  The Edinburgh Logical Framework (LF) is a dependently type lambda calculus
that can be used to encode formal systems. The versatility of LF allows
specifications to be constructed also about the encoded systems. The Twelf
system exploits the correspondence between formulas and types to give
specifications in LF a logic programming interpretation. By interpreting
particular arguments as input and others as output, specifications can be seen
as describing non-deterministic functions. If particular such functions can be
shown to be total, they represent constructive proofs of meta-theorems of the
encoded systems. Twelf provides a suite of tools for establishing totality.
However, all the resulting proofs of meta-theorems are implicit: Twelf's
totality checking does not yield a certificate that can be given to a proof
checker. We begin the process here of making these proofs explicit. We treat
the restricted situation in Twelf where context definitions (regular worlds)
and lemmas are not used. In this setting we describe and prove correct a
translation of the steps in totality checking into an actual proof in the
companion logic M2. We intend in the long term to extend our translation to all
of Twelf and to use this work as the basis for producing proofs in the related
Abella system.
