REAL

ACL2(r) support for real numbers
Major Section:  ACL2 Documentation

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. The Makefile provided with ACL2 has target large-acl2r for building ACL2(r) images. To see which image you have, see if the prompt includes the string ``(r)'', e.g.:

ACL2(r) !>
Or, look at (@ acl2-version) and see if ``(r)'' is a substring.

In ACL2 (as opposed to ACL2(r)), when we say ``real'' we mean ``rational.''

Caution: ACL2(r) should be considered experimental as of Version 2.5: although we (Kaufmann and Moore) have carefully completed Gamboa's integration of the reals into the ACL2 source code, our primary concern to date 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 this release we are unaware of soundness bugs in ACL2 Version 2.5. We are confident that ACL2(r) will behave much as it does now and will ultimately be sound; but we have not yet argued the soundness of every detail of the integration.

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.