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Research on integrating datalog & lambda calculus via monotonicity types
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Of the work of @AndreCensi at http://www.co-design.science ? A programming language to deal with optimization problems expressed with monotone functions. You might be able to apply your work to his...
Added expressivity compatible with your ideas: [Extensional Higher Order Prolog](https://billwadge.wordpress.com/2016/01/18/extensional-higher-order-prolog/) by Bill Wadge. There is also a very short paper specifically about datalog: [Kountouriotis, Vassilis, Panos Rondogiannis, and William W....