Planar languages offer an alternative to grammars and automata for representing languages. They are based on hy- perplanes in a feature space associated with a string kernel, which corresponds to a set of linear equalities over features. This makes planar languages inherently learnable, in the sense of being identifiable in the limit from positive data, i.e. learnable in an unsupervised setting, even under strong constraints on the learner's behaviour and on computa- tional resources used.