Abstract |
The parametric lambda calculus subsumes different existing $\lambda $-calculi, in particular the classical $\lambda \beta $-calculus and the $\lambda \beta $_{v}-calculus of Plotkin. Previously established results on the parametric calculus, such as as confluence and standardization, are primarily syntactical. In this paper our attention is mainly addressed to semantics, although we start again from a syntactical point of view. We propose an analysis of the notion of contextual preorders of usual operational semantics. Given a contextual preorder, we build parametric complete lattice based on a closure operator. This lattice provides a fully abstract model for the considered preorder, via a completion. |
@article{paolini08tcs,
volume = {398},
number = {1-3},
author = {Luca Paolini},
note = {Elsevier, Netherlands},
url = {http://www.di.unito.it/~paolini/papers/theories.pdf},
abstract = {The parametric lambda calculus subsumes different existing
$\lambda$-calculi, in particular the classical
$\lambda\beta$-calculus and the $\lambda\beta_v$-calculus of
Plotkin. Previously established results on the parametric
calculus, such as as confluence and standardization, are primarily
syntactical. In this paper our attention is mainly addressed to
semantics, although we start again from a syntactical point of
view. We propose an analysis of the notion of contextual preorders
of usual operational semantics. Given a contextual preorder, we
build parametric complete lattice based on a closure operator.
This lattice provides a fully abstract model for the considered
preorder, via a completion.},
title = {Parametric $\lambda$-Theories},
tag = {Theoretical Computer Science},
pages = {51-62},
journal = {Theoretical Computer Science},
year = 2008,
}
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