## Coalgebraic Semantics of an Imperative Class Based Language (2003)

Venue: | Dipartimento di Matematica e Infomatica, Universita’ di |

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Honsell03coalgebraicsemantics,

author = {Furio Honsell and Marina Lenisa},

title = {Coalgebraic Semantics of an Imperative Class Based Language},

institution = {Dipartimento di Matematica e Infomatica, Universita’ di},

year = {2003}

}

### OpenURL

### Abstract

We study two observational equivalences of Fickle programs. Fickle is a class-based object oriented imperative language...

### Citations

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Citation Context ... us to apply the standard coalgebraic approach, provided we move to a category where the functor F so defined admits a final coalgebra, e.g. the category Class ∗ of classes of non-wellfounded sets o=-=f [Acz88]. Then we can-=- define the coalgebraic semantics of P as the unique morphism [ ] P : (refobject, α) → (ΩF , αΩF ) into the final F -coalgebra (ΩF , αΩF ). An interesting issue now arises, namely that of... |

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Citation Context ...ld consider a more sophisticated notion of program specification, involving a first-order logic for expressing conditions on the fields. This would be useful for studying program refinement (see e.g. =-=[ST97]-=-). But, for our purposes, our simpler definition is sufficient. Two programs P1, P2, implementing the same program specification P, can be taken to be equivalent, when for any possible main method, th... |

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Citation Context ...m yield the same observations and equivalent next states. Introduction In recent years, in the Global Computing Community, there has been growing interest in class-based object oriented languages. In =-=[DDDG02]-=-, the imperative typed class-based language Fickle has been introduced, which extends Java with re-classification. Re-classification allows objects to change class membership dynamically, while retain... |

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Citation Context ...oalgebraic semantics originated with Aczel-Mendler, Rutten-Turi, for CCSlike languages,[Acz88,AM89,Acz93,RT94], and it was further generalized to λcalculus, [HL95], higher-order imperative languages,=-= [Len96],-=- object-oriented languages in a functional setting, [Rei95,Jac96], π-calculus, [HLMP98]. The gist of the coalgebraic semantics paradigm (final semantics) is to view the interpretation function from s... |

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Citation Context ...rograms w.r.t. the equivalences ≈P and �. Coalgebraic semantics originated with Aczel-Mendler, Rutten-Turi, for CCSlike languages,[Acz88,AM89,Acz93,RT94], and it was further generalized to λcalcu=-=lus, [HL95],-=- higher-order imperative languages, [Len96], object-oriented languages in a functional setting, [Rei95,Jac96], π-calculus, [HLMP98]. The gist of the coalgebraic semantics paradigm (final semantics) i... |

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Citation Context ...cannot be described, since they would produce a contravariant occurrence of the variable in the corresponding functor. Extensions of the coalgebraic paradigm to mixed functors have been considered in =-=[Tew00]-=-, but they are rather complex and they cover only a restricted range of cases. In this paper, we extend the approach of [Rei95,Jac96], in order to model, in an imperative setting, general programs, i.... |

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Three Case studies in FickleII
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Citation Context ...xpr := if e then e else e | var:=e | e;e | sVal this | var | new c | e.m(e ∗ ) | id⇓c var := x | e.f sVal := true | false | null id := this | x Table 1. Syntax of Fickle 4sExample 1 (Lists in Fick=-=le, [Dro02]-=-). The Fickle program below consists of three classes: the root class List (which is abstract, since it contains only a sequence of method declarations) together with two subclasses, EmptyList and Non... |

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Citation Context ...[Acz88,AM89,Acz93,RT94], and it was further generalized to λcalculus, [HL95], higher-order imperative languages, [Len96], object-oriented languages in a functional setting, [Rei95,Jac96], π-calculus=-=, [HLMP98]-=-. The gist of the coalgebraic semantics paradigm (final semantics) is to view the interpretation function from syntax to semantics as a final mapping in a suitable category. To this end the semantics ... |

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Citation Context ... a coalgebraic bisimilarity, i.e. as greatest coalgebraic bisimulation. The relations between coalgebraic and algebraic semantics have been studied in the general categorical setting of bialgebras by =-=[TP97].-=- Bialgebras combine an algebraic and a coalgebraic structure. When there is a connection between the two structures, i.e. in the case of λ-bialgebras of [TP97], then the final semantics coincides wit... |

1 | Let F : C → C. A F -coalgebra is a pair (X, αX), where αX : X → F X is an arrow in C. F -coalgebras can be endowed with the structure of a category by defining F -coalgebra morphisms as follows. f : (X, αX) → (Y, αY ) is an F -coalgebra morphism if f : X - Definition |