  Connection calculi allow for very compact implementations of goal-directed
proof search. We give an overview of our work related to connection tableaux
calculi: First, we show optimised functional implementations of clausal and
nonclausal proof search, including a consistent Skolemisation procedure for
machine learning. Then, we show two guidance methods based on machine learning,
namely reordering of proof steps with Naive Bayesian probablities, and
expansion of a proof search tree with Monte Carlo Tree Search. Finally, we give
a translation of connection proofs to LK, enabling proof certification and
automatic proof search in interactive theorem provers.
