  In this paper we introduce a term calculus ${\cal B}$ which adds to the
affine $\lambda$-calculus with pairing a new construct allowing for a
restricted form of contraction. We obtain a Curry-Howard correspondence between
${\cal B}$ and the sub-structural logical system which we call "minimal
{\L}ukasiewicz logic", also known in the literature as the logic of hoops (a
generalisation of MV-algebras). This logic lies strictly in between affine
minimal logic and standard minimal logic. We prove that ${\cal B}$ is strongly
normalising and has the Church-Rosser property. We also give examples of terms
in ${\cal B}$ corresponding to some important derivations from our work and the
literature. Finally, we discuss the relation between normalisation in ${\cal
B}$ and cut-elimination for a Gentzen-style formulation of minimal
{\L}ukasiewicz logic.
