Yes, of course there is a connection through the Chomskian mathematization of syntax.

But when we think about solving problems over domains and relations (e.g think about realizing that the problem of parsing requires traversing a tree like structure) we are dealing with mathematical-logical structures, not linguistic concepts. This is what I meant. I've seen a lot of OOP code that tried desperately to make code reflect the fuzzier relationships between linguistic concepts, rather than the precise ones of logical structure (a lot of this is a consequence of over-encapsulation and excessive information hiding)