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OAF: An Open Archive for Formalizations
The OAF Project builds a theoretical framework for interoperability of theorem prover libraries and implements an information system that host and align multiple libraries in a joint semantic setting.

From: 2014
To: June 2020


Funding: DFG
Program: Normalverfahren
Grant ID: KO 2428/13-1, RA 18723/1-1

Prof. Dr. Michael Kohlhase
PD Dr. Florian Rabe
Dr. Dennis Müller
M.Sc. Jonas Betzendahl
Kai Amann
Johannes-Sebastian See
M.Sc. Richard Marcus
Marcel Rupprecht
B.Sc. Annika Schmidt

Funds:
FrameIT
MathHub
MMT
MWS

OAF was a DFG-funded research project running from 2014-2020 and headed by Michael Kohlhase and Florian Rabe originally at Jacobs University Bremen and later at FAU Erlangen-Nürnberg. It centered on the integration of formal mathematical libraries.

Both the original proposal and the final report are available.

Formal/symbolic systems and their libraries are non-interoperable because they are based on differing, mutually incompatible foundations (e.g., set theory, higher-order logic, constructive type theory, etc.), library formats, and library structures, and much work is spent developing basic libraries for mathematics in each system. Moreover, the ensuing plurality of library formats forces implementors to spend time developing library organization features (e.g., distribution, browsing, search, change management) for each library format. All these investments bind resources that could be used to improve the core functionality of the systems and the scope of the libraries.

The OAF project tackled these interoperability and plurality problems by developing an open archive for formalizations, a common and open infrastructure for managing and sharing formalized mathematical knowledge such as theories, definitions, and proofs. The OAF infrastructure is designed to be scalable with respect to both the size of the knowledge base and the diversity of logical foundations. In particular, the OAF system is based on a uniform foundation-independent representation format for libraries, which allows formalizing the logical foundations alongside the libraries and thus acts as framework for aligning libraries.