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Strong Modular Proof Assistance
Reasoning Across Theories

Multiple available PhD and postdoc positions!

We invite applications for multiple PhD student and Postdoc positions funded by the ERC Starting Grant no. 714034 "SMART" at the Computational Logic research group of the Institute of Computer Science at the University of Innsbruck. Project dates: March 2017 - February 2022. Team:

Candidates for a PhD position must hold a MSc in computer science or mathematics and candidates for the postdoctoral position hold a PhD degree in computer science or mathematics.

A background in proof assistants or machine learning is a plus.

Knowledge of German is not required, the group is international and the language of communication is English.

Applications and informal inquiries are welcome, please contact Cezary Kaliszyk. Applications should include a CV and names and contact details of two references. For the Postdoc positions please include a brief research statement. Applications before June 15 will receive a full consideration.


Formal proof technology delivers an unparalleled level of certainty and security. Nevertheless, applying proof assistants to the verification of complex theories and designs is still extremely laborious. High profile certification projects, such as seL4, CompCert, and Flyspeck require tens of person-years. We recently demonstrated that this effort can be significantly reduced by combining reasoning and learning in so called hammer systems: 40% of the Flyspeck, HOL4, Isabelle/HOL, and Mizar top-level lemmas can be proved automatically.

Today’s early generation of hammers consists of individual systems limited to very few proof assistants. The accessible knowledge repositories are isolated, and there is no reuse of hammer components. It is possible to achieve a breakthrough in proof automation by developing new AI methods that combine reasoning knowledge and techniques into a smart hammer, that works over a very large part of today’s formalized knowledge. The main goal of the project is to develop a strong and uniform learning-reasoning system available for multiple logical foundations. To achieve this, we will develop: (a) uniform learning methods, (b) reusable ATP encoding components for different foundational aspects, (c) integration of proof reconstruction, and (d) methods for knowledge extraction, reuse and content merging. The single proof advice system will be made available for multiple proof assistants and their vast heterogeneous libraries.

The ultimate outcome is an advice system able to automatically prove half of Coq, ACL2, and Isabelle/ZF top-level theorems. Additionally we will significantly improve success rates for HOL provers and Mizar. The combined smart advice method together with the vast accumulated knowledge will result in a novel kind of tool, which allows working mathematicians to automatically find proofs of many simple conjectures, paving the way for the widespread use of formal proof in mathematics and computer science.