We consider the non-deterministic extension of the call-by-value lambda
calculus, which corresponds to the additive fragment of the linear-algebraic
lambda-calculus. We define a fine-grained type system, capturing the right
linearity present in such formalisms. After proving the subject reduction and
the strong normalisation properties, we propose a translation of this calculus
into the System F with pairs, which corresponds to a non linear fragment of
linear logic. The translation provides a deeper understanding of the linearity
in our setting.Comment: 15 pages. To appear in WoLLIC 201