An Investigation of Abadi and Cardelli's Untyped Calculus of Objects

Forfattere

  • Jacob Johannsen

DOI:

https://doi.org/10.7146/brics.v15i6.21941

Resumé

We study the relationship between the natural (big-step) semantics and the reduction (small-step) semantics of Abadi and Cardelli's untyped calculus of objects. By applying Danvy et al.'s functional correspondence to the natural semantics, we derive an abstract machine for this calculus, and by applying Danvy et al.'s syntactic correspondence to the reduction semantics, we also derive an abstract machines for this calculus. These two abstract machines are identical. The fact that the machines are identical, and the fact that they have been derived using meaning-preserving program transformations, entail that the derivation constitutes a proof of equivalence between natural semantics and the reduction semantics. The derivational nature of our proof contrasts with Abadi and Cardelli's soundness proof, which was carried out by pen and paper. We also note that the abstract machine is new.

To move closer to actual language implementations, we reformulate the calculus to use explicit substitutions. The reformulated calculus is new. By applying the functional and syntactic correspondences to natural and reduction semantics of this new calculus, we again obtain two abstract machines. These two machines are also identical, and as such, they establish the equivalence of the natural semantics and the reduction semantics of the new calculus.

Finally, we prove that the two abstract machines are strongly bisimilar. Therefore, the two calculi are computationally equivalent.

Downloads

Publiceret

2008-06-12

Citation/Eksport

Johannsen, J. (2008). An Investigation of Abadi and Cardelli’s Untyped Calculus of Objects. BRICS Report Series, 15(6). https://doi.org/10.7146/brics.v15i6.21941

Nummer

Nr. 6 (2008): RS-6 An Investigation of Abadi and Cardelli's Untyped Calculus of Objects

Sektion

Artikler

Licens

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

    1. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  1. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).