Major Section: ACL2 Documentation

A view of ACL2 proofs may be obtained by way of ``proof tree displays,'' which appear in proof output (see proofs-co) when proof-tree output is enabled (see below) When ACL2 starts a proof and proof-tree output is enabled, the proof output begins with the following string.

<< Starting proof tree logging >>Then for each goal encountered during the proof, a corresponding proof tree display (as described below) is printed into the proof output: first the characters in the constant string

`*proof-tree-start-delimiter*`

are
printed, then the proof tree display, and finally the characters in the
constant string `*proof-tree-end-delimiter*`

.External tools may present proof tree displays in a separate window. In
particular, a tool distributed with the ACL2 community books customizes the
emacs environment to provide window-based proof tree displays together with
commands for traversing the proof transcript; see the discussion of ``ACL2
proof-tree support'' in file `emacs/emacs-acl2.el`

distributed with ACL2.

The command `:start-proof-tree`

enables proof-tree output, while
`:stop-proof-tree`

disables proof-tree output; see start-proof-tree and
see stop-proof-tree.

### CHECKPOINT-FORCED-GOALS -- Cause forcing goals to be checkpointed in proof trees

### PROOF-TREE-DETAILS -- proof tree details not covered elsewhere

### PROOF-TREE-EXAMPLES -- proof tree example

### START-PROOF-TREE -- start displaying proof trees during proofs

### STOP-PROOF-TREE -- stop displaying proof trees during proofs

Here is an example of a proof tree display, with comments. Lines marked with ``c'' are considered ``checkpoints,'' i.e., goals whose scrutiny may be of particular value.

( DEFTHM PLUS-TREE-DEL ...) ;currently proving PLUS-TREE-DEL 1 Goal preprocess ;"Goal" creates 1 subgoal by preprocessing 2 | Goal' simp ;"Goal'" creates 2 subgoals by simplification c 0 | | Subgoal 2 PUSH *1 ;"Subgoal 2" pushes "*1" for INDUCT ++++++++++++++++++++++++++++++ ;first pass thru waterfall completed c 6 *1 INDUCT ;Proof by induction of "*1" has | <5 more subgoals> ; created 6 top-level subgoals. At ; this point, one of those 6 has been ; proved, and 5 remain to be proved. ; We are currently working on the ; first of those 5 remaining goals.See proof-tree-examples for many examples that contain proof tree displays. But first, we summarize the kinds of lines that may appear in a proof tree display. The simplest form of a proof tree display is a header showing the current event, followed by list of lines, each having one of the following forms.

n <goal> <process> ...Says that the indicated goal created

`n`

subgoals using the indicated
process. Here ``...'' refers to possible additional information.
c n <goal> <process> ...As above, but calls attention to the fact that this goal is a ``checkpoint'' in the sense that it may be of particular interest. Some displays may overwrite ``c'' with ``>'' to indicate the current checkpoint being shown in the proof transcript.

| <goal> ... | | <k subgoals>Indicates that the goal just above this line, which is pointed to by the rightmost vertical bar (``|''), has

`k`

subgoals, none of which have yet
been processed.
| <goal> ... | | <k more subgoals>As above, except that some subgoals have already been processed.

++++++++++++++++++++++++++++++Separates successive passes through the ``waterfall''. Thus, this ``fencepost'' mark indicates the start of a new proof by induction or of a new forcing round.

See proof-tree-examples for detailed examples. See checkpoint-forced-goals to learn how to mark goals as checkpoints that force the creation of goals in forcing rounds. Finally, see proof-tree-details for some points not covered elsewhere.