ′ ◦ Φ �� �� Mod ′ ◦ Φ �� �� Sign semi morphism s... |

28 | CSP-CASL: a new integration of process algebra and algebraic specification. Theor
- Roggenbach
- 1997
(Show Context)
Citation Context .... Actually, CF OL = is a subinstitution of Casl. Casl additionally admits the use of subsorts and partiality, but we omit these here for simplicity. Csp-CF OL = (actually a subinstitution of Csp-Casl =-=[36, 37]-=-) combines CF OL = with the process algebra CSP . Signatures and signature morphisms are those from CF OL = , but restricted to signature morphisms that are injective on sorts. There are several notio... |

27 | Towards heterogeneous specifications
- Tarlecki
- 2000
(Show Context)
Citation Context ...ased on Diaconescu’s notion of Grothendieck institution [12]. However, this approach has a limitation: only one type of translation between institution is used, namely institution morphisms. Tarlecki =-=[47]-=- is more general, he introduces a whole bunch of heterogeneous constructs for different kinds of translations. However, only one kind of translation can be used at a time. The goal of the present work... |

26 | Extra theory morphisms for institutions: logical semantics for multi-paradigm languages - Diaconescu - 1998 |

22 |
Relationships between Logical Formalisms
- Cerioli
- 1993
(Show Context)
Citation Context ...ms, and an “x” stand for folklore knowledge or trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th =-=[3, 8, 9, 24]-=- [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g... |

22 | Static semantic analysis and theorem proving for Casl - Mossakowski, Kolyang, et al. - 1997 |

20 |
Grothendieck institutions. Applied Categorical Structures, 10(4):383–402, 2002. Preliminary version appeared as
- Diaconescu
- 2000
(Show Context)
Citation Context ... is CafeOBJ with its cube of eight logics and twelve projections (formalized as institution morphisms) among them [13], and having a semantics based on Diaconescu’s notion of Grothendieck institution =-=[12]-=-. However, this approach has a limitation: only one type of translation between institution is used, namely institution morphisms. Tarlecki [47] is more general, he introduces a whole bunch of heterog... |

20 | Comorphism-based grothendieck logics
- Mossakowski
- 2002
(Show Context)
Citation Context ...lems is to flatten the graph of institutions and translations, as it is done with Diaconescu’s Grothendieck institution [12]. We here recall the Grothendieck institution for the comorphism-based case =-=[29]-=-: Definition 5. An indexed coinstitution is a functor I: Ind op −→CoIns into the category CoIns of institutions and institution comorphisms 8 . A discrete indexed coinstitution is one with Ind discret... |

19 | CASL-CHART: A Combination of Statecharts and the Algebraic Specification Language CASL - Reggio, Repetto |

18 |
Relationships between logical frameworks
- Astesiano, Cerioli
- 1993
(Show Context)
Citation Context ...ms, and an “x” stand for folklore knowledge or trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th =-=[3, 8, 9, 24]-=- [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g... |

18 | Integrating Hol-Casl into the development graph manager Maya - Autexier, Mossakowski - 2002 |

17 | Equivalences among various logical frameworks of partial algebras - Mossakowski - 1995 |

16 |
Unifying theories in different institutions
- Arrais, Fiadeiro
- 1996
(Show Context)
Citation Context ... case, “semi” denotes semi-morphisms, and an “x” stand for folklore knowledge or trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] =-=[2, 26]-=- x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Spe... |

16 |
Casl-Ltl : A Casl extension for dynamic reactive systems
- Reggio, Astesiano, et al.
(Show Context)
Citation Context ...eading to an LTS L with labels in the disjoint union of all carriers. Now M satisfies P iff M is equipped with L. Details can be found in [36, 37]. CF OL = -Ltl (actually a subinstitution of Casl-Ltl =-=[35]-=-) combines CF OL = with the computation tree logic CTL* [17] 6 . Signatures are CF OL = -signatures with – a distinguished set DS of dynamic sorts, – an injective assignment of label sorts Label ds (o... |

15 | Structured theories and institutions
- Durán, Meseguer
- 2003
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Citation Context |

15 | Extending development graphs with hiding
- Mossakowski, Autexier, et al.
- 2005
(Show Context)
Citation Context ...slation kinds. However, it is unclear how several kinds of translations will interact, e.g. with respect to amalgamation and interpolation properties, which are important for structured proof systems =-=[6, 32]-=-. Even if one does not use heterogeneous specifications simultaneously involving different kinds of translations, a unifying framework is highly desirable in order not to have to switch to a different... |

15 |
A soft stairway to institutions
- Salibra, Scollo
(Show Context)
Citation Context ...trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], (=-=[39, 40, 44]-=-) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. [19, 18]) of heterogeneity arises in the spe... |

14 | From abstract data types to logical frameworks - Meseguer, Mart'i-Oliet - 1995 |

12 |
Information Processing Systems -- Open Systems Interconnection -- LOTOS -- A Formal Description Technique Based on the Temporal Ordering of Observational Behaviour
- Brinksma
- 1989
(Show Context)
Citation Context ...36]. There seems to be no alternative formulation of Csp-CF OL = as an institution simplifying the above picture. Moreover, the problems to be solved when formalizing the quite popular language LOTOS =-=[7]-=- as an institution should be similar to those of Csp-CF OL = .s4 The Bi-Grothendieck Institution How can we give a precise meaning to the development graph involving several kinds of translations betw... |

11 | Feature Interactions: A Mixed Semantic Model Approach
- Gibson, Mermet, et al.
- 1997
(Show Context)
Citation Context ...25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. =-=[19, 18]-=-) of heterogeneity arises in the specification of reactive systems: some equational or first-order logic is used to specify the data (here, lists over arbitrary elements), some process algebra (here, ... |

11 | Heterogeneous development graphs and heterogeneous borrowing
- Mossakowski
- 2002
(Show Context)
Citation Context ...oroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction =-=[30]-=- th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. [19, 18]) of heterogeneity arises in the specification of reactive systems: some equational or ... |

11 | State-based extension of Casl - Baumeister, Zamulin - 2000 |

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

8 | A Valid Environment for LOTOS
- Ghribi, Logrippo
- 1993
(Show Context)
Citation Context ...25–28, 31, 33, 45] th [5, 48], ([39, 40, 44]) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. =-=[19, 18]-=-) of heterogeneity arises in the specification of reactive systems: some equational or first-order logic is used to specify the data (here, lists over arbitrary elements), some process algebra (here, ... |

8 |
Equivalence and difference of institutions: Simulating Horn clause logic with based algebras
- Kreowski, Mossakowski
- 1995
(Show Context)
Citation Context |

6 |
Interpolation and compactness in categories of preinstitutions
- Salibra, Scollo
- 1996
(Show Context)
Citation Context ...trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], (=-=[39, 40, 44]-=-) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. [19, 18]) of heterogeneity arises in the spe... |

6 | Logical Semantics of CafeOBJ - Diaconescu, Futatsugi - 1996 |

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

5 |
On the engineering of logics
- Scollo
- 1993
(Show Context)
Citation Context ...trivialities): (semi) morphism (theoroidal) comorphism (theoroidal) forward morphism forward comorphism Inclusion [41] [2, 26] x x Coding ([41, 1]) 4 th [3, 8, 9, 24] [25–28, 31, 33, 45] th [5, 48], (=-=[39, 40, 44]-=-) 5 Projection [2, 41, 13] Feature interaction [30] th Implementation semi [43, 46, 41] x [48] 3 Heterogeneous Specification One typical scenario (cf. e.g. [19, 18]) of heterogeneity arises in the spe... |

5 | Unifying theories in dierent institutions - Arrais, Fiadeiro - 1996 |

5 | Logical systems for structured speci - Borzyszkowski - 2002 |