Lexical type assignments don't have to be handcrafted: Buszkowski and Penn (1990) model the acquisition of the lexicon as a process of solving type equations. Their unification-based algorithms take function-argument structures as input (binary trees with a distinguised head daughter); one obtains variations depending on whether the solution should assign a unique type to every vocabulary item (so-called rigid grammars), or whether one accepts multiple assignments (k-valued grammars, with k as the maximal lexical ambiguity factor). Kanazawa (1998) studies learnable classes of grammars from this perspective, in the sense of Gold’s notion of identifiability ‘in the limit’. This line of research is by now well established, for typelogical grammars proper, and for the related pregroup formalism discussed under §6.