Meta Logical Frameworks and QPQ Position Paper

Deductive software as opposed to numerical software is gaining more and more importance in industrial applications. Numerical software can be found in components prevalent in control systems that are built into cars, trains, space vehicles, and plants, recognition systems for voice, vision, and access control, but also our internet infrastructure such as load balancing servers, and routers. Regarding fault tolerance, safety, security, and correctness, many branches of industry are employing or are thinking of employing deductive software such as model checkers, theorem provers, type checkers, and counter example generators to improve designs cost-efficiently before releasing a product. Complementary to the functionality commonly associated with deductive software is the question of how to represent derivations, proofs, traces of model checkers, counter examples, and other non-numerical domains if at all. Due to efficiency reasons, many implementations of theorem provers refrain from the explicit creation and maintenance of deductions, making it more difficult, almost impossible to connect and import deductions from one component to another, and consequently render independent third party verification of deductions impossible. For others that do, deductions are merely mathematical objects that can be manipulated, constructed, deconstructed, combined, exchanged, inspected and satisfy far reaching mathematical properties and laws. The structure of deductions is in general richer then that of numbers. Questions about how to represent axioms, inference rules, hypotheses, conclusions, formulas, terms, quantifiers, and judgments, are often a matter of personal choice and preference, leading to a significant amount of syntactical and semantical ambiguity and prohibiting the free exchange and sharing of deductive objects among software components, or entire software systems. In fact once committed to a particular representation, interfacing a deductive software system to another component can be prohibitively difficult, and the associated cost is often thought to outweigh the expected benefits. The deductions prevalent in deductive software components range from derivations in various logics, such as, temporal, first-order, or modal logics, to witness traces of model checkers. Ultimately, deductions should have adequate representations in software and should not only be described by the properties they satisfy. Of course, all of this complexity is mirrored in the deductions as well as the deductive software components whose implementations are tedious and often difficult to get right. Model checkers, for example, exploit symmetry properties to prune the state space, and theorem provers employ various optimization tech