Major Section: ACL2-TUTORIAL
When you start up ACL2, you'll probably find yourself inside the ACL2 command loop, as indicated by the following prompt.
ACL2 !>If not, you should type
(LP). See lp, which has a lot more information about the ACL2 command loop.
You should now be in ACL2. The current ``default-defun-mode'' is
logic; the other mode is
program, which would cause the letter
to be printed in the prompt.
Logic means that any function we
define is not only executable but also is axiomatically defined in
the ACL2 logic. See defun-mode and
see default-defun-mode. For example we can define a function
my-cons as follows. (You may find it useful to start up ACL2 and
submit this and other commands below to the ACL2 command loop, as we
won't include output below.)
ACL2 !>(defun my-cons (x y) (cons x y))An easy theorem may then be proved: the
(my-cons a b)is A.
ACL2 !>(defthm car-my-cons (equal (car (my-cons a b)) a))
You can place raw Lisp forms to evaluate at start-up into file
acl2-init.lsp in your home directory, except on Windows systems. For
example, if you put the following into
acl2-init.lsp, then ACL2 will
print "HI" when it starts up.
(print "HI")But be careful; all bets are off when you submit forms to raw Lisp, so this capability should only be used when you are hacking or when you are setting some Lisp parameters (e.g.,
(setq si::*notify-gbc* nil)to turn off garbage collection notices in GCL).
Notice that unlike Nqthm, the theorem command is
defthm rather than
prove-lemma. See defthm, which explains (among other things)
that the default is to turn theorems into rewrite rules.
Various keyword commands are available to query the ACL2 ``world'',
or database. For example, we may view the definition of
invoking a command to print events, as follows.
ACL2 !>:pe my-consAlso see pe. We may also view all the lemmas that rewrite terms whose top function symbol is
carby using the following command, whose output will refer to the lemma
ACL2 !>:pl carAlso see pl. Finally, we may print all the commands back through the initial world as follows.
ACL2 !>:pbt 0See history for a list of commands, including these, for viewing the current ACL2 world.
Continue with the documentation for annotated-acl2-scripts to see a simple but illustrative example in the use of ACL2 for reasoning about functions.