DoughertydLS16 (In proceedings)
|
Author(s) | Daniel J. Dougherty, Ugo de' Liguoro, Luigi Liquori and Claude Stolze |
Title | « A Realizability Interpretation for Intersection and Union Types » |
In | Programming Languages and Systems - 14th Asian Symposium, APLAS 2016, Hanoi, Vietnam, November 21-23, 2016, Proceedings |
Series | Lecture Notes in Computer Science |
Volume | 10017 |
Page(s) | 187-205 |
Year | 2016 |
Abstract |
Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional con- nectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. In this paper we present a typed lambda calculus, enriched with strong products, strong sums, and a related proof-functional logic. This calculus, directly derived from a typed calculus previously defined by two of the current authors, has been proved isomorphic to the well-known Barbanera-Dezani-Ciancaglini-deᅵLiguoro type assignment system. We present a logic featuring two proof-functional connectives, namely strong conjunction and strong disjunction. We prove the typed calculus to be isomorphic to the logic and we give a realizability semantics using Mintsᅵ realizers and a completeness theorem. A prototype implementation is also described. |
Download the complete article:
@inproceedings{DoughertydLS16,
volume = {10017},
author = {Daniel J. Dougherty and Ugo de' Liguoro and Luigi Liquori and Claude
Stolze},
series = {Lecture Notes in Computer Science},
booktitle = {Programming Languages and Systems - 14th Asian Symposium, {APLAS}
2016, Hanoi, Vietnam, November 21-23, 2016, Proceedings},
tag = {{APLAS 2016}},
localfile = {http://www.di.unito.it/~deligu/papers/APLAS-RealizIntUnion.pdf},
title = {A Realizability Interpretation for Intersection and Union Types},
abstract = {Proof-functional logical connectives allow reasoning about the
structure of logical proofs, in this way giving to the latter the
status of first-class objects. This is in contrast to classical
truth-functional con- nectives where the meaning of a compound
formula is dependent only on the truth value of its subformulas.
In this paper we present a typed lambda calculus, enriched with
strong products, strong sums, and a related proof-functional
logic. This calculus, directly derived from a typed calculus
previously defined by two of the current authors, has been proved
isomorphic to the well-known
Barbanera-Dezani-Ciancaglini-de�Liguoro type assignment system.
We present a logic featuring two proof-functional connectives,
namely strong conjunction and strong disjunction. We prove the
typed calculus to be isomorphic to the logic and we give a
realizability semantics using Mints� realizers and a
completeness theorem. A prototype implementation is also
described.},
doi = {10.1007/978-3-319-47958-3_11},
pages = {187-205},
year = {2016},
}
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