  We present a calculus, called the scheme-calculus, that permits to express
natural deduction proofs in various theories. Unlike $\lambda$-calculus, the
syntax of this calculus sticks closely to the syntax of proofs, in particular,
no names are introduced for the hypotheses. We show that despite its
non-determinism, some typed scheme-calculi have the same expressivity as the
corresponding typed $\lambda$-calculi.
