## Inheritance As Implicit Coercion (1991)

Venue: | Information and Computation |

Citations: | 116 - 3 self |

### BibTeX

@ARTICLE{Breazu-tannen91inheritanceas,

author = {Val Breazu-tannen and Thierry Coquand and Carl A. Gunter and Andre Scedrov},

title = {Inheritance As Implicit Coercion},

journal = {Information and Computation},

year = {1991},

volume = {93}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. Our goal is to interpret inheritances in Fun via coercion functions which are definable in the target of the translation. Existing techniques in the theory of semantic domains can be then used to interpret the extended polymorphic lambda calculus, thus providing many models for the original language. This technique makes it possible to model a rich type discipline which includes parametric polymorphism and recursive types as well as inheritance. A central difficulty in providing interpretations for explicit type disciplines featuring inheritance in the sense discussed in this paper arises from the fact that programs can type-check in more than one way. Since interpretations follow the type...

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Citation Context ...ions. The domain-theoretic interpretations that we have examined so far are summarized in the following table. The necessary properties for all but the last row can be found in [TT87, HP89b], [CGW89],=-=[ABL86]-=-, [CGW87], and [Gir87] respectively. The properties needed for the last row can be checked in a manner similar to [Gir87]. TYPES TERMS COERCIONS VARIANTS Algebraic lattices bistrict maps sep sum of la... |

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Citation Context ...e application of a constant function to a divergent argument will diverge in general. Semantically, this means that terms of higher type must be interpreted as strict functions. In a subsequent paper =-=[BGS90]-=-, three of the authors of the current document have explored the operational semantics of inheritance with a coercion semantics in a call-by-value setting. The results there are intuitively pleasing, ... |

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Citation Context ... which interpret these inheritances. Moreover, we expect that our methods will extend to the functional part of Quest [Car89a] and to the language described in [CM89], using the techniques of Coquand =-=[Coq88]-=- and Lamarche [Lam88]. Current work on inheritance and subtyping such as [CHC90] and [Mit90] will provide new challenges. We do not claim that every interesting aspect of inheritance can necessarily b... |

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Citation Context ... Bruce and Longo [BL88]. Their model interprets inheritances as identity relations between partial equivalence relations (PER's). Another model of Fun, using the interval interpretation of Cartwright =-=[Car85]-=- has been given by Martini [Mar88]. In Martini's semantics, inheritance is interpreted as a form of inclusion between intervals. This model also includes a general recursion operator for functions (bu... |

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Citation Context ...roofs of the relevant lemmas in this paper hold between the the constant coercions which interpret these inheritances. Moreover, we expect that our methods will extend to the functional part of Quest =-=[Car89a]-=- and to the language described in [CM89], using the techniques of Coquand [Coq88] and Lamarche [Lam88]. Current work on inheritance and subtyping such as [CHC90] and [Mit90] will provide new challenge... |

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Citation Context ...r a presentation of commutation rules). The so-called commutation rules for sums in proof theory are closely related to the equations fVART-CRN?g where P is an "evaluation" map (see the Appe=-=ndix B of [Gir88]-=-). 7 Conclusions and directions for further investigation The development of calculi for the representation of inheritance polymorphism and the semantics of such calculi is a growing and dynamic area ... |

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Citation Context ...erivation). For the full calculus the answer is still unknown as this paper is being written. Amadio's thesis contains some results about the relationship between explicit coercions and PER inclusion =-=[Ama91]-=-. Equational Theory. The reader has probably noted that we have never offered an equational theory for SOURCE, only one for TARGET. At the current time, the proper equational theory for SOURCE is stil... |