## Section: Scientific Foundations

### Proof environments

We study how to improve mechanical tools for searching and verifying mathematical proofs so that they become practical for engineers and mathematicians to develop software and formal mathematical theories. There are two complementary objectives. The first is to improve the means of interaction between users and computers, so that the tools become usable by engineers, who have otherwise little interest in proof theory, and by mathematicians, who have little interest in programming or other kinds of formal constraints. The second objective is to make it easier to maintain large formal mathematical developments, so they can be re-used in a wide variety of contexts. Thus, we hope to increase the use of formal methods in software development, both by making it easier for beginners and by making it more efficient for expert users.