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Yes, you have certainly hit upon an interesting class of ideas.
You might want to explore the literature on "declarative" and
"relational" languages, check out the PROLOG language, and perhaps
look at a couple of papers Sussman and I wrote on constraint
languages (one is in the proceedings of APL '79, and another in
the AI Journal a couple of years ago).  These all have some related
notions, though not exactly what you have suggested.  You might
ponder the notions that your idea requires (1) a general method
for inverting functions calls to which appear as lambda parameters,
and (2) some means of dealing with multiple solutions when the
inverses turn out to be one-many relations.