10. 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.
10.1 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 “Search ” 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).
10.2 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 (-R,-Q,-I options). 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
-R) and a list of the files of the
project, see the Coq reference manual, Section
“Building a Coq project”.
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
processes as well as for
coqc when you use
the auto compilation feature, Automatic Compilation in Detail. For the example above, Proof General will start
coqtop -emacs -foo3 -R foo bar -I foo2 (remark:
-emacs is always added to the options).
-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
NOTE: the Coq project file cannot define which version of
coqtop is launched. You need either to launch emacs with the
right executable in the path or use See (emacs)File Variables or
See (emacs)Directory Variables. See Using file variables
|10.2.1 Changing the name of the coq project file|
|10.2.2 Disabling the coq project file mechanism|
10.2.1 Changing the name of the coq project file
To change the name of the Coq project file, configure
coq-project-filename (select menu
Advanced -> Customize -> Coq and scroll down to “Coq Project
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-locals.el file, See (emacs)Directory Variables.
.dir-locals.el should then contain
((coq-mode . ((coq-project-filename . "myprojectfile"))))
Note that variables set in
.dir-locals.el are automatically
made buffer local (such that files in different directories can
have their independent setting of
If you make complex customizations using
.dir-locals.el, you might want to add appropriate calls to
Documentation of the user option
- Variable: coq-project-filename
The name of coq project file.
The coq project file of a coq development (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 Proof General to infer the ‘
coq-load-path’ and the ‘
coq-prog-args’ variables that set the coqtop invocation by Proof General. 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.
10.2.2 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 ‘
You can also use the .dir-locals.el as above to configure this setting on a per project basis.
10.3 Proof using annotations
In order to process files asynchronously and pre-compile files (.vos and .vok files), it is advised (inside sections) to list the section variables (and hypothesis) on which each lemma depends on. This must be done at the beginning of a proof with this syntax:
Lemma foo: ... . Proof using x y H1 H2.
If the annotation is missing, then at Qed time (i.e. later in the script) coq complains with a warning and a suggestion of a correct annotation that should be added. ProofGeneral intercepts this suggestion and stores relevant information. Then depending on user preference it can either
- insert immediately the “using...” annotation after “Proof”, without replaying the proof.
- highlight the place where the annotation should be inserted and
allow the user to perform the insertion later either via right click
menu on the proof or by
M-x coq-insert-suggested-dependency(it won’t replay the proof)
- ask the user each time which of the two solutions above he wants
- ignore completely the suggestion.
This can be configured either via Coq menu or by setting variable
coq-accept-proof-using-suggestion to one of the following values:
10.4 Multiple File Support
Since version 4.1 Coq Proof General has multiple file support. It consists of the following points:
coqtopwhen changing the active scripting buffer
Different buffers may require different load path’ or different sets of
-Ioptions. Because Coq cannot undo changes in the load path, Proof General is forced to restart
coqtopwhen the active scripting buffer changes.
- Locking ancestors
Requirecommand is processed it may be necessary to save some buffers and compile some files. When automatic (re-)compilation is enabled (it’s off by default), one can freely work in different buffers within one Proof General session. Proof General will compile the necessary files whenever a
Requirecommand 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. Compiled interfaces (
-vosfor Coq 8.11 or newer) and quick compilation (
-viofor Coq 8.5 or newer) is supported with various modes, Quick and inconsistent compilation.
- 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. Neither quick nor vos compilation is supported with synchronously compilation.
To enable the automatic compilation feature, you have to follow these points:
Set the option
Coq -> Auto Compilation -> Compile Before Require) to enable compilation before processing
Requirecommands. By default, this enables parallel asynchronous compilation.
Nonstandard load path elements must be configured via a
Coq project file (this is the recommended option),
Using the Coq project file or via
coq-prog-argsmust be deleted.
coq-max-background-compilation-jobsif you want to limit the number of parallel background jobs and set
Coq -> Auto Compilation -> Keep going) to let compilation continue after the first error.
To abort parallel background compilation, use
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
|10.4.1 Automatic Compilation in Detail|
|10.4.2 Locking Ancestors|
|10.4.3 Quick and inconsistent compilation|
|10.4.4 Customizing Coq Multiple File Support|
|10.4.5 Current Limitations|
10.4.1 Automatic Compilation in Detail
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 has finished.
Declare ML Module commands are currently not recognized
and dependencies on ML Modules reported by
Proof General uses
coqdep to determine which libraries a
Require command will load and which files must be
up-to-date. 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
One can use
C-x ` (bound to
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
Proof General supports both vos and quick/vio
compilation to speed up compilation of required modules at the
price of consistency. Because quick/vio compilation does not seem
to have a benefit with vos compilation present, the former is
only supported for Coq before 8.11. Both can be configured via
and via menu entries in
Coq -> Auto Compilation,
Quick and inconsistent compilation.
make -k, background compilation can be
configured to continue as far as possible after the first error,
Coq -> Auto
Compilation -> Keep going). The keep-going option applies
to errors from
coqc. However, when
coqdep fails), the compilation is immediately aborted.
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
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-gto interrupt compilation. This method supports compilation via an external command (such as
make), see option
coq-compile-commandin Customizing Coq Multiple File Support below. Synchronous compilation does neither support quick/vio nor vos compilation.
- Parallel asynchronous compilation
This is the newer, recommended and default version added in Proof General version 4.3. It runs up to
coq-max-background-compilation-jobscoqdep and coqc jobs in parallel in asynchronous subprocesses (or uses all your CPU cores if
'all-cpus). Your Emacs will stay responsive during compilation. To abort the background compilation process, use
proof-interrupt-process), the tool bar interrupt icon, the menu entry
Abort Background Compilation(menu
Coq -> Auto Compilation) or kill the Coq toplevel via
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.
Parallel asynchronous compilation supports both vos and quick/vio compilation, but exclusively, depending on the Coq version, Quick and inconsistent compilation.
10.4.2 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-General -> Quick Options ->
Read Only -> Undo On Edit). Then typing in some ancestor will
immediately retract your current scripting buffer and unlock that
You have two choices, if you don’t like ancestor locking in its
You can either switch ancestor locking completely off via
Coq -> Auto Compilation -> Lock Ancestors or
coq-lock-ancestors (Customizing Coq Multiple File Support). Alternatively, you can generally permit editing in locked
sections with selecting
Quick Options ->
Freely Edit (which will set the option
[The right behaviour for Coq, namely to retract the current
scripting buffer only up to the appropriate
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
10.4.3 Quick and inconsistent compilation
Coq now supports two different modes for speeding up compilation
at the price of consistency. Since Coq 8.11,
.vos files and since Coq 8.5
.vio files. Proof
General supports both modes with parallel asynchronous
compilation, but exclusively, depending on the detected Coq
version. For Coq 8.11 or newer only
-vos can be used.
There are a number of different compilation options supported,
For Coq 8.11 or newer (decided by the automatic Coq version
detection of Proof General or by the setting
coq-pinned-version) required modules are either compiled
.vos files, depending on the setting
coq-compile-vos, which can also be set on menu
-> Auto Compilation -> vos compilation. There are four choices:
First compile using
-vos, skipping proofs. When compilation finished, run
coqc -vokin a second stage to check proofs on all files that require it. Some universe constraints might be missed, rendering this method possibly inconsistent.
Only compile using
-vos, skipping proofs. No
coqc -vokrun to check proofs. Obviously inconsistent.
.vofiles, checking all proofs and universe constraints. Only consistent choice.
- unset (
coq-compile-quick(see below) equals
quick-no-vio2vo. Otherwise compile without
.vo. This value provides an upgrade path for users that configured
coq-compile-quickin the past.
vos-and-vok the second
-vok stage runs
after the last
Require command has been processed. Errors
might pop up later and interrupt your normal interaction with
Coq. Because the second stage is not time critical, it runs on
coq-max-background-second-stage-percentage per cent of the
cores configured for the first stage. When
coq-compile-keep-going is configured and an error occurs,
-vok stage is run on those dependencies not
affected by the error.
For Coq version 8.5 until before 8.11, Proof General supports
quick or vio compilation with parallel asynchronous compilation.
There are 4 modes that can be
coq-compile-quick or by selecting one of
the radio buttons in the
Coq -> Auto Compilation -> Quick
compilation menu. For Coq before 8.11
no-quick was provided for the transition, for those
that have not switched there development to
Proof using. Use
quick-no-vio2vo, if you want quick
recompilation without producing .vo files. Option
quick-and-vio2vo recompiles with
quick-no-vio2vo does, but schedules a second vio2vo stage
.vo files. Finally, use
ensure-vo for only importing
.vo files with
complete universe checks.
Note that with all of
quick-and-vio2vo your development might be unsound because
proofs might have been skipped and
universe constraints are not fully present in
There are a few peculiarities of quick compilation in Coq 8.5 and possibly also in other versions.
Quick compilation runs noticeably slower when section
variables are not declared via
Even when section variables are declared, quick compilation runs
slower on very small files, probably because of the
comparatively big size of the
.viofiles. You can speed up quick compilation noticeably by running on a RAM disk.
If both, the
.viofiles are present, Coq loads the more recent one, regardless of whether
-quick, and emits a warning when the
.viois more recent than the
Under some circumstances, files compiled when only the
.viofile of some library was present are not compatible with (other) files compiled when also the
.vofile 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
makeinsists on building all prerequisites as either
.vofiles, Proof General just checks whether an up-to-date compiled library file is present.
To ensure soundness, all library dependencies must be compiled as
.vofiles and loaded into one Coq instance.
Detailed description of the 4 possible settings of
Compile outdated prerequisites without
.vofiles, but don’t compile prerequisites for which an up-to-date
.viofile exists. Delete or overwrite outdated
Compile outdated prerequisites with
.viofiles, but don’t compile prerequisites for which an up-to-date
.vofile exists. Delete or overwrite outdated
quick-no-vio2vo, but start a second vio2vo stage for missing
.vofiles. Everything described previously for the second
-vokstage applies here as well.
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-second-stage-delay, Customizing Coq Multiple File Support.
Ensure that all library dependencies are present as
.vofiles and delete outdated
.viofiles that are more recent than the corresponding
.vofile. This setting is the only one that ensures soundness.
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.
10.4.4 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
M-x customize-group coq-auto-compile or select
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-coqto confirm saving all modified Coq buffers,
'ask-allto confirm saving all modified buffers,
'save-coqto save all modified Coq buffers without confirmation and
'save-allto save all modified buffers without confirmation.
This option can be set via menu ‘Coq -> Auto Compilation -> Auto Save’.
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 ‘
This option can be set/reset via menu ‘Coq -> Auto Compilation -> Compile Parallel In Background’.
are described in detail above, Quick and inconsistent compilation.
- 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-second-stage-percentage
Percentage of ‘
coq-max-background-compilation-jobs’ for the second stage.
This setting configures the maximal number of ‘`-vok’’ or vio2vo background jobs running in a second stage as percentage of ‘
For backward compatibility, if this option is not customized, it is initialized from the now deprecated option ‘
- Variable: coq-compile-second-stage-delay
Delay in seconds before starting the second stage compilation.
The delay is applied to both ‘`-vok’’ and vio2vo second stages. For Coq < 8.11 and vio2vo delay helps to avoid running into a library inconsistency with
'quick-and-vio2vo, see Coq issue #5223.
For backward compatibility, if this option is not customized, it is initialized from the now deprecated option ‘
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.
This option can be set via menu ‘Coq -> Auto Compilation -> Lock Ancestors’.
The sequential compilation setting supports an external
compilation command (which could be a parallel running
make). For this set
configure the compilation command in
- 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 -> Auto Compilation -> 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 ‘
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 ‘
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
which does not output dependencies to these directories.
The internal dependency check can also ignore additional
- 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.
10.4.5 Current Limitations
No support for
Declare ML Modulecommands and files depending on an ML module.
- 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.
10.5 Omitting proofs for speed
To speed up asserting larger chunks, Proof General can omit
complete opaque proofs by silently replacing the whole proof
Admitted, Script processing commands.
This works when
- proofs are not nested
opaque and non-opaque proofs start with
opaque proofs end with
non-opaque proofs or definition end with
Aborted proofs can be present if they start with a variant of
Proof and end with
Abort. They are handled like
non-opaque proofs (i.e., not omitted).
To enable omitting proofs, configure
proof-omit-proofs-option or select
Quick Options -> Processing -> Omit Proofs.
With a prefix argument, both
proof-process-buffer will temporarily disable the omit
proofs feature and send the full proof script to Coq.
If a nested proof is detected while searching for opaque proofs to omit, a warning is displayed and the complete remainder of the asserted region is sent unmodified to Coq.
If the proof script relies on sections, it is highly recommended to use
Proof using annotation for all lemmas contained in a Section,
Coq will compute a wrong type for these lemmas when
this omitting-proofs feature is enabled.
To automate this, we recall that ProofGeneral provides a dedicated
feature to generate these
Proof using annotations (a defective
form being e.g.
Proof using Type if no section hypothesis is
used), see the menu command
Coq > "Proof using" mode and
Proof using annotations for details.
10.6 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 synchronization.
Special note: The old feature that moved nested proofs outside the current proof is disabled.
10.7 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 "
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: "
coq-user-state-changing-commands: example: "
coq-user-state-changing-tactics: example: "
coq-user-state-preserving-tactics: example: "
This variables are regexp string lists. See their documentations in
C-h v coq-user...) for details on how to set them in your
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 section Escaping script management) or
C-c C-v to re-issue an erroneously back-tracked tactic without
recording it in the script.
10.8 Indentation tweaking
Indentation of Coq script is provided by Proof General, but it may
behave badly especially if you use syntax extensions. You can sometimes
fix this problem by telling PG that some token should be considered as
identical to other ones by the indentation mechanism. Use the two
coq-smie-monadic-tokens. This variables contains associations
between user tokens and the existing pg tokens they should be equated
this is where users should put ther own tokens. For instance:
(setq coq-smie-user-tokens '((\"xor\" . \"or\") (\"ifb\" . \"if\")))
to have token \"xor\" and \"ifb\" be considered as having
is specific to monadic operators: it contains usual monadic notations by default (but you can redefine it if needed).
Specific tokens are defined for the two usual monadic forms:
"let monadic" E "<- monadic" E "in monadic" E E "<- monadic" E ";; monadic" E
The default value of
coq-smie-monadic-tokensgives the following concrete syntax to these tokens:
((";;" . ";; monadic") ("do" . "let monadic") ("<-" . "<- monadic") (";" . "in monadic"))
thus allowing for the following:
do x <- foo; do y <- bar; ...
x <- foo;; y <- bar;; ...
NOTE: This feature is experimental.
NOTE: the “pg tokens” are actually the ones PG generates internally by exploring the file around the indentation point. Consequently this refers to internals of PoofGeneral. Contact the Proof General team if you need help.
10.9 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.
10.10 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 section Graphical Proof-Tree Visualization. To find out which versions of Prooftree are compatible with this version of Proof General, see section Graphical Proof-Tree Visualization or the Prooftree website.
For the visualization to work properly, proofs must be started
Proof, which is encouraged practice anyway (see Coq Bug
Proof you lose the initial proof goal,
possibly having two or more initial goals in the display.
Grab Existential Variables Prooftree can
actually display several graphically independent proof trees in
10.11 Showing Proof Diffs
Coq 8.10 supports automatically highlighting the differences between successive proof steps in Proof General. The feature is described in the Coq Documentation, section Showing differences between proof steps.
The Coq proof diff does more than a basic "diff" operation. For example:
- diffs are computed on a per-token basis (as determined by the Coq lexer) rather than on a per-character basis, probably a better match for how people understand the output. (For example, a token-based diff between "abc" and "axc" will highlight all of "abc" and "axc" as a difference, while a character-based diff would indicate that "a" and "c" are in common and that only the "b"/"x" is a difference.)
- diffs ignore the order of hypotheses
- tactics that only change the proof view are handled specially, for example "swap" after a "split" will show the diffs between before "split" and after "swap", which is more useful
- some error messages have been instrumented to show diffs where it is helpful
To enable or disable diffs, set
coq-diffs (select menu
Coq -> Diffs)
to "on", "off" or "removed". "on" highlights added tokens with the background
diff-refine-added. "removed" highlights removed tokens
with the background color from
diff-refine-removed. With the "removed" setting,
lines that have both added and removed text may be shown twice, as "before" and
To preserve the settings for the next time you start Proof General,
Coq -> Settings -> Save Settings.
The colors used to highlight diffs are configurable in the
Proof-General -> Advanced -> Customize -> Proof Faces menu.
Coq Diffs ... faces control the highlights. Lines that
have added or removed tokens are shown with the entire line highlighted with
Coq Diffs ... Bg face. The added or removed tokens themselves are highlighted
10.12 Opam-switch-mode support
Coq can be installed using
opam (the OCaml package manager),
which makes it easy to manage several different switches, having each
a different version of Coq.
Instead of running a command like
opam switch ... in a terminal
and restarting emacs to benefit from a different switch, one can:
opam-switch-mode and use the dedicated mode bar menu
Configure Proof General using the customization option
coq-kill-coq-on-opam-switch, so that the Coq background process is killed when changing the opam switch through
- Variable: coq-kill-coq-on-opam-switch
If t kill coq when the opam switch changes (requires ‘opam-switch-mode’).
When ‘opam-switch-mode’ is loaded and the user changes the opam switch through ‘opam-switch-mode’ then this option controls whether the coq background process (the proof shell) is killed such that the next assert command starts a new proof shell, probably using a different coq version from a different opam switch.
See https://github.com/ProofGeneral/opam-switch-mode for ‘opam-switch-mode’
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