Several formal developments in ACL2 and Coq/SSReflect about this process have been documented at [20, 21, 24].
Namely, ACL2 when we want to be near the Common Lisp Kenzo code, Isabelle/HOL when constructiveness is not ensured and Coq/SSReflect when the objective is to execute higher order programs in a certified environment.
For instance, Isabelle/HOL (as Coq) is based on higher-order logic, while ACL2 is based on a (restricted) first order logic.
The final step of this study is to analyze whether the ACL2 schema can be completed to a full Hermite formalization, and to compare the process with a from scratch ACL2 proof (comparison from several points of view: time of design, time of development, numbers of code lines, and so on); this is still on-going work.
To export specifications from Isabelle to ACL2 (in the concrete case of matrix manipulation, let us insist at that point) we have used as an intermediary language OCL, the Object Constraint Language for UML .
The answer is affirmative (and this put again some pressure towards an ACL2 formalization, and therefore towards interoperability).
Rubio, Exporting specifications from Isabelle to ACL2 through OCL.
Pascual, A Hierarchy of Mathematical Structures in ACL2, 2012, http://www.
However, many other systems now have user communities of their own, some sizable: NQTHM, ACL2, and RRL, for example, and the higher-order logic systems HOL, NUPRL, ISABELLE, PVS, COQ, and TPS.
Some systems that are partially successful in combining techniques are PVS, NQTHM, ACL2, HOL, EVES (Craigen et al.
Verification, the most immediate commercial application, need not be done by using higher-order logic, as NQTHM and ACL2 demonstrate.