Abstract:We begin by explaining how any context-free grammar encodes a functor of
operads from a freely generated operad into a certain "operad of spliced
words". This motivates a more general notion of CFG over any category $C$,
defined as a finite species $S$ equipped with a color denoting the start symbol
and a functor of operads $p : Free[S] \to W[C]$ into the operad of spliced
arrows in $C$. We show that many standard properties of CFGs can be formulated
within this framework, and that usual closure properties of … Show more
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