ACL2(r) support for real numbers
ACL2 supports rational numbers but not real numbers. However, starting with Version 2.5, a variant of ACL2 called ``ACL2(r)'' supports the real numbers by way of non-standard analysis. ACL2(r) was conceived and first implemented by Ruben Gamboa in his Ph.D. dissertation work, supervised by Bob Boyer with active participation by Matt Kaufmann.
ACL2(r) has the same source files as ACL2. After you download ACL2, you
can build ACL2(r) by executing the following command on the command line in
your acl2-sources directory, replacing
make large-acl2r LISP=<your_lisp>
This will create an executable in your acl2-sources directory named
Note that if you download community-books as tarfiles, then you will
automatically be obtaining the books to be certified with ACL2(r). They can
be certified from your acl2-sources directory, shown here as
make regression ACL2=<DIR>/saved_acl2r
To check that you are running ACL2(r), see if the prompt includes the
Or, look at
In ACL2 (as opposed to ACL2(r)), when we say ``real'' we mean ``rational.''
Caution: ACL2(r) should be considered experimental: although we (Kaufmann and Moore) have carefully completed Gamboa's integration of the reals into the ACL2 source code, our primary concern has been to ensure unchanged behavior when ACL2 is compiled in the default manner, i.e., without the non-standard extensions. As for every release of ACL2, at the time of a release we are unaware of soundness bugs in ACL2 or ACL2(r).
There is only limited documentation on the non-standard features of ACL2(r). We hope to provide more documentation for such features in future releases. Please feel free to query the authors if you are interested in learning more about ACL2(r). Gamboa's dissertation may also be helpful.