## 11 Coq Proof General

Coq Proof General is an instantiation of Proof General for the Coq proof assistant. It supports most of the generic features of Proof General.

### 11.1 Coq-specific commands

Coq Proof General supplies the following key-bindings:

`C-c C-a C-i`

  Inserts “intros ” and also introduces the name of the hypothesis proposed by coq on the current goal.

`C-c C-a C-s`

  Show the goal (enter for the current goal, i <enter> for the ith goal).

  Add the prefix C-u to see the answer with all pretty printing options temporarily disable (Set Printing All).

`C-c C-a C-c`

  Prompts for “Check ” query arguments, the default input name is built from the identifier under the cursor.

  Add the prefix C-u to see the answer with all pretty printing options temporarily disable (Set Printing All).

`C-c C-a C-p`

  The same for a “Print ” query.

`C-c C-a C-b`

  The same for a “About ” query.

`C-c C-a C-a`

  The same for a “SearchAbout ” query (no C-u prefix).

`C-c C-a C-o`

  The same for a Search “SearchIsos” (no C-u prefix).

`C-c C-a C-)`

  Inserts “End <section-name>.” (this should work well with nested sections).

### 11.2 Using the Coq project file

The Coq project file is the recommended way to configure the Coq load path and the mapping of logical module names to physical file path’. The project file is typically named `_CoqProject` and must be located at the directory root of your Coq project. Proof General searches for the Coq project file starting at the current directory and walking the directory structure upwards. The Coq project file contains the common options (especially `-R`) and a list of the files of the project, see the Coq reference manual, Section 15.3, “Creating a Makefile for Coq modules”.

The Coq project file should contain something like:

    -R foo bar
    -I foo2
    -arg -foo3
    file.v
    bar/other_file.v
    ...

Proof General only extracts the common options from the Coq project file and uses them for `coqtop` background processes as well as for `coqdep` and `coqc` when you use the auto compilation feature, Automatic Compilation in Detail. For the example above, Proof General will start `coqtop -foo3 -R foo bar -I foo2`.

Remarque: `-arg` must be followed by one and only one option to pass to coqtop/coqc, use several `-arg` to issue several options. One per line (limitation of Proof General).

For backward compatibility, one can also configure the load path with the option `coq-load-path`, but this is not compatible with `CoqIde` or `coq_makefile`.

#### 11.2.1 Changing the name of the coq project file

To change the name of the Coq project file, configure `coq-project-filename` (select menu `Proof-General -> Advanced -> Customize -> Coq` and scroll down to “Coq Project Filename”). Customizing `coq-project-filename` this way will change the Coq project file name permanently and globally.

If you only want to change the name of the Coq project file for one project you can set the option as local file variable, Using file variables. This can be done either directly in every file or once for all files of a directory tree with a `.dir-local.el` file, See (emacs)Directory Variables. The file `.dir-local.el` should then contain

    ((coq-mode . ((coq-project-filename . "myprojectfile"))))

Note that variables set in `.dir-local.el` are automatically made buffer local (such that files in different directories can have their independent setting of `coq-project-filename`). If you make complex customizations using `eval` in `.dir-local.el`, you might want to add appropriate calls to `make-local-variable`.

Documentation of the user option `coq-project-filename`:

Variable: coq-project-filename

  The name of coq project file.
  The coq project file of a coq developpement (Cf Coq documentation on "makefile generation") should contain the arguments given to coq_makefile. In particular it contains the -I and -R options (preferably one per line). If ‘`coq-use-coqproject`’ is t (default) the content of this file will be used by proofgeneral to infer the ‘``coq-load-path``’ and the ‘``coq-prog-args``’ variables that set the coqtop invocation by proofgeneral. This is now the recommended way of configuring the coqtop invocation. Local file variables may still be used to override the coq project file’s configuration. .dir-locals.el files also work and override project file settings.

#### 11.2.2 Disabling the coq project file mechanism

To disable the Coq project file feature in Proof General, set `coq-use-project-file` to nil (select menu `Proof-General -> Advanced -> Customize -> Coq` and scroll down to “Coq Use Project File”).

Variable: coq-use-project-file

  If t, when opening a coq file read the dominating _CoqProject.
  If t, when a coq file is opened, Proof General will look for a project file (see ‘``coq-project-filename``’) somewhere in the current directory or its parent directories. If there is one, its contents are read and used to determine the arguments that must be given to coqtop. In particular it sets the load path (including the -R lib options) (see ‘``coq-load-path``’).

You can also use the .dir-locals.el as above to configure this setting on a per project basis.

### 11.3 Multiple File Support

Since version 4.1 Coq Proof General has multiple file support. It consists of the following points:

Restarting `coqtop` when changing the active scripting buffer

  Different buffers may require different load path’ or different sets of `-I` options. Because Coq cannot undo changes in the load path, Proof General is forced to restart `coqtop` when the active scripting buffer changes.

Locking ancestors

  Locking those buffers on which the current active scripting buffer depends. This is controlled by the user option `coq-lock-ancestors`, Customizing Coq Multiple File Support and Locking Ancestors.

(Re-)Compilation

  Before a `Require` command is processed it may be necessary to save and compile some buffers. Because this feature conflicts with existing customization habits, it is switched off by default. When it is properly configured, one can freely switch between different buffers. Proof General will compile the necessary files whenever a `Require` command is processed.

  The compilation feature does currently not support ML modules.

There are actually two implementations of the Recompilation feature.

Parallel asynchronous compilation (stable, default)

  With parallel compilation, coqdep and coqc are launched in the background and Proof General stays responsive during compilation. Up to ‘coq-max-background-compilation-jobs’ coqdep and coqc processes may run in parallel. Coq 8.5 quick compilation is supported with various modes, Quick compilation and .vio Files.

Synchronous single threaded compilation (obsolete)

  With synchronous compilation, coqdep and coqc are called synchronously for each Require command. Proof General is locked until the compilation finishes. Coq 8.5 quick compilation is not supported with synchronously compilation.

To enable the automatic compilation feature, you have to follow these points:

- Set the option `coq-compile-before-require` (menu `Coq -> Auto Compilation -> Compile Before Require`) to enable compilation before processing `Require` commands and set `coq-compile-parallel-in-background` (menu `Coq -> Auto Compilation -> Parallel background compilation`) for parallel asynchronous compilation (recommended).
- Nonstandard load path elements must be configured via a Coq project file (this is the recommended option), Using the Coq project file or via option `coq-load-path`. `-I` or `-R` options in `coq-prog-name` or `coq-prog-args` must be deleted.
- Configure `coq-max-background-compilation-jobs` if you want to limit the number of parallel background jobs and set `coq-compile-keep-going` (menu `Coq -> Auto Compilation -> Keep going`) to let compilation continue after the first error.

To abort parallel background compilation, use `C-c C-c` (`proof-interrupt-process`), the tool bar interrupt icon, the menu entry `Abort Background Compilation` (menu `Coq -> Auto Compilation`) or kill the Coq toplevel via `C-c C-x` (`proof-shell-exit`). To abort synchronous single threaded compilation, simply hit `C-g`.

#### 11.3.1 Automatic Compilation in Detail

When `coq-compile-before-require` is enabled, Proof General looks for `Require` commands in text that gets asserted (i.e., in text that is moved from the editing region to the queue region, Locked queue and editing regions). If Proof General finds a `Require` command, it checks the dependencies and (re-)compiles files as necessary. The Require command and the following text is only sent to Coq after the compilation finished.

`Declare ML Module` commands are currently not recognized.

Proof General uses `coqdep` in order to translate the qualified identifiers in `Require` commands to coq library file names and to determine library dependencies. Because Proof General cannot know whether files are updated outside of Emacs, it checks for every `Require` command the complete dependency tree and recompiles files as necessary.

Output from the compilation is only shown in case of errors. It then appears in the buffer `*coq-compile-response*`. One can use `C-x `` (bound to `next-error`, See (emacs)Compilation Mode) to jump to error locations. Sometimes the compilation commands do not produce error messages with location information, then `C-x `` does only work in a limited way.

For Coq version 8.5 or newer, the option `coq-compile-quick` controls how `-quick` and `.vio` files are used, Quick compilation and .vio Files. This can also be configured in the menu `Coq -> Auto Compilation`.

Similar to `make -k`, background compilation can be configured to continue as far as possible after the first error, see option `coq-compile-keep-going` (menu `Coq -> Auto Compilation -> Keep going`). The keep-going option only applies to errors from `coqdep` and `coqc`. For all other errors (for instance when the translation from logical module names to physical files fails or when starting `coqc` or `coqdep` fails), the compilation is immediately aborted.

When a `Require` command causes a compilation of some files, one may wish to save some buffers to disk beforehand. The option `coq-compile-auto-save` controls how and which files are saved. There are two orthogonal choices: One may wish to save all or only the Coq source files, and, one may or may not want to confirm the saving of each file.

With ‘coq-compile-parallel-in-background’ (menu `Coq -> Settings -> Compile Parallel In Background`) you can choose between two implementations of internal compilation.

Synchronous single threaded compilation

  This is the old, now outdated version supported since Proof General 4.1. This method starts coqdep and coqc processes one after each other in synchronous subprocesses. Your Emacs session will be locked until compilation finishes. Use `C-g` to interrupt compilation. This method supports compilation via an external command (such as `make`), see option `coq-compile-command` in Customizing Coq Multiple File Support below. Synchronous compilation does not support the quick compilation of Coq 8.5.

Parallel asynchronous compilation

  This is the newer and default version added in Proof General version 4.3. It runs up to `coq-max-background-compilation-jobs` coqdep and coqc jobs in parallel in asynchronous subprocesses (or uses all your CPU cores if `coq-max-background-compilation-jobs` equals `'all-cpus`). Your Emacs will stay responsive during compilation. To abort the background compilation process, use `C-c C-c` (`proof-interrupt-process`), the tool bar interrupt icon, the menu entry `Abort Background Compilation` (menu `Coq -> Auto Compilation`) or kill the Coq toplevel via `C-c C-x` (`proof-shell-exit`).

  For the usual case, you have at most ‘coq-max-background-compilation-jobs’ parallel processes including your Proof General process. The usual case applies, when the Require commands are the first commands in the file. If you have other commands between two Require commands or before the first Require, then you may see Proof General and Coq running in addition to ‘coq-max-background-compilation-jobs’ compilation jobs.

  Depending on the setting of `coq-compile-quick` (which can also be set via menu `Coq -> Auto Compilation`) Proof General produces `.vio` or `.vo` files and deletes outdated `.vio` or `.vo` files to ensure Coq does not load outdated files. When `quick-and-vio2vo` is selected a vio2vo compilation starts when the `Require` command had been processed, Quick compilation and .vio Files.

  Actually, even with this method, not everything runs asynchronously. To translate module identifiers from the Coq sources into file names, Proof General runs coqdep on an automatically generated, one-line file. These coqdep jobs run synchronously while the Require commands are parsed. The coqdep jobs on the real source files do run asynchronously in the background.

#### 11.3.2 Locking Ancestors

Locking ancestor files works as a side effect of dependency checking. This means that ancestor locking does only work when Proof General performs dependency checking and compilation itself. If an external command is used, Proof General does not see all dependencies and can therefore only lock direct ancestors.

In the default setting, when you want to edit a locked ancestor, you are forced to completely retract the current scripting buffer. You can simplify this by setting `proof-strict-read-only` to `'retract` (menu `Proof-General -> Quick Options -> Read Only -> Undo On Edit`). Then typing in some ancestor will immediately retract you current scripting buffer and unlock that ancestor.

You have two choices, if you don’t like ancestor locking in its default way. You can either switch ancestor locking completely off via `coq-lock-ancestors` (Customizing Coq Multiple File Support) or you can generally permit editing in locked sections with selecting `Proof-General` -> `Quick Options` -> `Read Only` -> `Freely Edit` (which will set the option `proof-strict-read-only` to `nil`).

[The right behaviour for Coq, namely to retract the current scripting buffer only up to the appropriate `Require` command, would be quite difficult to implement in the current Proof General infrastructure. Further, it has only dubious benefit, as Require commands are usually on the top of each file.]

#### 11.3.3 Quick compilation and .vio Files

Proof General supports quick compilation only with the parallel asynchronous compilation. There are 4 modes that can be configured with `coq-compile-quick` or by selecting one of the radio buttons in the `Coq -> Auto Compilation` menu.

Use the default `no-quick`, if you have not yet switched to `Proof using`. Use `quick-no-vio2vo`, if you want quick recompilation without producing .vo files. Option `quick-and-vio2vo` recompiles with `-quick` as `quick-no-vio2vo` does, but schedules a vio2vo compilation for missing `.vo` files after a certain delay. Finally, use `ensure-vo` for only importing `.vo` files with complete universe checks.

Note that with all of `no-quick`, `quick-no-vio2vo` and `quick-and-vio2vo` your development might be unsound because universe constraints are not fully present in `.vio` files.

There are a few peculiarities of quick compilation in Coq 8.5 that one should be aware of.

- Quick compilation runs noticeably slower when section variables are not declared via `Proof using`.
- Even when section variables are declared, quick compilation runs slower on very small files, probably because of the comparatively big size of the `.vio` files. You can speed up quick compilation noticeably by running on a RAM disk.
- If both, the `.vo` and the `.vio` files are present, Coq load the more recent one, regardless of whether `-quick`, and emits a warning when the `.vio` is more recent than the `.vo`.
- Under some circumstances, files compiled when only the `.vio` file of some library was present are not compatible with (other) files compiled when also the `.vo` file of that library was present, see Coq issue #5223 for details. As a rule of thumb one should run vio2vo compilation only before or after library loading.
- Apart from the previous point, Coq works fine when libraries are present as a mixture of `.vio` and `.vo` files. While `make` insists on building all prerequisites as either `.vio` or `.vo` files, Proof General just checks whether an up-to-date compiled library file is present.
- To ensure soundness, all library dependencies must be compiled as `.vo` files and loaded into one Coq instance.

Detailed description of the 4 modes:

`no-quick`

  Compile outdated prerequisites without `-quick`, producing `.vo` files, but don’t compile prerequisites for which an up-to-date `.vio` file exists. Delete or overwrite outdated `.vo` files.

`quick-no-vio2vo`

  Compile outdated prerequisites with `-quick`, producing `.vio` files, but don’t compile prerequisites for which an up-to-date `.vo` file exists. Delete or overwrite outdated `.vio` files.

`quick-and-vio2vo`

  Same as `quick-no-vio2vo`, but start vio2vo processes for missing `.vo` files after a certain delay when library compilation for the current queue region has finished. With this mode you might see asynchronous errors from vio2vo compilation while you are processing stuff far below the last require. vio2vo compilation is done on a subset of the available cores controlled by option `coq-compile-vio2vo-percentage`, Customizing Coq Multiple File Support. When `coq-compile-keep-going` is set, vio2vo compilation is scheduled for those files for which `coqc` compilation was successful.

  Warning: This mode does only work when you process require commands in batches. Slowly single-stepping through require’s might lead to inconsistency errors when loading some libraries, see Coq issue #5223. To mitigate this risk, vio2vo compilation only starts after a certain delay after the last require command of the current queue region has been processed. This is controlled by `coq-compile-vio2vo-delay`, Customizing Coq Multiple File Support.

`ensure-vo`

  Ensure that all library dependencies are present as `.vo` files and delete outdated `.vio` files or `.vio` files that are more recent than the corresponding `.vo` file. This setting is the only one that ensures soundness.

The options `no-quick` and `ensure-vo` are compatible with Coq 8.4 or older. When Proof General detects such an older Coq version, it changes the quick compilation mode automatically. For this to work, the option `coq-compile-quick` must only be set via the customization system or via the menu.

#### 11.3.4 Customizing Coq Multiple File Support

The customization settings for multiple file support of Coq Proof General are in a separate customization group, the `coq-auto-compile` group. To view all options in this group do `M-x customize-group coq-auto-compile` or select menu entry `Proof-General -> Advanced -> Customize -> Coq -> Coq Auto Compile -> Coq Auto Compile`.

Variable: coq-compile-before-require

  If non-nil, check dependencies of required modules and compile if necessary.
  If non-nil ProofGeneral intercepts "Require" commands and checks if the required library module and its dependencies are up-to-date. If not, they are compiled from the sources before the "Require" command is processed.

  This option can be set/reset via menu ‘`Coq -> Auto Compilation -> Compile Before Require`’.

Variable: coq-compile-auto-save

  Buffers to save before checking dependencies for compilation.
  There are two orthogonal choices: Firstly one can save all or only the coq buffers, where coq buffers means all buffers in coq mode except the current buffer. Secondly, Emacs can ask about each such buffer or save all of them unconditionally.

  This makes four permitted values: `'ask-coq` to confirm saving all modified Coq buffers, `'ask-all` to confirm saving all modified buffers, `'save-coq` to save all modified Coq buffers without confirmation and `'save-all` to save all modified buffers without confirmation.

The following options configure parallel compilation.

Variable: coq-compile-parallel-in-background

  Choose the internal compilation method.
  When Proof General compiles itself, you have the choice between two implementations. If this setting is nil, then Proof General uses the old implementation and compiles everything sequentially with synchronous job. With this old method Proof General is locked during compilation. If this setting is t, then the new method is used and compilation jobs are dispatched in parallel in the background. The maximal number of parallel compilation jobs is set with ‘``coq-max-background-compilation-jobs``’.

  This option can be set/reset via menu ‘`Coq -> Auto Compilation -> Compile Parallel In Background`’.

The option `coq-compile-quick` is described in detail above, Quick compilation and .vio Files

Variable: coq-compile-keep-going

  Continue compilation after the first error as far as possible.
  Similar to ‘``make -k`’’, with this option enabled, the background compilation continues after the first error as far as possible. With this option disabled, background compilation is immediately stopped after the first error.

  This option can be set/reset via menu ‘`Coq -> Auto Compilation -> Keep going`’.

Variable: coq-max-background-compilation-jobs

  Maximal number of parallel jobs, if parallel compilation is enabled.
  Use the number of available CPU cores if this is set to `'all-cpus`. This variable is the user setting. The value that is really used is ‘``coq--internal-max-jobs``’. Use ‘``coq-max-jobs-setter``’ or the customization system to change this variable. Otherwise your change will have no effect, because ‘``coq--internal-max-jobs``’ is not adapted.

Variable: coq-max-background-vio2vo-percentage

  Percentage of ‘``coq-max-background-vio2vo-percentage``’ for vio2vo jobs.
  This setting configures the maximal number of vio2vo background jobs (if you set ‘``coq-compile-quick``’ to `'quick-and-vio2vo`) as percentage of ‘``coq-max-background-compilation-jobs``’.

Variable: coq-compile-vio2vo-delay

  Delay in seconds for the vio2vo compilation.
  This delay helps to avoid running into a library inconsistency with `'quick-and-vio2vo`, see Coq issue #5223.

Locking ancestors can be disabled with the following option.

Variable: coq-lock-ancestors

  If non-nil, lock ancestor module files.
  If external compilation is used (via ‘``coq-compile-command``’) then only the direct ancestors are locked. Otherwise all ancestors are locked when the "Require" command is processed.

The sequential compilation setting supports an external compilation command (which could be a parallel running `make`). For this set `coq-compile-parallel-in-background` to `nil` and configure the compilation command in `coq-compile-command`.

Variable: coq-compile-command

  External compilation command. If empty ProofGeneral compiles itself.
  If unset (the empty string) ProofGeneral computes the dependencies of required modules with coqdep and compiles as necessary. This internal dependency checking does currently not handle ML modules.

  If a non-empty string, the denoted command is called to do the dependency checking and compilation. Before executing this command the following keys are substituted as follows:

        %p  the (physical) directory containing the source of
            the required module
        %o  the Coq object file in the physical directory that will
            be loaded
        %s  the Coq source file in the physical directory whose
            object will be loaded
        %q  the qualified id of the "Require" command
        %r  the source file containing the "Require"

  For instance, "make -C %p %o" expands to "make -C bar foo.vo" when module "foo" from directory "bar" is required.

  After the substitution the command can be changed in the minibuffer if ‘``coq-confirm-external-compilation``’ is t.

Variable: coq-confirm-external-compilation

  If set let user change and confirm the compilation command.
  Otherwise start the external compilation without confirmation.

  This option can be set/reset via menu ‘`Coq -> Settings -> Confirm External Compilation`’.

The preferred way to configure the load path and the mapping of logical library names to physical file path is the Coq project file, Using the Coq project file. Alternatively one can configure these things with the following options.

Variable: coq-load-path

  Non-standard coq library load path.
  This list specifies the LoadPath extension for coqdep, coqc and coqtop. Usually, the elements of this list are strings (for "-I") or lists of two strings (for "-R" dir path and "-Q" dir path).

  The possible forms of elements of this list correspond to the 4 forms of include options (‘`-I`’ ‘`-Q`’ and ‘`-R`’). An element can be

        - A list of the form ‘(’ocamlimport dir)', specifying (in 8.5) a
          directory to be added to ocaml path (‘-I’).
        - A list of the form ‘(’rec dir path)' (where dir and path are
          strings) specifying a directory to be recursively mapped to the
          logical path ‘path’ (‘-R dir path’).
        - A list of the form ‘(’recnoimport dir path)' (where dir and
          path are strings) specifying a directory to be recursively
          mapped to the logical path ‘path’ (‘-Q dir path’), but not
          imported (modules accessible for import with qualified names
          only).  Note that -Q dir "" has a special, nonrecursive meaning.
        - A list of the form (8.4 only) ‘(’nonrec dir path)', specifying a
          directory to be mapped to the logical path 'path' ('-I dir -as path').

  For convenience the symbol ‘`rec`’ can be omitted and entries of the form ‘`(dir path)`’ are interpreted as ‘`(rec dir path)`’.

  A plain string maps to -Q ... "" in 8.5, and -I ... in 8.4.

  Under normal circumstances this list does not need to contain the coq standard library or "." for the current directory (see ‘``coq-load-path-include-current``’).

  warning: if you use coq <= 8.4, the meaning of these options is not the same (-I is for coq path).

Variable: coq-load-path-include-current

  If ‘`t`’ let coqdep search the current directory too.
  Should be ‘`t`’ for normal users. If ‘`t`’ pass -Q dir "" to coqdep when processing files in directory "dir" in addition to any entries in ‘``coq-load-path``’.

  This setting is only relevant with Coq < 8.5.

During library dependency checking Proof General does not dive into the Coq standard library or into libraries that are installed as user contributions. This stems from `coqdep`, which does not output dependencies to these directories. The internal dependency check can also ignore additional libraries.

Variable: coq-compile-ignored-directories

  Directories in which ProofGeneral should not compile modules.
  List of regular expressions for directories in which ProofGeneral should not compile modules. If a library file name matches one of the regular expressions in this list then ProofGeneral does neither compile this file nor check its dependencies for compilation. It makes sense to include non-standard coq library directories here if they are not changed and if they are so big that dependency checking takes noticeable time. The regular expressions in here are always matched against the .vo file name, regardless whether ‘``-quick`’’ would be used to compile the file or not.

#### 11.3.5 Current Limitations

- No support `Declare ML Module` commands.
- When a compiled library has the same time stamp as the source file, it is considered outdated. Some old file systems (for instance ext3) or Emacs before version 24.3 support only time stamps with one second granularity. On such configurations Proof General will perform some unnecessary compilations.

### 11.4 Editing multiple proofs

Coq allows the user to enter top-level commands while editing a proof script. For example, if the user realizes that the current proof will fail without an additional axiom, he or she can add that axiom to the system while in the middle of the proof. Similarly, the user can nest lemmas, beginning a new lemma while in the middle of an earlier one, and as the lemmas are proved or their proofs aborted they are popped off a stack.

Coq Proof General supports this feature of Coq. Top-level commands entered while in a proof are well backtracked. If new lemmas are started, Coq Proof General lets the user work on the proof of the new lemma, and when the lemma is finished it falls back to the previous one. This is supported to any nesting depth that Coq allows.

Warning! Using Coq commands for navigating inside the different proofs (`Resume` and especially `Suspend`) are not supported, backtracking will break syncronization.

Special note: The old feature that moved nested proofs outside the current proof is disabled.

### 11.5 User-loaded tactics

Another feature that Coq allows is the extension of the grammar of the proof assistant by new tactic commands. This feature interacts with the proof script management of Proof General, because Proof General needs to know when a tactic is called that alters the proof state. When the user tries to retract across an extended tactic in a script, the algorithm for calculating how far to undo has a default behavior that is not always accurate in proof mode: do "`Undo`".

Coq Proof General does not currently support dynamic tactic extension in Coq: this is desirable but requires assistance from the Coq core. Instead we provide a way to add tactic and command names in the `.emacs` file. Four Configurable variables allows to register personal new tactics and commands into four categories:

- state changing commands, which need "`Back`" to be backtracked;
- state changing tactics, which need "`Undo`" to be backtracked;
- state preserving commands, which do not need to be backtracked;
- state preserving tactics, which do not need to be backtracked;

We give an example of existing commands that fit each category.

- `coq-user-state-preserving-commands`: example: "`Print`"
- `coq-user-state-changing-commands`: example: "`Require`"
- `coq-user-state-changing-tactics`: example: "`Intro`"
- `coq-user-state-preserving-tactics`: example: "`Idtac`"

This variables are regexp string lists. See their documentations in emacs (`C-h v coq-user...`) for details on how to set them in your `.emacs` file.

Here is a simple example:

    (setq coq-user-state-changing-commands
          '("MyHint" "MyRequire"))
    (setq coq-user-state-preserving-commands
          '("Show\\s-+Mydata"))

The regexp character sequence `\\s-+` means "one or more whitespaces". See the Emacs documentation of `regexp-quote` for the syntax and semantics. WARNING: you need to restart Emacs to make the changes to these variables effective.

In case of losing synchronization, the user can use `C-c C-z` to move the locked region to the proper position, (`proof-frob-locked-end`, see Escaping script management) or `C-c C-v` to re-issue an erroneously back-tracked tactic without recording it in the script.

### 11.6 Holes feature

Holes are an experimental feature for complex expression editing by filling in templates. It is inspired from other tools, like Pcoq (http://www-sop.inria.fr/lemme/pcoq/index.html). The principle is simple, holes are pieces of text that can be "filled" by various means. The Coq command insertion menu system makes use of the holes system. Almost all holes operations are available in the Holes menu.

Notes: Holes make use of the Emacs abbreviation mechanism, it will work without problem if you don’t have an abbrev table defined for Coq in your config files. Use `C-h v abbrev-file-name` to see the name of the abbreviation file.

If you already have such a table it won’t be automatically overwritten (so that you keep your own abbreviations). But you must read the abbrev file given in the Proof General sources to be able to use the command insertion menus. You can do the following to merge your abbreviations with ProofGeneral’s abbreviations: `M-x read-abbrev-file`, then select the file named `coq-abbrev.el` in the `ProofGeneral/coq` directory. At Emacs exit you will be asked if you want to save abbrevs; answer yes.

### 11.7 Proof-Tree Visualization

Starting with Proof General version 4.2 and Coq version 8.4, Coq Proof General has full support for proof-tree visualization, see Graphical Proof-Tree Visualization. To find out which versions of Prooftree are compatible with this version of Proof General, see Graphical Proof-Tree Visualization or the Prooftree website.

For the visualization to work properly, proofs must be started with `Proof`, which is encouraged practice anyway (see Coq Bug #2776). Without `Proof` you lose the initial proof goal, possibly having two or more initial goals in the display.

To support `Grab Existential Variables` Prooftree can actually display several graphically independent proof trees in several layers.