Nuprl and HOL are both tactic based interactive theorem provers for higher order logic and both have been used in many sub stantial applications over the last decade However the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardware and software veri cation This collection would be of great bene t in applying Nuprl to veri cation problem...

Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings are powerful tools proving properties about the relation between two processes, include reasoning about convergence of distributions and stochastic dominance—a...

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/ HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As ne...

Institutions with proof-theoretic structure, here called ‘institutions with proofs’, provide a complete formal notion for the intuitive notion of logic, including both the model and the proof theoretic sides. This paper introduces a concept of proof rules for institutions and argues that the proof systems of the actual institutions with proofs are freely generated by their presentations as syst...