  The call-by-value lambda calculus can be endowed with permutation rules,
arising from linear logic proof-nets, having the advantage of unblocking some
redexes that otherwise get stuck during the reduction. We show that such an
extension allows to define a satisfying notion of B\"ohm(-like) tree and a
theory of program approximation in the call-by-value setting. We prove that all
lambda terms having the same B\"ohm tree are observationally equivalent, and
characterize those B\"ohm-like trees arising as actual B\"ohm trees of lambda
terms.
  We also compare this approach with Ehrhard's theory of program approximation
based on the Taylor expansion of lambda terms, translating each lambda term
into a possibly infinite set of so-called resource terms. We provide sufficient
and necessary conditions for a set of resource terms in order to be the Taylor
expansion of a lambda term. Finally, we show that the normal form of the Taylor
expansion of a lambda term can be computed by performing a normalized Taylor
expansion of its B\"ohm tree. From this it follows that two lambda terms have
the same B\"ohm tree if and only if the normal forms of their Taylor expansions
coincide.
