The aim of this implementation was first to implement Krivine's Af2 [1,2,3] type system, that is a system which allows to derive programs for proofs of their specifications.
The aim is now also to realize a Proof Checker used for teaching purposes in mathematical logic or even in ``usual'' mathematics.
The requirements for this new proof assistant are (it will be very difficult to reach all of them):
Anyway it is always possible to represent any first order theory, you can add axioms and first order axiom's schematas are replaced by second order axioms. You can represent this way set theory ZF in 1.2.