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Being by no means an expert in the field, I do however know of solvers such as Z3 that can generate a correct program, provided you can express your constraints as a set of logical rules, such as here.

However, in the example given above, logical rules are designed "by hand" from a set of examples, so the "compilation step" from the examples to the set of rules must be done in the user's head.

Does a system automating this "compilation step" exist (i.e automated rule set deduction from a set of examples), that would allow the user to see and make use of the set of rules?

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This is an active research topic.

Consider reading

My hope is to get funded so that RefPerSys could (in a few years) be able to deduce some rules and metarules.

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