Abstract
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.
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Prost, F. (2007). Taming Non-compositionality Using New Binders. In: Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T. (eds) Unconventional Computation. UC 2007. Lecture Notes in Computer Science, vol 4618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73554-0_15
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DOI: https://doi.org/10.1007/978-3-540-73554-0_15
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