  In addition to their limpid interface with semantics, categorial grammars
enjoy another important property: learnability. This was first noticed by
Buskowsky and Penn and further studied by Kanazawa, for Bar-Hillel categorial
grammars.
  What about Lambek categorial grammars? In a previous paper we showed that
product free Lambek grammars where learnable from structured sentences, the
structures being incomplete natural deductions. These grammars were shown to be
unlearnable from strings by Foret and Le Nir. In the present paper we show that
Lambek grammars, possibly with product, are learnable from proof frames that
are incomplete proof nets.
  After a short reminder on grammatical inference \`a la Gold, we provide an
algorithm that learns Lambek grammars with product from proof frames and we
prove its convergence. We do so for 1-valued also known as rigid Lambek
grammars with product, since standard techniques can extend our result to
$k$-valued grammars. Because of the correspondence between cut-free proof nets
and normal natural deductions, our initial result on product free Lambek
grammars can be recovered.
  We are sad to dedicate the present paper to Philippe Darondeau, with whom we
started to study such questions in Rennes at the beginning of the millennium,
and who passed away prematurely.
  We are glad to dedicate the present paper to Jim Lambek for his 90 birthday:
he is the living proof that research is an eternal learning process.
