Plugging-in proof development environments using Locks in LF

We present two extensions of the LF Constructive Type Theory featuring monadic locks. A lock is a monadic type construct that captures the effect of an external call to an oracle. Such calls are the basic tool for plugging-in, i.e. gluing together, different Type Theories and proof development environments. The oracle can be invoked either to check that a constraint holds or to provide a suitable witness. The systems are presented in the canonical style developed by the "CMU School". The first system, CLLFP , is the canonical version of the system LLFP, presented earlier by the authors. The second system, CLLF P? , features the possibility of invoking the oracle to obtain also a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value λ-calculi, systems of Light Linear Logic, and partial functions.