Section: Software and Platforms

Profound

Participant : Kaustuv Chaudhuri [correspondant] .

Profound is a new interactive theorem proving and proof-exploration tool based on the idea of building formal proofs without the use of formal proof languages. The core concepts are a generalization of deep inference for the underlying logical formalism, and proof-by-pointing for the user-interaction metaphors.

A user proves a theorem in Profound by using the keyboard and mouse to select subformulas of the theorem and dragging them to their suitable “destination”. For instance, the formula $(A\to C)\to (A\wedge B\to C)$ is proved by dragging the two $A$s and the two $C$s to each other. This kind of direct manipulation is nevertheless constrained by the system to be both correct—meaning that no manipulation is logically unsound—and complete—meaning that every provable theorem can be proved using these metaphors.

The system is still in its early stages, but it currently supports first-order classical linear logic. It has been documented in a paper at ITP 2013 [18] .

We are in the process of extending the system to intuitionistic logics, and adding a back-end exporter for more traditional proof systems with formal proof languages such as Coq and Isabelle.