  This paper shows equivalence of several versions of applicative similarity
and contextual approximation, and hence also of applicative bisimilarity and
contextual equivalence, in LR, the deterministic call-by-need lambda calculus
with letrec extended by data constructors, case-expressions and Haskell's
seq-operator. LR models an untyped version of the core language of Haskell. The
use of bisimilarities simplifies equivalence proofs in calculi and opens a way
for more convenient correctness proofs for program transformations. The proof
is by a fully abstract and surjective transfer into a call-by-name calculus,
which is an extension of Abramsky's lazy lambda calculus. In the latter
calculus equivalence of our similarities and contextual approximation can be
shown by Howe's method. Similarity is transferred back to LR on the basis of an
inductively defined similarity. The translation from the call-by-need letrec
calculus into the extended call-by-name lambda calculus is the composition of
two translations. The first translation replaces the call-by-need strategy by a
call-by-name strategy and its correctness is shown by exploiting infinite trees
which emerge by unfolding the letrec expressions. The second translation
encodes letrec-expressions by using multi-fixpoint combinators and its
correctness is shown syntactically by comparing reductions of both calculi. A
further result of this paper is an isomorphism between the mentioned calculi,
which is also an identity on letrec-free expressions.
