Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas
In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Open Publishing Association
2010-06-01
|
Series: | Electronic Proceedings in Theoretical Computer Science |
Online Access: | http://arxiv.org/pdf/1006.1413v1 |
id |
doaj-6ea97cc8aac642e0b60b7f9469f99d12 |
---|---|
record_format |
Article |
spelling |
doaj-6ea97cc8aac642e0b60b7f9469f99d122020-11-24T23:39:54ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802010-06-0125Proc. GANDALF 201021423010.4204/EPTCS.25.20Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulasDavide AnconaGiovanni LagorioIn recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type systems defined in this way are idealized, since in the most interesting instantiations both the terms of the coinductive Herbrand universe and goal derivations cannot be finitely represented. However, sound and quite expressive approximations can be implemented by considering only regular terms and derivations. In doing so, it is essential to introduce a proper subtyping relation formalizing the notion of approximation between types. In this paper we study a subtyping relation on coinductive terms built on union and object type constructors. We define an interpretation of types as set of values induced by a quite intuitive relation of membership of values to types, and prove that the definition of subtyping is sound w.r.t. subset inclusion between type interpretations. The proof of soundness has allowed us to simplify the notion of contractive derivation and to discover that the previously given definition of subtyping did not cover all possible representations of the empty type. http://arxiv.org/pdf/1006.1413v1 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Davide Ancona Giovanni Lagorio |
spellingShingle |
Davide Ancona Giovanni Lagorio Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas Electronic Proceedings in Theoretical Computer Science |
author_facet |
Davide Ancona Giovanni Lagorio |
author_sort |
Davide Ancona |
title |
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas |
title_short |
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas |
title_full |
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas |
title_fullStr |
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas |
title_full_unstemmed |
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas |
title_sort |
coinductive subtyping for abstract compilation of object-oriented languages into horn formulas |
publisher |
Open Publishing Association |
series |
Electronic Proceedings in Theoretical Computer Science |
issn |
2075-2180 |
publishDate |
2010-06-01 |
description |
In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type systems defined in this way are idealized, since in the most interesting instantiations both the terms of the coinductive Herbrand universe and goal derivations cannot be finitely represented. However, sound and quite expressive approximations can be implemented by considering only regular terms and derivations. In doing so, it is essential to introduce a proper subtyping relation formalizing the notion of approximation between types. In this paper we study a subtyping relation on coinductive terms built on union and object type constructors. We define an interpretation of types as set of values induced by a quite intuitive relation of membership of values to types, and prove that the definition of subtyping is sound w.r.t. subset inclusion between type interpretations. The proof of soundness has allowed us to simplify the notion of contractive derivation and to discover that the previously given definition of subtyping did not cover all possible representations of the empty type. |
url |
http://arxiv.org/pdf/1006.1413v1 |
work_keys_str_mv |
AT davideancona coinductivesubtypingforabstractcompilationofobjectorientedlanguagesintohornformulas AT giovannilagorio coinductivesubtypingforabstractcompilationofobjectorientedlanguagesintohornformulas |
_version_ |
1725511836736946176 |