  Using a call-by-value functional language as an example, this article
illustrates the use of coinductive definitions and proofs in big-step
operational semantics, enabling it to describe diverging evaluations in
addition to terminating evaluations. We formalize the connections between the
coinductive big-step semantics and the standard small-step semantics, proving
that both semantics are equivalent. We then study the use of coinductive
big-step semantics in proofs of type soundness and proofs of semantic
preservation for compilers. A methodological originality of this paper is that
all results have been proved using the Coq proof assistant. We explain the
proof-theoretic presentation of coinductive definitions and proofs offered by
Coq, and show that it facilitates the discovery and the presentation of the
results.
