Extracting BB′IW Inhabitants of Simple Types From Proofs in the Sequent Calculus $${LT_\to^{t}}$$ L T → t for Implicational Ticket Entailment

The decidability of the logic of pure ticket entailment means that the problem of inhabitation of simple types by combinators over the base { B, B′, I, W } is decidable too. Type-assignment systems are often formulated as natural deduction systems. However, our decision procedure for this logic, which we presented in earlier papers, relies on two sequent calculi and it does not yield directly a combinator for a theorem of ${T_\to}$. Here we describe an algorithm to extract an inhabitant from a sequent calculus proof—without translating the proof into another proof system.