Relationships between logical frameworks

Astesiano, Egidio; Cerioli, Maura

doi:10.1007/3-540-56379-2_37

Cited by 23 publications

(11 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These frameworks fit the preinstitutions scheme, as well as the drastically general scheme proposed in Ehrig et al (1992). A first comparison with the approach proposed in Astesiano and Cerioli (1993) can be found in Section 6 of Salibra and Scollo (1993a), while further analysis of related work is extensively carried out in Cerioli (1993), to which we refer the reader interested in a survey of the field.…”

Section: Ultraproductsmentioning

confidence: 99%

Interpolation and compactness in categories of pre-institutions

Salibra

Scollo

1996

Math. Struct. Comp. Sci.

View full text Add to dashboard Cite

An analysis of relationships between Craig-style interpolation, compactness, and other related model-theoretic properties is carried out in the softer framework of categories of pre-institutions. While the equivalence between sentence interpolation and the Robinson property under compactness and Boolean closure is well known, a similar result under different assumptions (not involving compactness) is newly established for presentation interpolation. The standard concept of naturality of model transformation is enriched by a new property, termed restriction adequacy, which proves useful for the reduction of interpolation along pre-institution transformations. A distinct reduction theorem for the Robinson property is presented as well. A variant of the ultraproduct concept is further introduced, and the related closure property for pre-institutions is shown to be equivalent to compactness.* resting at some floor of 'palais Grothendieck'. * REL is the category of sets with binary relations as morphisms, |C| is the set of objects of category C, while ||C|| is the set of morphisms of category C. A. Salibra and G. Scollo 276Proposition 4.7. If 9~ :J-+f is adequate, then (ET)^-£ E$-%$-for all signature morphisms T:XI->^2 and I^-presentations E in ,/.Prao/ E(=T(ET) by Proposition 4.5(vi), hence E^-|=(T(ET))^ by Proposition 2.7(ii) since 3~ is adequate, therefore E#-\=Ty-(Er)y-by naturality of presentation transformation. Proposition 4.5(vi) also entails E$-\= T$-{E$-r$-), but in fact, according to Definition 4.4(ii), EJTTT is the largest set

show abstract

Section: Ultraproductsmentioning
confidence: 99%

Interpolation and compactness in categories of pre-institutions
Salibra
¹
,
Scollo
²

1996
Math. Struct. Comp. Sci.
15
0
9
0
View full text Add to dashboard Cite

show abstract

“…gcd(x, y) = if x < y then gcd(x, y -x) else if x > y then gcd (x -y, y) elsex Some specific kinds of translation implementations have been studied by Orejas (1985), Bauer and Wirsing (1988), and Kapur and Srivas (1988). The general problem of relating specifications written in terms of different logics has been treated in the framework of institutions by the definition of different kinds of institution morphisms (see, for example, Goguen and Burstall (1984), Meseguer (1989), Sannella and Tarlecki (1988a) and, especially, Astesiano and Cerioli (1993)).…”

Section: What Is An Implementation?mentioning
confidence: 99%

Algebraic implementation of abstract data types: a survey of concepts and new compositionality results
Orejas
¹
,
Navarro
²
,
Sánchez
³

1996
Math. Struct. Comp. Sci.
7
0
6
0
View full text Add to dashboard Cite

In this paper we try to shed some light on the similarities and differences in the different approaches denning the notions of implementation and implementation correctness. For obvious reasons, we do not discuss all existing approaches individually. Instead, a formal framework is introduced in order to discuss the most important ones. Additionally, we discuss some issues, which in our opinion are often misunderstood, concerning transitivity of implementation correctness and its role in the software development process. In particular, on the one hand, we show that for reasonable notions of implementation, it is almost impossible to prove transitivity of implementation correctness at the specification level. On the other hand, we show that this is not really important if the programming language satisfies the properties of horizontal and vertical composition.

show abstract

“…• •,a n )\ then f A (a) = f A '(a x ,..., a n ), otherwise f A (a) is undefined, where for each a G sf x p ... x p s 4 let a, be a(i), if a(i) is defined, ± Sj otherwise. For each arrow h' in dom{$) the translation h = ^{h') is the restriction of h to By applying some results from Astesiano and Cerioli (1993), we get that the initial model is preserved by ^0 • Definition 4.8. Let ^: / -> / b e a simulation.…”

Section: -^Df(±f)mentioning
confidence: 99%

“…Since the domain of the simulation fi D is the model class of a set of axioms, by applying a result from Astesiano and Cerioli (1993), it is possible to translate inference systems from the total disjunctive frame (which is a fragment of first-order logic) into the non-strict frame in such a way that soundness and completeness are preserved.…”

Section: Preserving Logicsmentioning
confidence: 99%

Non-strict don't care algebras and specifications
Astesiano¹,
Cerioli²
1996
Math. Struct. Comp. Sci.
Self Cite
2
0
0
0
View full text Add to dashboard Cite

Non-strict don't care functions, whose foremost representative is the ubiquitous if_then_else, play an essential role in computer science. As far as the semantics is concerned, they can be modelled by their totalizations with the appropriate use of elements representing undefinedness, as D. Scott has shown in his denotational approach. The situation is not so straightforward when we consider non-strict functions in the context of an algebraic framework; this point is discussed in the last section, where we explore the relationship between non-strict don't care and total algebras. The central part of this paper, after presenting the basic properties of the category of non-strict algebras, is an investigation of conditional algebraic specifications. It is shown that non-strict conditional specifications are equivalent to disjunctive specifications, and necessary and sufficient conditions for the existence of initial models are given. Since non-strict don't care specifications generalize both the total and the partial case, it is shown how the results for initiality can be obtained as specializations.

show abstract

Relationships between logical frameworks

Cited by 23 publications

References 11 publications

Interpolation and compactness in categories of pre-institutions

Interpolation and compactness in categories of pre-institutions

Algebraic implementation of abstract data types: a survey of concepts and new compositionality results

Non-strict don't care algebras and specifications

Contact Info

Product

Resources

About