And, Or, Not, and [something atomic] data types: What am I doing?

I am considering the problem of representing search results in a graph database. (Define such a database as a collection N of nodes and E of labeled edges, where a labeled edge consists of a triplet (l, n1, n2), where l is some kind of label and n1 and n2 are members of N.) I think a type something like the following would be useful: data Search = Fan { origin :: Node , label :: Label , members :: [Node] } | And Search Search | Or Search Search | Not Search In a Fan with origin o, members would be the set of Nodes p such that (label, o, p) is an edge. A Search is ultimately built out of Fans. I've seen this kind of thing before, and I believe it will lead me to some substantial problems that other people have already solved. What should I study?
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Jeffrey Brown