Pure Type Systems are usually described in two different ways, one that uses an external notion of computation like beta-reduction,
and one that relies on a typed judgment of equality, directly in the typing system.
For a long time, the question to know whether both presentations described the same theory. A first step toward this equivalence has
been made by Adams for a particular class of PTS called functional. Then, his result has been relaxed to all semi-full PTS in previous work.
In this paper, we finally give a positive answer to the general issue, and prove that equivalence holds for any Pure Type System.
tar file: Tested with the trunk version of Coq and v8.3. Please modify the Makefile to point out where coqc is located.
Helper file to link my phd dissertation to the .v files.
A dependency graph of the modules involved.