We present the spine calculus S-> -o & T as an efficient representation for the linear lambda-calculus lambda-> -o & T which includes intuitionistic functions (->), linear functions (-o), additive pairing (&), and additive unit (T). S-> -o & T enhances the representation of Church's simply typed lambda-calculus as abstract Böhm trees by enforcing extensionality and by incorporating linear constructs. This approach permits procedures such as unification to retain the efficient head access that characterizes first-order term languages without the overhead of performing eta-conversions at run time. Potential applications lie in proof search, logic programming, and logical frameworks based on linear type theories. We define the spine calculus, give translations of lambda-> -o & T into S-> -o & T and vice-versa, prove their soundness and completeness with respect to typing and reductions, and show that the spine calculus is strongly normalizing and admits unique canonical forms.