A verified theorem prover backend supported by a monotonic library.

*(English)*Zbl 1409.68262
Barthe, Gilles (ed.) et al., LPAR-22. 22nd international conference on logic for programming, artificial intelligence and reasoning, Awassa, Ethiopia, November 17–21, 2018. Selected papers. Manchester: EasyChair. EPiC Ser. Comput. 57, 564-582 (2018).

Summary: Building a verified proof assistant entails implementing and mechanizing the concept of a library, as well as adding support for standard manipulations on it. In this work, we develop such a mechanism for the Nuprl proof assistant, and integrate it into the formalization of
Nuprl’s meta-theory in Coq. We formally verify that standard operations on the library preserve its validity. This is a key property for any interactive theorem prover, since it ensures consistency. Some unique features of Nuprl, such as the presence of undefined abstractions, make the proof of this property nontrivial. Thus, e.g., to achieve monotonicity, the semantics of sequents had to be refined. On a broader view, this work provides a backend for a verified version of Nuprl. We use it, in turn, to develop a tool that converts proofs exported from the Nuprl proof assistant into proofs in the Coq formalization of Nuprl’s meta-theory, so as to be verified.

For the entire collection see [Zbl 1407.68021].

For the entire collection see [Zbl 1407.68021].

##### MSC:

68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |