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Untersuchungsergebnis.rst Download desPython {Python[98] Latech[115] Fortran[148]}zum Wurzelverzeichnis wechseln
.. _vernacularcommands:
Vernacular commands
=============================
.. _displaying:
Displaying
--------------
.. _Print:
.. cmd:: Print @qualid
:name: Print
This command displays on the screen information about the declared or
defined object referred by :n:`@qualid`.
Error messages:
.. exn:: @qualid not a defined object.
:undocumented:
.. exn:: Universe instance should have length @num.
:undocumented:
.. exn:: This object does not support universe names.
:undocumented:
.. cmdv:: Print Term @qualid
:name: Print Term
This is a synonym of :cmd:`Print` :n:`@qualid` when :n:`@qualid`
denotes a global constant.
.. cmdv:: Print {? Term } @qualid\@@name
This locally renames the polymorphic universes of :n:`@qualid`.
An underscore means the usual name is printed.
.. cmd:: About @qualid
:name: About
This displays various information about the object
denoted by :n:`@qualid`: its kind (module, constant, assumption, inductive,
constructor, abbreviation, …), long name, type, implicit arguments and
argument scopes. It does not print the body of definitions or proofs.
.. cmdv:: About @qualid\@@name
This locally renames the polymorphic universes of :n:`@qualid`.
An underscore means the usual name is printed.
.. cmd:: Print All
This command displays information about the current state of the
environment, including sections and modules.
.. cmdv:: Inspect @num
:name: Inspect
This command displays the :n:`@num` last objects of the
current environment, including sections and modules.
.. cmdv:: Print Section @ident
The name :n:`@ident` should correspond to a currently open section,
this command displays the objects defined since the beginning of this
section.
.. _flags-options-tables:
Flags, Options and Tables
-----------------------------
Coq has many settings to control its behavior. Setting types include flags, options
and tables:
* A :production:`flag` has a boolean value, such as :flag:`Asymmetric Patterns`.
* An :production:`option` generally has a numeric or string value, such as :opt:`Firstorder Depth`.
* A :production:`table` contains a set of strings or qualids.
* In addition, some commands provide settings, such as :cmd:`Extraction Language`.
.. FIXME Convert "Extraction Language" to an option.
Flags, options and tables are identified by a series of identifiers, each with an initial
capital letter.
.. cmd:: {? {| Local | Global | Export } } Set @flag
:name: Set
Sets :token:`flag` on. Scoping qualifiers are
described :ref:`here <set_unset_scope_qualifiers>`.
.. cmd:: {? {| Local | Global | Export } } Unset @flag
:name: Unset
Sets :token:`flag` off. Scoping qualifiers are
described :ref:`here <set_unset_scope_qualifiers>`.
.. cmd:: Test @flag
Prints the current value of :token:`flag`.
.. cmd:: {? {| Local | Global | Export } } Set @option {| @num | @string }
:name: Set @option
Sets :token:`option` to the specified value. Scoping qualifiers are
described :ref:`here <set_unset_scope_qualifiers>`.
.. cmd:: {? {| Local | Global | Export } } Unset @option
:name: Unset @option
Sets :token:`option` to its default value. Scoping qualifiers are
described :ref:`here <set_unset_scope_qualifiers>`.
.. cmd:: Test @option
Prints the current value of :token:`option`.
.. cmd:: Print Options
Prints the current value of all flags and options, and the names of all tables.
.. cmd:: Add @table {| @string | @qualid }
:name: Add @table
Adds the specified value to :token:`table`.
.. cmd:: Remove @table {| @string | @qualid }
:name: Remove @table
Removes the specified value from :token:`table`.
.. cmd:: Test @table for {| @string | @qualid }
:name: Test @table for
Reports whether :token:`table` contains the specified value.
.. cmd:: Print Table @table
:name: Print Table @table
Prints the values in :token:`table`.
.. cmd:: Test @table
A synonym for :cmd:`Print Table @table`.
.. cmd:: Print Tables
A synonym for :cmd:`Print Options`.
.. _set_unset_scope_qualifiers:
Scope qualifiers for :cmd:`Set` and :cmd:`Unset`
`````````````````````````````````````````````````
:n:`{? {| Local | Global | Export } }`
Flag and option settings can be global in scope or local to nested scopes created by
:cmd:`Module` and :cmd:`Section` commands. There are four alternatives:
* no qualifier: the original setting is *not* restored at the end of the current module or section.
* **Local**: the setting is applied within the current scope. The original value of the option
or flag is restored at the end of the current module or section.
* **Global**: similar to no qualifier, the original setting is *not* restored at the end of the current
module or section. In addition, if the value is set in a file, then :cmd:`Require`-ing
the file sets the option.
* **Export**: similar to **Local**, the original value of the option or flag is restored at the
end of the current module or section. In addition, if the value is set in a file, then :cmd:`Import`-ing
the file sets the option.
Newly opened scopes inherit the current settings.
.. _requests-to-the-environment:
Requests to the environment
-------------------------------
.. cmd:: Check @term
This command displays the type of :n:`@term`. When called in proof mode, the
term is checked in the local context of the current subgoal.
.. cmdv:: @selector: Check @term
This variant specifies on which subgoal to perform typing
(see Section :ref:`invocation-of-tactics`).
.. cmd:: Eval @redexpr in @term
This command performs the specified reduction on :n:`@term`, and displays
the resulting term with its type. The term to be reduced may depend on
hypothesis introduced in the first subgoal (if a proof is in
progress).
.. seealso:: Section :ref:`performingcomputations`.
.. cmd:: Compute @term
This command performs a call-by-value evaluation of term by using the
bytecode-based virtual machine. It is a shortcut for ``Eval vm_compute in``
:n:`@term`.
.. seealso:: Section :ref:`performingcomputations`.
.. cmd:: Print Assumptions @qualid
This commands display all the assumptions (axioms, parameters and
variables) a theorem or definition depends on. Especially, it informs
on the assumptions with respect to which the validity of a theorem
relies.
.. cmdv:: Print Opaque Dependencies @qualid
:name: Print Opaque Dependencies
Displays the set of opaque constants :n:`@qualid` relies on in addition to
the assumptions.
.. cmdv:: Print Transparent Dependencies @qualid
:name: Print Transparent Dependencies
Displays the set of transparent constants :n:`@qualid` relies on
in addition to the assumptions.
.. cmdv:: Print All Dependencies @qualid
:name: Print All Dependencies
Displays all assumptions and constants :n:`@qualid` relies on.
.. cmd:: Search @qualid
This command displays the name and type of all objects (hypothesis of
the current goal, theorems, axioms, etc) of the current context whose
statement contains :n:`@qualid`. This command is useful to remind the user
of the name of library lemmas.
.. exn:: The reference @qualid was not found in the current environment.
There is no constant in the environment named qualid.
.. cmdv:: Search @string
If :n:`@string` is a valid identifier, this command
displays the name and type of all objects (theorems, axioms, etc) of
the current context whose name contains string. If string is a
notation’s string denoting some reference :n:`@qualid` (referred to by its
main symbol as in `"+"` or by its notation’s string as in `"_ + _"` or
`"_ 'U' _"`, see Section :ref:`notations`), the command works like ``Search`` :n:`@qualid`.
.. cmdv:: Search @string%@ident
The string string must be a notation or the main
symbol of a notation which is then interpreted in the scope bound to
the delimiting key :token:`ident` (see Section :ref:`LocalInterpretationRulesForNotations`).
.. cmdv:: Search @term_pattern
This searches for all statements or types of
definition that contains a subterm that matches the pattern
:token:`term_pattern` (holes of the pattern are either denoted by `_` or by
:n:`?@ident` when non linear patterns are expected).
.. cmdv:: Search {+ {? -}@term_pattern_string}
where
:n:`@term_pattern_string` is a term_pattern, a string, or a string followed
by a scope delimiting key `%key`. This generalization of ``Search`` searches
for all objects whose statement or type contains a subterm matching
:n:`@term_pattern` (or :n:`@qualid` if :n:`@string` is the notation for a reference
qualid) and whose name contains all string of the request that
correspond to valid identifiers. If a term_pattern or a string is
prefixed by `-`, the search excludes the objects that mention that
term_pattern or that string.
.. cmdv:: Search {+ {? -}@term_pattern_string} inside {+ @qualid }
This restricts the search to constructions defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: Search {+ {? -}@term_pattern_string} outside {+ @qualid }
This restricts the search to constructions not defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: @selector: Search {+ {? -}@term_pattern_string}
This specifies the goal on which to search hypothesis (see
Section :ref:`invocation-of-tactics`).
By default the 1st goal is searched. This variant can
be combined with other variants presented here.
.. example::
.. coqtop:: in
Require Import ZArith.
.. coqtop:: all
Search Z.mul Z.add "distr".
Search "+"%Z "*"%Z "distr" -positive -Prop.
Search (?x * _ + ?x * _)%Z outside OmegaLemmas.
.. cmdv:: SearchAbout
:name: SearchAbout
.. deprecated:: 8.5
Up to |Coq| version 8.4, :cmd:`Search` had the behavior of current
:cmd:`SearchHead` and the behavior of current :cmd:`Search` was obtained with
command :cmd:`SearchAbout`. For compatibility, the deprecated name
:cmd:`SearchAbout` can still be used as a synonym of :cmd:`Search`. For
compatibility, the list of objects to search when using :cmd:`SearchAbout`
may also be enclosed by optional ``[ ]`` delimiters.
.. cmd:: SearchHead @term
This command displays the name and type of all hypothesis of the
current goal (if any) and theorems of the current context whose
statement’s conclusion has the form `(term t1 .. tn)`. This command is
useful to remind the user of the name of library lemmas.
.. example::
.. coqtop:: reset all
SearchHead le.
SearchHead (@eq bool).
.. cmdv:: SearchHead @term inside {+ @qualid }
This restricts the search to constructions defined in the modules named
by the given :n:`qualid` sequence.
.. cmdv:: SearchHead @term outside {+ @qualid }
This restricts the search to constructions not defined in the modules
named by the given :n:`qualid` sequence.
.. exn:: Module/section @qualid not found.
No module :n:`@qualid` has been required (see Section :ref:`compiled-files`).
.. cmdv:: @selector: SearchHead @term
This specifies the goal on which to
search hypothesis (see Section :ref:`invocation-of-tactics`).
By default the 1st goal is searched. This variant can be combined
with other variants presented here.
.. note:: Up to |Coq| version 8.4, ``SearchHead`` was named ``Search``.
.. cmd:: SearchPattern @term
This command displays the name and type of all hypothesis of the
current goal (if any) and theorems of the current context whose
statement’s conclusion or last hypothesis and conclusion matches the
expressionterm where holes in the latter are denoted by `_`.
It is a variant of :n:`Search @term_pattern` that does not look for subterms
but searches for statements whose conclusion has exactly the expected
form, or whose statement finishes by the given series of
hypothesis/conclusion.
.. example::
.. coqtop:: in
Require Import Arith.
.. coqtop:: all
SearchPattern (_ + _ = _ + _).
SearchPattern (nat -> bool).
SearchPattern (forall l : list _, _ l l).
Patterns need not be linear: you can express that the same expression
must occur in two places by using pattern variables `?ident`.
.. example::
.. coqtop:: all
SearchPattern (?X1 + _ = _ + ?X1).
.. cmdv:: SearchPattern @term inside {+ @qualid }
This restricts the search to constructions defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: SearchPattern @term outside {+ @qualid }
This restricts the search to constructions not defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: @selector: SearchPattern @term
This specifies the goal on which to
search hypothesis (see Section :ref:`invocation-of-tactics`).
By default the 1st goal is
searched. This variant can be combined with other variants presented
here.
.. cmd:: SearchRewrite @term
This command displays the name and type of all hypothesis of the
current goal (if any) and theorems of the current context whose
statement’s conclusion is an equality of which one side matches the
expression term. Holes in term are denoted by “_”.
.. example::
.. coqtop:: in
Require Import Arith.
.. coqtop:: all
SearchRewrite (_ + _ + _).
.. cmdv:: SearchRewrite @term inside {+ @qualid }
This restricts the search to constructions defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: SearchRewrite @term outside {+ @qualid }
This restricts the search to constructions not defined in the modules
named by the given :n:`qualid` sequence.
.. cmdv:: @selector: SearchRewrite @term
This specifies the goal on which to
search hypothesis (see Section :ref:`invocation-of-tactics`).
By default the 1st goal is
searched. This variant can be combined with other variants presented
here.
.. note::
.. table:: Search Blacklist @string
:name: Search Blacklist
Specifies a set of strings used to exclude lemmas from the results of :cmd:`Search`,
:cmd:`SearchHead`, :cmd:`SearchPattern` and :cmd:`SearchRewrite` queries. A lemma whose
fully-qualified name contains any of the strings will be excluded from the
search results. The default blacklisted substrings are ``_subterm``, ``_subproof`` and
``Private_``.
Use the :cmd:`Add @table` and :cmd:`Remove @table` commands to update the set of
blacklisted strings.
.. cmd:: Locate @qualid
This command displays the full name of objects whose name is a prefix
of the qualified identifier :n:`@qualid`, and consequently the |Coq| module in
which they are defined. It searches for objects from the different
qualified namespaces of |Coq|: terms, modules, Ltac, etc.
.. example::
.. coqtop:: all
Locate nat.
Locate Datatypes.O.
Locate Init.Datatypes.O.
Locate Coq.Init.Datatypes.O.
Locate I.Dont.Exist.
.. cmdv:: Locate Term @qualid
As Locate but restricted to terms.
.. cmdv:: Locate Module @qualid
As Locate but restricted to modules.
.. cmdv:: Locate Ltac @qualid
As Locate but restricted to tactics.
.. seealso:: Section :ref:`locating-notations`
.. _printing-flags:
Printing flags
-------------------------------
.. flag:: Fast Name Printing
When turned on, |Coq| uses an asymptotically faster algorithm for the
generation of unambiguous names of bound variables while printing terms.
While faster, it is also less clever and results in a typically less elegant
display, e.g. it will generate more names rather than reusing certain names
across subterms. This flag is not enabled by default, because as Ltac
observes bound names, turning it on can break existing proof scripts.
.. _loading-files:
Loading files
-----------------
|Coq| offers the possibility of loading different parts of a whole
development stored in separate files. Their contents will be loaded as
if they were entered from the keyboard. This means that the loaded
files are ASCII files containing sequences of commands for |Coq|’s
toplevel. This kind of file is called a *script* for |Coq|. The standard
(and default) extension of |Coq|’s script files is .v.
.. cmd:: Load @ident
This command loads the file named :n:`ident`.v, searching successively in
each of the directories specified in the *loadpath*. (see Section
:ref:`libraries-and-filesystem`)
Files loaded this way cannot leave proofs open, and the ``Load``
command cannot be used inside a proof either.
.. cmdv:: Load @string
Loads the file denoted by the string :n:`@string`, where
string is any complete filename. Then the `~` and .. abbreviations are
allowed as well as shell variables. If no extension is specified, |Coq|
will use the default extension ``.v``.
.. cmdv:: Load Verbose @ident
Load Verbose @string
Display, while loading,
the answers of |Coq| to each command (including tactics) contained in
the loaded file.
.. seealso:: Section :ref:`controlling-display`.
.. exn:: Can’t find file @ident on loadpath.
:undocumented:
.. exn:: Load is not supported inside proofs.
:undocumented:
.. exn:: Files processed by Load cannot leave open proofs.
:undocumented:
.. _compiled-files:
Compiled files
------------------
This section describes the commands used to load compiled files (see
Chapter :ref:`thecoqcommands` for documentation on how to compile a file). A compiled
file is a particular case of module called *library file*.
.. cmd:: Require @qualid
This command looks in the loadpath for a file containing module :n:`@qualid`
and adds the corresponding module to the environment of |Coq|. As
library files have dependencies in other library files, the command
:cmd:`Require` :n:`@qualid` recursively requires all library files the module
qualid depends on and adds the corresponding modules to the
environment of |Coq| too. |Coq| assumes that the compiled files have been
produced by a valid |Coq| compiler and their contents are then not
replayed nor rechecked.
To locate the file in the file system, :n:`@qualid` is decomposed under the
form :n:`dirpath.@ident` and the file :n:`@ident.vo` is searched in the physical
directory of the file system that is mapped in |Coq| loadpath to the
logical path dirpath (see Section :ref:`libraries-and-filesystem`). The mapping between
physical directories and logical names at the time of requiring the
file must be consistent with the mapping used to compile the file. If
several files match, one of them is picked in an unspecified fashion.
.. cmdv:: Require Import @qualid
:name: Require Import
This loads and declares the module :n:`@qualid`
and its dependencies then imports the contents of :n:`@qualid` as described
:ref:`here <import_qualid>`. It does not import the modules on which
qualid depends unless these modules were themselves required in module
:n:`@qualid`
using :cmd:`Require Export`, as described below, or recursively required
through a sequence of :cmd:`Require Export`. If the module required has
already been loaded, :cmd:`Require Import` :n:`@qualid` simply imports it, as
:cmd:`Import` :n:`@qualid` would.
.. cmdv:: Require Export @qualid
:name: Require Export
This command acts as :cmd:`Require Import` :n:`@qualid`,
but if a further module, say `A`, contains a command :cmd:`Require Export` `B`,
then the command :cmd:`Require Import` `A` also imports the module `B.`
.. cmdv:: Require {| Import | Export } {+ @qualid }
This loads the
modules named by the :token:`qualid` sequence and their recursive
dependencies. If
``Import`` or ``Export`` is given, it also imports these modules and
all the recursive dependencies that were marked or transitively marked
as ``Export``.
.. cmdv:: From @dirpath Require @qualid
:name: From ... Require ...
This command acts as :cmd:`Require`, but picks
any library whose absolute name is of the form :n:`@dirpath.@dirpath’.@qualid`
for some :n:`@dirpath’`. This is useful to ensure that the :token:`qualid` library
comes from a given package by making explicit its absolute root.
.. exn:: Cannot load qualid: no physical path bound to dirpath.
:undocumented:
.. exn:: Cannot find library foo in loadpath.
The command did not find the
file foo.vo. Either foo.v exists but is not compiled or foo.vo is in a
directory which is not in your LoadPath (see Section :ref:`libraries-and-filesystem`).
.. exn:: Compiled library @ident.vo makes inconsistent assumptions over library qualid.
The command tried to load library file :n:`@ident`.vo that
depends on some specific version of library :n:`@qualid` which is not the
one already loaded in the current |Coq| session. Probably :n:`@ident.v` was
not properly recompiled with the last version of the file containing
module :token:`qualid`.
.. exn:: Bad magic number.
The file :n:`@ident.vo` was found but either it is not a
|Coq| compiled module, or it was compiled with an incompatible
version of |Coq|.
.. exn:: The file :n:`@ident.vo` contains library dirpath and not library dirpath’.
The library file :n:`@dirpath’` is indirectly required by the
``Require`` command but it is bound in the current loadpath to the
file :n:`@ident.vo` which was bound to a different library name :token:`dirpath` at
the time it was compiled.
.. exn:: Require is not allowed inside a module or a module type.
This command
is not allowed inside a module or a module type being defined. It is
meant to describe a dependency between compilation units. Note however
that the commands ``Import`` and ``Export`` alone can be used inside modules
(see Section :ref:`Import <import_qualid>`).
.. seealso:: Chapter :ref:`thecoqcommands`
.. cmd:: Print Libraries
This command displays the list of library files loaded in the
current |Coq| session. For each of these libraries, it also tells if it
is imported.
.. cmd:: Declare ML Module {+ @string }
This commands loads the OCaml compiled files
with names given by the :token:`string` sequence
(dynamic link). It is mainly used to load tactics dynamically. The
files are searched into the current OCaml loadpath (see the
command :cmd:`Add ML Path`).
Loading of OCaml files is only possible under the bytecode version of
``coqtop`` (i.e. ``coqtop`` called with option ``-byte``, see chapter
:ref:`thecoqcommands`), or when |Coq| has been compiled with a
version of OCaml that supports native Dynlink (≥ 3.11).
.. cmdv:: Local Declare ML Module {+ @string }
This variant is not exported to the modules that import the module
where they occur, even if outside a section.
.. exn:: File not found on loadpath: @string.
:undocumented:
.. exn:: Loading of ML object file forbidden in a native Coq.
:undocumented:
.. cmd:: Print ML Modules
This prints the name of all OCaml modules loaded with :cmd:`Declare ML Module`.
To know from where these module were loaded, the user
should use the command :cmd:`Locate File`.
.. _loadpath:
Loadpath
------------
Loadpaths are preferably managed using |Coq| command line options (see
Section `libraries-and-filesystem`) but there remain vernacular commands to manage them
for practical purposes. Such commands are only meant to be issued in
the toplevel, and using them in source files is discouraged.
.. cmd:: Pwd
This command displays the current working directory.
.. cmd:: Cd @string
This command changes the current directory according to :token:`string` which
can be any valid path.
.. cmdv:: Cd
Is equivalent to Pwd.
.. cmd:: Add LoadPath @string as @dirpath
This command is equivalent to the command line option
:n:`-Q @string @dirpath`. It adds the physical directory string to the current
|Coq| loadpath and maps it to the logical directory dirpath.
.. cmdv:: Add LoadPath @string
Performs as :n:`Add LoadPath @string @dirpath` but
for the empty directory path.
.. cmd:: Add Rec LoadPath @string as @dirpath
This command is equivalent to the command line option
:n:`-R @string @dirpath`. It adds the physical directory string and all its
subdirectories to the current |Coq| loadpath.
.. cmdv:: Add Rec LoadPath @string
Works as :n:`Add Rec LoadPath @string as @dirpath` but for the empty
logical directory path.
.. cmd:: Remove LoadPath @string
This command removes the path :n:`@string` from the current |Coq| loadpath.
.. cmd:: Print LoadPath
This command displays the current |Coq| loadpath.
.. cmdv:: Print LoadPath @dirpath
Works as :cmd:`Print LoadPath` but displays only
the paths that extend the :n:`@dirpath` prefix.
.. cmd:: Add ML Path @string
This command adds the path :n:`@string` to the current OCaml
loadpath (see the command `Declare ML Module`` in Section :ref:`compiled-files`).
.. cmd:: Add Rec ML Path @string
This command adds the directory :n:`@string` and all its subdirectories to
the current OCaml loadpath (see the command :cmd:`Declare ML Module`).
.. cmd:: Print ML Path @string
This command displays the current OCaml loadpath. This
command makes sense only under the bytecode version of ``coqtop``, i.e.
using option ``-byte``
(see the command Declare ML Module in Section :ref:`compiled-files`).
.. _locate-file:
.. cmd:: Locate File @string
This command displays the location of file string in the current
loadpath. Typically, string is a ``.cmo`` or ``.vo`` or ``.v`` file.
.. cmd:: Locate Library @dirpath
This command gives the status of the |Coq| module dirpath. It tells if
the module is loaded and if not searches in the load path for a module
of logical name :n:`@dirpath`.
.. _backtracking:
Backtracking
----------------
The backtracking commands described in this section can only be used
interactively, they cannot be part of a vernacular file loaded via
``Load`` or compiled by ``coqc``.
.. cmd:: Reset @ident
This command removes all the objects in the environment since :n:`@ident`
was introduced, including :n:`@ident`. :n:`@ident` may be the name of a defined or
declared object as well as the name of a section. One cannot reset
over the name of a module or of an object inside a module.
.. exn:: @ident: no such entry.
:undocumented:
.. cmdv:: Reset Initial
Goes back to the initial state, just after the start
of the interactive session.
.. cmd:: Back
This command undoes all the effects of the last vernacular command.
Commands read from a vernacular file via a :cmd:`Load` are considered as a
single command. Proof management commands are also handled by this
command (see Chapter :ref:`proofhandling`). For that, Back may have to undo more than
one command in order to reach a state where the proof management
information is available. For instance, when the last command is a
:cmd:`Qed`, the management information about the closed proof has been
discarded. In this case, :cmd:`Back` will then undo all the proof steps up to
the statement of this proof.
.. cmdv:: Back @num
Undo :n:`@num` vernacular commands. As for Back, some extra
commands may be undone in order to reach an adequate state. For
instance Back :n:`@num` will not re-enter a closed proof, but rather go just
before that proof.
.. exn:: Invalid backtrack.
The user wants to undo more commands than available in the history.
.. cmd:: BackTo @num
This command brings back the system to the state labeled :n:`@num`,
forgetting the effect of all commands executed after this state. The
state label is an integer which grows after each successful command.
It is displayed in the prompt when in -emacs mode. Just as :cmd:`Back` (see
above), the :cmd:`BackTo` command now handles proof states. For that, it may
have to undo some extra commands and end on a state :n:`@num′ ≤ @num` if
necessary.
.. cmdv:: Backtrack @num @num @num
:name: Backtrack
.. deprecated:: 8.4
:cmd:`Backtrack` is a *deprecated* form of
:cmd:`BackTo` which allows explicitly manipulating the proof environment. The
three numbers represent the following:
+ *first number* : State label to reach, as for :cmd:`BackTo`.
+ *second number* : *Proof state number* to unbury once aborts have been done.
|Coq| will compute the number of :cmd:`Undo` to perform (see Chapter :ref:`proofhandling`).
+ *third number* : Number of :cmd:`Abort` to perform, i.e. the number of currently
opened nested proofs that must be canceled (see Chapter :ref:`proofhandling`).
.. exn:: Invalid backtrack.
The destination state label is unknown.
.. _quitting-and-debugging:
Quitting and debugging
--------------------------
.. cmd:: Quit
This command permits to quit |Coq|.
.. cmd:: Drop
This is used mostly as a debug facility by |Coq|’s implementers and does
not concern the casual user. This command permits to leave |Coq|
temporarily and enter the OCaml toplevel. The OCaml
command:
::
#use "include";;
adds the right loadpaths and loads some toplevel printers for all
abstract types of |Coq|- section_path, identifiers, terms, judgments, ….
You can also use the file base_include instead, that loads only the
pretty-printers for section_paths and identifiers. You can return back
to |Coq| with the command:
::
go();;
.. warning::
#. It only works with the bytecode version of |Coq| (i.e. `coqtop.byte`,
see Section `interactive-use`).
#. You must have compiled |Coq| from the source package and set the
environment variable COQTOP to the root of your copy of the sources
(see Section `customization-by-environment-variables`).
.. TODO : command is not a syntax entry
.. cmd:: Time @command
This command executes the vernacular command :n:`@command` and displays the
time needed to execute it.
.. cmd:: Redirect @string @command
This command executes the vernacular command :n:`@command`, redirecting its
output to ":n:`@string`.out".
.. cmd:: Timeout @num @command
This command executes the vernacular command :n:`@command`. If the command
has not terminated after the time specified by the :n:`@num` (time
expressed in seconds), then it is interrupted and an error message is
displayed.
.. opt:: Default Timeout @num
:name: Default Timeout
This option controls a default timeout for subsequent commands, as if they
were passed to a :cmd:`Timeout` command. Commands already starting by a
:cmd:`Timeout` are unaffected.
.. cmd:: Fail @command
For debugging scripts, sometimes it is desirable to know
whether a command or a tactic fails. If the given :n:`@command`
fails, the ``Fail`` statement succeeds, without changing the proof
state, and in interactive mode, the system
prints a message confirming the failure.
If the given :n:`@command` succeeds, the statement is an error, and
it prints a message indicating that the failure did not occur.
.. exn:: The command has not failed!
:undocumented:
.. _controlling-display:
Controlling display
-----------------------
.. flag:: Silent
This option controls the normal displaying.
.. opt:: Warnings "{+, {? {| - | + } } @ident }"
:name: Warnings
This option configures the display of warnings. It is experimental, and
expects, between quotes, a comma-separated list of warning names or
categories. Adding - in front of a warning or category disables it, adding +
makes it an error. It is possible to use the special categories all and
default, the latter containing the warnings enabled by default. The flags are
interpreted from left to right, so in case of an overlap, the flags on the
right have higher priority, meaning that `A,-A` is equivalent to `-A`.
.. flag:: Search Output Name Only
This option restricts the output of search commands to identifier names;
turning it on causes invocations of :cmd:`Search`, :cmd:`SearchHead`,
:cmd:`SearchPattern`, :cmd:`SearchRewrite` etc. to omit types from their
output, printing only identifiers.
.. opt:: Printing Width @num
:name: Printing Width
This command sets which left-aligned part of the width of the screen is used
for display. At the time of writing this documentation, the default value
is 78.
.. opt:: Printing Depth @num
:name: Printing Depth
This option controls the nesting depth of the formatter used for pretty-
printing. Beyond this depth, display of subterms is replaced by dots. At the
time of writing this documentation, the default value is 50.
.. flag:: Printing Compact Contexts
This option controls the compact display mode for goals contexts. When on,
the printer tries to reduce the vertical size of goals contexts by putting
several variables (even if of different types) on the same line provided it
does not exceed the printing width (see :opt:`Printing Width`). At the time
of writing this documentation, it is off by default.
.. flag:: Printing Unfocused
This option controls whether unfocused goals are displayed. Such goals are
created by focusing other goals with bullets (see :ref:`bullets` or
:ref:`curly braces <curly-braces>`). It is off by default.
.. flag:: Printing Dependent Evars Line
This option controls the printing of the “(dependent evars: …)” line when
``-emacs`` is passed.
.. _vernac-controlling-the-reduction-strategies:
Controlling the reduction strategies and the conversion algorithm
----------------------------------------------------------------------
|Coq| provides reduction strategies that the tactics can invoke and two
different algorithms to check the convertibility of types. The first
conversion algorithm lazily compares applicative terms while the other
is a brute-force but efficient algorithm that first normalizes the
terms before comparing them. The second algorithm is based on a
bytecode representation of terms similar to the bytecode
representation used in the ZINC virtual machine :cite:`Leroy90`. It is
especially useful for intensive computation of algebraic values, such
as numbers, and for reflection-based tactics. The commands to fine-
tune the reduction strategies and the lazy conversion algorithm are
described first.
.. cmd:: Opaque {+ @qualid }
This command has an effect on unfoldable constants, i.e. on constants
defined by :cmd:`Definition` or :cmd:`Let` (with an explicit body), or by a command
assimilated to a definition such as :cmd:`Fixpoint`, :cmd:`Program Definition`, etc,
or by a proof ended by :cmd:`Defined`. The command tells not to unfold the
constants in the :n:`@qualid` sequence in tactics using δ-conversion (unfolding
a constant is replacing it by its definition).
:cmd:`Opaque` has also an effect on the conversion algorithm of |Coq|, telling
it to delay the unfolding of a constant as much as possible when |Coq|
has to check the conversion (see Section :ref:`conversion-rules`) of two distinct
applied constants.
.. cmdv:: Global Opaque {+ @qualid }
:name: Global Opaque
The scope of :cmd:`Opaque` is limited to the current section, or current
file, unless the variant :cmd:`Global Opaque` is used.
.. seealso::
Sections :ref:`performingcomputations`, :ref:`tactics-automating`,
:ref:`proof-editing-mode`
.. exn:: The reference @qualid was not found in the current environment.
There is no constant referred by :n:`@qualid` in the environment.
Nevertheless, if you asked :cmd:`Opaque` `foo` `bar` and if `bar` does
not exist, `foo` is set opaque.
.. cmd:: Transparent {+ @qualid }
This command is the converse of :cmd:`Opaque` and it applies on unfoldable
constants to restore their unfoldability after an Opaque command.
Note in particular that constants defined by a proof ended by Qed are
not unfoldable and Transparent has no effect on them. This is to keep
with the usual mathematical practice of *proof irrelevance*: what
matters in a mathematical development is the sequence of lemma
statements, not their actual proofs. This distinguishes lemmas from
the usual defined constants, whose actual values are of course
relevant in general.
.. cmdv:: Global Transparent {+ @qualid }
:name: Global Transparent
The scope of Transparent is limited to the current section, or current
file, unless the variant :cmd:`Global Transparent` is
used.
.. exn:: The reference @qualid was not found in the current environment.
There is no constant referred by :n:`@qualid` in the environment.
.. seealso::
Sections :ref:`performingcomputations`,
:ref:`tactics-automating`, :ref:`proof-editing-mode`
.. _vernac-strategy:
.. cmd:: Strategy @level [ {+ @qualid } ]
This command generalizes the behavior of Opaque and Transparent
commands. It is used to fine-tune the strategy for unfolding
constants, both at the tactic level and at the kernel level. This
command associates a level to the qualified names in the :n:`@qualid`
sequence. Whenever two
expressions with two distinct head constants are compared (for
instance, this comparison can be triggered by a type cast), the one
with lower level is expanded first. In case of a tie, the second one
(appearing in the cast type) is expanded.
.. prodn:: level ::= {| opaque | @num | expand }
Levels can be one of the following (higher to lower):
+ ``opaque`` : level of opaque constants. They cannot be expanded by
tactics (behaves like +∞, see next item).
+ :n:`@num` : levels indexed by an integer. Level 0 corresponds to the
default behavior, which corresponds to transparent constants. This
level can also be referred to as transparent. Negative levels
correspond to constants to be expanded before normal transparent
constants, while positive levels correspond to constants to be
expanded after normal transparent constants.
+ ``expand`` : level of constants that should be expanded first (behaves
like −∞)
.. cmdv:: Local Strategy @level [ {+ @qualid } ]
These directives survive section and module closure, unless the
command is prefixed by ``Local``. In the latter case, the behavior
regarding sections and modules is the same as for the :cmd:`Transparent` and
:cmd:`Opaque` commands.
.. cmd:: Print Strategy @qualid
This command prints the strategy currently associated to :n:`@qualid`. It
fails if :n:`@qualid` is not an unfoldable reference, that is, neither a
variable nor a constant.
.. exn:: The reference is not unfoldable.
:undocumented:
.. cmdv:: Print Strategies
Print all the currently non-transparent strategies.
.. cmd:: Declare Reduction @ident := @redexpr
This command allows giving a short name to a reduction expression, for
instance ``lazy beta delta [foo bar]``. This short name can then be used
in :n:`Eval @ident in` or ``eval`` directives. This command
accepts the
``Local`` modifier, for discarding this reduction name at the end of the
file or module. For the moment, the name is not qualified. In
particular declaring the same name in several modules or in several
functor applications will be rejected if these declarations are not
local. The name :n:`@ident` cannot be used directly as an Ltac tactic, but
nothing prevents the user from also performing a
:n:`Ltac @ident := @redexpr`.
.. seealso:: :ref:`performingcomputations`
.. _controlling-locality-of-commands:
Controlling the locality of commands
-----------------------------------------
.. cmd:: Local @command
Global @command
Some commands support a Local or Global prefix modifier to control the
scope of their effect. There are four kinds of commands:
+ Commands whose default is to extend their effect both outside the
section and the module or library file they occur in. For these
commands, the Local modifier limits the effect of the command to the
current section or module it occurs in. As an example, the :cmd:`Coercion`
and :cmd:`Strategy` commands belong to this category.
+ Commands whose default behavior is to stop their effect at the end
of the section they occur in but to extend their effect outside the module or
library file they occur in. For these commands, the Local modifier limits the
effect of the command to the current module if the command does not occur in a
section and the Global modifier extends the effect outside the current
sections and current module if the command occurs in a section. As an example,
the :cmd:`Arguments <Arguments (implicits)>`, :cmd:`Ltac` or :cmd:`Notation` commands belong
to this category. Notice that a subclass of these commands do not support
extension of their scope outside sections at all and the Global modifier is not
applicable to them.
+ Commands whose default behavior is to stop their effect at the end
of the section or module they occur in. For these commands, the ``Global``
modifier extends their effect outside the sections and modules they
occur in. The :cmd:`Transparent` and :cmd:`Opaque`
(see Section :ref:`vernac-controlling-the-reduction-strategies`) commands
belong to this category.
+ Commands whose default behavior is to extend their effect outside
sections but not outside modules when they occur in a section and to
extend their effect outside the module or library file they occur in
when no section contains them.For these commands, the Local modifier
limits the effect to the current section or module while the Global
modifier extends the effect outside the module even when the command
occurs in a section. The :cmd:`Set` and :cmd:`Unset` commands belong to this
category.
.. _internal-registration-commands:
Internal registration commands
--------------------------------
Due to their internal nature, the commands that are presented in this section
are not for general use. They are meant to appear only in standard libraries and
in support libraries of plug-ins.
.. _exposing-constants-to-ocaml-libraries:
Exposing constants to OCaml libraries
````````````````````````````````````````````````````````````````
.. cmd:: Register @qualid__1 as @qualid__2
This command exposes the constant :n:`@qualid__1` to OCaml libraries under
the name :n:`@qualid__2`. This constant can then be dynamically located
calling :n:`Coqlib.lib_ref "@qualid__2"`; i.e., there is no need to known
where is the constant defined (file, module, library, etc.).
As a special case, when the first segment of :n:`@qualid__2` is :g:`kernel`,
the constant is exposed to the kernel. For instance, the `Int63` module
features the following declaration:
.. coqdoc::
Register bool as kernel.ind_bool.
This makes the kernel aware of what is the type of boolean values. This
information is used for instance to define the return type of the
:g:`#int63_eq` primitive.
.. seealso:: :ref:`primitive-integers`
Inlining hints for the fast reduction machines
````````````````````````````````````````````````````````````````
.. cmd:: Register Inline @qualid
This command gives as a hint to the reduction machines (VM and native) that
the body of the constant :n:`@qualid` should be inlined in the generated code.
Registering primitive operations
````````````````````````````````
.. cmd:: Primitive @ident__1 := #@ident__2.
Declares :n:`@ident__1` as the primitive operator :n:`#@ident__2`. When
running this command, the type of the primitive should be already known by
the kernel (this is achieved through this command for primitive types and
through the :cmd:`Register` command with the :g:`kernel` name-space for other
types).
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