4 Related Work 3 Computational Reeection in Getfol

Metafunctions: proving them correct and using them eeciently as new proof procedures. In this paper we have presented how computational reeective capabilities and mechanized logical deduction can be integrated. We have explained how this integration is achieved in GETFOL, a theorem prover where a logical metatheory MT describes both the logical properties of the object theory OT and the code implementing deduction in OT. This seems a promising step towards systems that are able to modify deductively and automatically their underlying computation machinery. In fact: 1. The code implementing the logical metatheory MT constitutes the embedded account of the system, i.e. the computational description of the system code. 2. Self introspection can be automated by means of a general purpose lifting process that, given the system code and data structures, automatically generates the embedded account. 3. Self modiication can be performed correctly by means of a general purpose attening process that, given theorems generated by the theorem prover, maps them into either new or new versions of programs 4. The mechanized MT and the lifting and attening processes allow for a exible control over computational reeection, i.e. the object level computation system and its metalevel representation can be connected with diierent, application dependent control mechanisms. Acknowledgements The work presented in this paper owes a lot to all the members of the Mechanized Reasoning Groups in Trento and Genoa. The authors would like to thank in particular Fausto Giunchiglia that has supervised and worked at the GETFOL project since 1989: without him the research described in this paper could have never been done. Other members of the Mechanized Reasoning Group in Trento and in Genoa are working on related issues. have provided useful feedback on various aspects of the work described in this paper. 14 taken this work as a starting point to deene the correct and complete logical metatheory MT, to write the suitable system code and relate it to MT, and to deene and implement lifting and attening thus providing computational reeection via logical deduction. Other deductive reasoning systems have been proposed that provide logical reeection, but that do not provide computational reeection, i.e. that do not have the possibility of using the results of deduction to produce modiications of the underlying system code. Notice that this is the case also of deductive systems that provide a logic that can be mapped to programs and to computation, like for …