Subformula linking as an interaction method

Current techniques for building formal proofs interactively involve one or several proof languages for instructing an interpreter of the languages to build or check the proof being described. These linguistic approaches have a drawback: the languages are not generally portable, even though the nature of logical reasoning is universal. We propose a somewhat speculative alternative method that lets the user directly manipulate the text of the theorem, using non-linguistic metaphors. It uses a proof formalism based on linking subformulas, which is a variant of deep inference (inference rules are allowed to apply in any formula context) where the relevant formulas in a rule are allowed to be arbitrarily distant. We substantiate the design with a prototype implementation of a linking-based interactive prover for first-order classical linear logic.