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Published in:
2007 | OriginalPaper | Chapter
Taming Non-compositionality Using New Binders
Author : Frédéric Prost
Published in: Unconventional Computation
Publisher: Springer Berlin Heidelberg
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We propose an extension of the traditional
λ
-calculus in which terms are used to control an outside computing device (quantum computer, DNA computer...). We introduce two new binders:
ν
and
ρ
. In
νx
.
M
,
x
denotes an abstract resource of the outside computing device, whereas in
ρx
.
M
,
x
denotes a concrete resource. These two binders have different properties (in terms of
α
-conversion, scope extrusion, convertibility) than the ones of standard
λ
-binder. We illustrate the potential benefits of our approach with a study of a quantum computing language in which these new binders prove meaningful. We introduce a typing system for this quantum computing framework in which linearity is only required for concrete quantum bits offering a greater expressiveness than previous propositions.