## Relating CASL with Other Specification Languages: the Institution Level (2000)

### Cached

### Download Links

- [www.tzi.de]
- [www.informatik.uni-bremen.de]
- DBLP

### Other Repositories/Bibliography

Citations: | 34 - 16 self |

### BibTeX

@MISC{Mossakowski00relatingcasl,

author = {Till Mossakowski},

title = {Relating CASL with Other Specification Languages: the Institution Level},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEP-theories, as well as various sublanguages of Casl that more or less directly correspond to these. All these languages are translated to an appropriate sublanguage of Casl. The translation mainly concerns the level of specification in-the-small: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification in-the-large. Thus, we obtain one hand translations of any of the abovementioned specification languages to an appropriate sublanguage of Casl. This allows us to take libraries and case studies that have been developed for other languages and re-use them in Casl. On the other hand, we set up institution repre...

### Citations

255 |
Abstract and Concrete Categories
- Adamek, Herrlich, et al.
- 1990
(Show Context)
Citation Context ...e problem still comes in with derive. Namely, in general the image of the reduct functor Mod(σ) is not closed under isomorphism (the reason for this behaviour is that the functor is not transportable =-=[1]-=-). It would make much sense to close up model classes of specifications under isomorphism. (Indeed, this would need to be done only for presentations and hidings — the other structuring operations pre... |

231 |
Fundamentals of Algebraic Specification 1
- Ehrig, Mahr
- 1985
(Show Context)
Citation Context ... as follows: Given a Σ-model M, γΣ(M) := FιΣ (M)|κΣ . It is tedious but not difficult to check that ιΣ is sufficiently complete, i.e. M ∼ = FιΣ (M)|ιΣ via the unit of the adjunction. By Lemma 8.14 of =-=[28]-=-, we can choose FιΣ such that the identity is the unit of the adjunction, i.e. M = FιΣ (M)|ιΣ . But then, since the unique determination of a partial function through (8) and (9) is the 12 Though this... |

220 |
Locally Presentable and Accessible Categories
- Adámek, Rosický
- 1994
(Show Context)
Citation Context ...d e2 to get the image f[A]: ker f e1 e2 e � A ��� ��� f �� B �� m f[A] By the universal property of the coequalizer, there exists a unique m: f[A]−→ B with f = m ◦ e. By remarks 3.4(2) and 5.13(2) of =-=[2]-=-, if T belongs to GHorn = , e is surjective, which implies that m is injective, hence a monomorphism, and (e, m) is a (regular epi,mono)-factorization of f. This is the well-known theorem of homomorph... |

116 |
Module algebra
- Bergstra, Heering, et al.
- 1990
(Show Context)
Citation Context ...1 (written SP1 � SP2), if Mod(SP2) ⊆ Mod(SP1). A specification not containing derive is called flattenable. This is because it is easy to normalize flattenable specifications into flat specifications =-=[10]-=-: Definition 2.5 Given a flattenable specification SP over an institution I, its normal form NF (SP ) is inductively defined as follows: • NF (〈Σ, Γ〉) := 〈Σ, Γ〉 • If SP = SP 1 ∪ SP 2, let NF (SPi) = 〈... |

114 |
Algebraic Specification
- Bergstra, Heering, et al.
- 1989
(Show Context)
Citation Context ...e the claim that Casl subsumes many existing specification languages. We will consider the relation of both specification languages (Larch [40], OBJ3 and functional CafeOBJ [31,26], ACT ONE [20], ASF =-=[11]-=-, HEP-theories [70]) and common tool-supported logics (e.g. first-order logic, conditional equational logic) to Casl. As a first step, we deal with specification in-the-small, i.e. unstructured specif... |

88 | Logical support for modularisation
- Diaconescu, Goguen, et al.
- 1993
(Show Context)
Citation Context ...� Sig(Φ(Σ1)) Sig(Φ(Σ2)) ����� ���� Φ(θ2) ��� ������������� Φ(θ1) Sig(Φ(Σ ′)) Ax(Φ(Σ ′ )) = Φ(θ2)(Ax(Φ(Σ1))) ∪ Φ(θ1)(Ax(Φ(Σ2))). Proof. Follows from the construction of colimits of presentationss, see =-=[27,33]-=-. ✷ We now generalize a result from [12] to the case of institution representations that map signatures to theories (and not just signatures): Proposition 2.21 Let I and J be two institutions having w... |

55 | CASL: the common algebraic specification language
- Astesiano, Bidoit, et al.
- 2002
(Show Context)
Citation Context ...algebraic specification languages and to provide a standard language for the specification and development of modular software systems. The design of Casl is explained in another paper in this volume =-=[4]-=-, see also [22]. Actually, Casl is a central language in a whole family of languages. Casl concentrates on the specification of abstract data types and (first-order) functional requirements, while som... |

48 |
I borrow your logic? (Transporting logical structure along maps
- Cerioli, Meseguer
(Show Context)
Citation Context ...h a translation will be an institution with good tool support, and the translation will have the property that the tool support can be lifted against the translation (this has been called “borrowing” =-=[18]-=-). We also present some new results concerning such lifting properties. The level of languages constructs is not discussed formally in this paper. This would require detailed language definitions, whi... |

47 |
Axioms for Abstract Model Theory
- Barwise
- 1974
(Show Context)
Citation Context ...-large. 52.1 Institutions A specification formalism is usually based on some notion of signature, model, sentence and satisfaction. These are the usual ingredients of Barwise’s abstract model theory =-=[7]-=-. Contrary to Barwise’s notions, institutions of Goguen and Burstall [33] do not assume that signatures are algebraic signatures and thus cover a much larger variety of logics. Indeed, the theory of i... |

41 |
The Common Framework Initiative for algebraic specification and development, electronic archives, Notes and Documents accessible from http://www.cofi. info
- CoFI
(Show Context)
Citation Context ... relations 118 References 119 1 Introduction Casl is a specification language that has been designed by CoFI, the international Common Framework Initiative for algebraic specification and development =-=[65,21]-=-, with the goal to subsume many previous algebraic specification languages and to provide a standard language for the specification and development of modular software systems. The design of Casl is e... |

33 | Fundamentals of Algebraic Speci 1 - Ehrig, Mahr - 1985 |

33 | Operational semantics of order-sorted algebra - Goguen, Jouannaud, et al. - 1985 |

28 | Extra-theory morphisms in institutions: logical semantics for multi-paradigm languages
- Diaconescu
- 1998
(Show Context)
Citation Context ...so βΣ ◦ γΣ ∼ = id. If we have even βΣ ◦ γΣ = id, then µ is called strongly persistently liberal. We write (µ, γ) if we want to chose a particular γ. ✷ We here use the term liberal (in accordance with =-=[24]-=-) since it stresses the connection with liberality of institutions. Meseguer [49] has introduced persistently liberal representations under the name of extensions. He additionally requires that the is... |

23 |
Relationships between logical formalisms
- Cerioli
- 1993
(Show Context)
Citation Context ...oof techniques such as conditional term rewriting and paramodulation [67] and semantical constructions such as initial models. These work only if strong equations are not allowed in the premises (see =-=[16,5]-=-). Let SubP CHorn = be the restriction of SubP CF OL = to sentences of form ∀x1 : s1 . . . ∀xk : sk • ϕ1 ∧ . . . ∧ ϕm ⇒ ϕ where the ϕi and ϕ are atomic formulas such that none of the ϕi is a strong eq... |

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 ...sort s, • αΣ(F ) = F , • αΣ(ϕ ∧ ψ) = αΣ(ϕ) ∧ αΣ(ψ), • αΣ(ϕ ⇒ ψ) = αΣ(ϕ) ⇒ αΣ(ψ), • αΣ(∀x : s•ϕ) = ∀x : s•αΣ(ϕ). Satisfaction The representation condition essentially is the proposition on page 326 of =-=[13]-=-. 4.1.6 (4 ′ ), (4a ′ ) and (4b ′ ): Mapping P CF OL = to CF OL = The representation (4a′) extends the model-bijective institution representation (4a) described above. Due to the need to translate sor... |

19 | From total equational to partial first order
- Cerioli, Mossakowski, et al.
- 1998
(Show Context)
Citation Context ... variable assignment may be undefined, due to the application of a partial function during the evaluation of the term. The evaluation of a term w.r.t. a variable assignment is defined as follows (see =-=[19]-=-): Given a variable valuation ν: X −→ M for X in M, the term evaluation ν #: TΣ(X)→? M is inductively defined by: • ν # s (x) = ν(x) for all x ∈ Xs and all s ∈ S, ⎧ • ν # ⎪⎨ s (fw,s(t1, . . . , tn)) =... |

16 |
A model theoretic approach to partial algebras. Akademie
- Burmeister
- 1986
(Show Context)
Citation Context ...ism βΣ. ✷ Example 2.42 The institution representation from Example 2.17 is strongly persistently liberal: γΣ totalizes a partial model by adding “undefined” values freely (this is the free completion =-=[14,15]-=-). ✷ Let us now study how persistently liberal institution representations interact with liberality, strengthening a result of [44] (we can now drop the assumption of the existence of Mod I (σ)-free m... |

13 | Permissive subsorted partial logic in Casl, Algebraic Methodology and Software
- Cerioli, Haxthausen, et al.
- 1997
(Show Context)
Citation Context ...guage combining subsorts, partiality, first-order logic and induction (the latter is expressed using so-called sort generation constraints). The institution underlying Casl is introduced in two steps =-=[23,17]-=-: first, we introduce many-sorted partial first-order logic with sort generation constraints and equality (P CF OL = ), and then, subsorted partial first-order logic with sort generation constraints a... |

11 | State-based extension of Casl
- Baumeister, Zamulin
- 2000
(Show Context)
Citation Context ...ct data types and (first-order) functional requirements, while some (currently still prototypical) extensions of Casl also consider the specification of higher-order functions [60,72] and of reactive =-=[9,68,69]-=- and object-oriented [3,43] behaviour. Several restrictions of Casl to sublanguages make it possible to use specialized tool support. 3The aim of the present paper is to substantiate the claim that C... |

9 |
Free objects and equational deduction for partial conditional specifications
- Astesiano, Cerioli
- 1995
(Show Context)
Citation Context ...oof techniques such as conditional term rewriting and paramodulation [67] and semantical constructions such as initial models. These work only if strong equations are not allowed in the premises (see =-=[16,5]-=-). Let SubP CHorn = be the restriction of SubP CF OL = to sentences of form ∀x1 : s1 . . . ∀xk : sk • ϕ1 ∧ . . . ∧ ϕm ⇒ ϕ where the ϕi and ϕ are atomic formulas such that none of the ϕi is a strong eq... |

9 |
Algebraic Specification Techniques and Tools for Software Development: The ACT Approach. World Scientific
- Classen, Ehrig, et al.
- 1993
(Show Context)
Citation Context ...ubstantiate the claim that Casl subsumes many existing specification languages. We will consider the relation of both specification languages (Larch [40], OBJ3 and functional CafeOBJ [31,26], ACT ONE =-=[20]-=-, ASF [11], HEP-theories [70]) and common tool-supported logics (e.g. first-order logic, conditional equational logic) to Casl. As a first step, we deal with specification in-the-small, i.e. unstructu... |

8 | Algebraic Speci - Bergstra, Heering, et al. - 1989 |

8 | Relations between Abstract Datatypes modeled as Abstract Datatypes
- Baumeister
- 1998
(Show Context)
Citation Context ...and Its Translation to CF OAlg = There is no explicit logic given in the Larch report [39]. Therefore, we here introduce an institution LSL that fits to interpret the LSL constructs, mostly following =-=[8]-=-. Most of LSL will be inherited from Eq = . Signatures LSL-signatures and signature morphisms are those of Eq = . Models LSL-models and reducts are those of Eq = . Sentences Let Σ = (S, TF ) be an LSL... |

8 |
Algebraic specifications with generating constraints
- Ehrig, Wagner, et al.
- 1983
(Show Context)
Citation Context ...l M2 with M1|σ1 some Σ ′-model M ′ with M ′|θ2 = M1 and M ′|θ1 = M2. Σ2 = M2|σ2, there exists ✷ It is well known that in institutions with weak amalgamation, there is a normal form for specifications =-=[29,10,12]-=-, having the format derive from 〈Σ, Γ〉 by σ. Since the construction of a normal form involves pushouts and these are only determined up to isomorphism, also the normal form is only determined up to 10... |

4 | Extending Casl by late binding - Ancona, Cerioli, et al. - 2000 |

4 |
Models of Horn theories
- Barr
- 1989
(Show Context)
Citation Context ...arate GCond = from GHorn = use essentially the same intuition. In GCond = , all model categories have a dense set of regular projectives, whereas GHorn = lacks this property (see [2, 3.19, 3.21]; see =-=[6]-=- for a similar property). ✷ 5.3 Level 3 versus Level 2: conditional equational logic and partial equational logic The difference of level 3 and level 2 lies in the presence of conditional axioms at le... |

3 | From total equational to partial order logic - Cerioli, Mossakowski, et al. - 1999 |

3 |
Logical systems for structured specifications, Theoretical Computer Science 286
- Borzyszkowski
- 2002
(Show Context)
Citation Context ...l M2 with M1|σ1 some Σ ′-model M ′ with M ′|θ2 = M1 and M ′|θ1 = M2. Σ2 = M2|σ2, there exists ✷ It is well known that in institutions with weak amalgamation, there is a normal form for specifications =-=[29,10,12]-=-, having the format derive from 〈Σ, Γ〉 by σ. Since the construction of a normal form involves pushouts and these are only determined up to isomorphism, also the normal form is only determined up to 10... |

2 | casl: The Common Algebraic Speci Language. Theoretical Computer Science - Astesiano, Bidoit, et al. - 2002 |

2 | Logical systems for structured speci Theoretical Computer Science 286 - Borzyszkowski - 2002 |

1 | Pushout complements for attributed algebras - Burmeister, Llabres, et al. |

1 | Algebraic Speci Techniques and Tools for Software Development: The ACT Approach. World Scienti - Classen, Ehrig, et al. - 1993 |