Context-free multilanguages

Abstract

This article is a sketch of ideas that were once intended to appear in the author's famous series, "The Art of Computer Programming". He generalizes the notion of a context-free language from a set to a multiset of words over an alphabet. The idea is to keep track of the number of ways to parse a string. For example, "fruit flies like a banana" can famously be parsed in two ways; analogous examples in the setting of programming languages may yet be important in the future. The treatment is informal but essentially rigorous.