$\begin{split}\newcommand{\as}{\kw{as}} \newcommand{\case}{\kw{case}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} \newcommand{\emptyf}{\textsf{emptyf}} \newcommand{\End}{\kw{End}} \newcommand{\kwend}{\kw{end}} \newcommand{\even}{\textsf{even}} \newcommand{\evenO}{\textsf{even}_\textsf{O}} \newcommand{\evenS}{\textsf{even}_\textsf{S}} \newcommand{\Fix}{\kw{Fix}} \newcommand{\fix}{\kw{fix}} \newcommand{\for}{\textsf{for}} \newcommand{\forest}{\textsf{forest}} \newcommand{\Functor}{\kw{Functor}} \newcommand{\In}{\kw{in}} \newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[4]{\kw{Ind}_{#4}[#1](#2:=#3)} \newcommand{\Indpstr}[5]{\kw{Ind}_{#4}[#1](#2:=#3)/{#5}} \newcommand{\injective}{\kw{injective}} \newcommand{\kw}[1]{\textsf{#1}} \newcommand{\length}{\textsf{length}} \newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} \newcommand{\List}{\textsf{list}} \newcommand{\lra}{\longrightarrow} \newcommand{\Match}{\kw{match}} \newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} \newcommand{\ModImp}[3]{{\kw{Mod}}({#1}:{#2}:={#3})} \newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} \newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} \newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} \newcommand{\mto}{.\;} \newcommand{\nat}{\textsf{nat}} \newcommand{\Nil}{\textsf{nil}} \newcommand{\nilhl}{\textsf{nil\_hl}} \newcommand{\nO}{\textsf{O}} \newcommand{\node}{\textsf{node}} \newcommand{\nS}{\textsf{S}} \newcommand{\odd}{\textsf{odd}} \newcommand{\oddS}{\textsf{odd}_\textsf{S}} \newcommand{\ovl}[1]{\overline{#1}} \newcommand{\Pair}{\textsf{pair}} \newcommand{\plus}{\mathsf{plus}} \newcommand{\SProp}{\textsf{SProp}} \newcommand{\Prop}{\textsf{Prop}} \newcommand{\return}{\kw{return}} \newcommand{\Set}{\textsf{Set}} \newcommand{\Sort}{\mathcal{S}} \newcommand{\Str}{\textsf{Stream}} \newcommand{\Struct}{\kw{Struct}} \newcommand{\subst}[3]{#1\{#2/#3\}} \newcommand{\tl}{\textsf{tl}} \newcommand{\tree}{\textsf{tree}} \newcommand{\trii}{\triangleright_\iota} \newcommand{\Type}{\textsf{Type}} \newcommand{\WEV}[3]{\mbox{#1[] \vdash #2 \lra #3}} \newcommand{\WEVT}[3]{\mbox{#1[] \vdash #2 \lra}\\ \mbox{ #3}} \newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} \newcommand{\WFE}[1]{\WF{E}{#1}} \newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} \newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} \newcommand{\with}{\kw{with}} \newcommand{\WS}[3]{#1[] \vdash #2 <: #3} \newcommand{\WSE}[2]{\WS{E}{#1}{#2}} \newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} \newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} \newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} \newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} \newcommand{\zeroone}[1]{[{#1}]} \end{split}$

# Coq commands¶

There are several Coq commands:

• coqide: a graphical integrated development environment, described here. In addition, there are several other IDEs such as Proof General, vsCoq and Coqtail that are not included with the Coq installation.

• coqtop: a legacy terminal-oriented, non-graphical interfaces for Coq

• coqc: the Coq compiler (batch compilation)

• coqchk: the Coq checker (validation of compiled libraries)

Many of the parameters to start these tools are shared and are described below. Passing the -help option on the command line will print a summary of the available command line parameters. There are also man pages for each of these, but they are probably less current than -help or this document).

## Interactive use (coqtop)¶

In the interactive mode, also known as the Coq toplevel, users can develop their theories and proofs step by step. The Coq toplevel is run by the command coqtop.

There are two different binary images of Coq: the byte-code one and the native-code one (if OCaml provides a native-code compiler for your platform, which is supposed in the following). By default, coqtop executes the native-code version; run coqtop.byte to get the byte-code version.

The byte-code toplevel is based on an OCaml toplevel (to allow dynamic linking of tactics). You can switch to the OCaml toplevel with the command Drop., and come back to the Coq toplevel with the command Coqloop.loop();;.

Flag Coqtop Exit On Error

This flag, off by default, causes coqtop to exit with status code 1 if a command produces an error instead of recovering from it.

## Batch compilation (coqc)¶

The coqc command compiles a Coq proof script file with a ".v" suffix to create a compiled file with a ".vo" suffix. (See Compiled files.) The last component of the filename must be a valid Coq identifier as described in Lexical conventions; it should contain only letters, digits or underscores (_) with a ".v" suffix on the final component. For example /bar/foo/toto.v is valid, but /bar/foo/to-to.v is not.

We recommend specifying a logical path (which is also the module name) with the -R or the -Q options. Generally we recommend using utilities such as make (using coq_makefile to generate the Makefile) or dune to build Coq projects. See Building a Coq project with coq_makefile (details) and Building a Coq project with Dune.

If foo.v is in Coq's current directory, you can use coqc foo.v to compile it and then Require foo. in your script. But this doesn't scale well for larger projects.

Generally it's better to define a new module: To compile foo.v as part of a module Mod1 that is rooted at . (i.e. the directory containing foo.v), run coqc -Q . Mod1 foo.v.

To make the module available in CoqIDE, include the following line in the _CoqProject file (see Building a Coq project with coq_makefile (details)) in the directory from which you start CoqIDE or give it as an argument to the coqide command. <PATH> is the pathname of the directory containing the module, which can be an absolute path or relative to Coq's current directory. For now, you must close and reload a named script file for CoqIDE to pick up the change, or restart CoqIDE. The project file name is configurable in Edit / Preferences / Project.

-R <PATH> Mod1

## Command parameters¶

There are 3 mechanisms for passing parameters to Coq commands. In order of importance they are:

• the coqrc start up script

### coqrc start up script¶

When Coq is launched, it can implicitly prepend a startup script to any document read by Coq, whether it is an interactive session or a file to compile. The startup script can come from a configuration directory or it can be specified on the command line.

Coq uses the first file found in this list as the startup script:

• $XDG_CONFIG_HOME/coqrc.<VERSION> •$XDG_CONFIG_HOME/coqrc

• $HOME/.coqrc.<VERSION> •$HOME/.coqrc

where $XDG_CONFIG_HOME is an environment variable.$HOME is the user's home directory. <VERSION> is the version of Coq (as shown by coqc --version, for example).

-init-file file on the command line uses the specified file instead of a startup script from a configuration directory. -q prevents the use of a startup script.

### Environment variables¶

$COQPATH can be used to specify the load path. It is a list of directories separated by : (; on Windows). Coq will also honor$XDG_DATA_HOME and $XDG_DATA_DIRS (see Section Logical paths and the load path). Some Coq commands call other Coq commands. In this case, they look for the commands in directory specified by$COQBIN. If this variable is not set, they look for the commands in the executable path.

$COQ_COLORS can be used to specify the set of colors used by coqtop to highlight its output. It uses the same syntax as the$LS_COLORS variable from GNU’s ls, that is, a colon-separated list of assignments of the form name=attr*; where name is the name of the corresponding highlight tag and each attr is an ANSI escape code. The list of highlight tags can be retrieved with the -list-tags command-line option of coqtop.

The string uses ANSI escape codes to represent attributes. For example:

sets the highlights for added text in diffs to underlined (the 4) with a background RGB color (0, 0, 240) and for removed text in diffs to a red background. Note that if you specify COQ_COLORS, the predefined attributes are ignored.

$OCAMLRUNPARAM, described here, can be used to specify certain runtime and memory usage parameters. In most cases, experimenting with these settings will likely not cause a significant performance difference and should be harmless. If the variable is not set, Coq uses the default values, except that space_overhead is set to 120 and minor_heap_size is set to 32Mwords (256MB with 64-bit executables or 128MB with 32-bit executables). Specifies which components produce events when using the Profiling system. It is a comma separated list of component names. If the variable is not set, all components produce events. Component names are internally defined, but command which corresponds to the interpretation of one command is particularly notable. ### Command line options¶ The following command-line options are recognized by the commands coqc and coqtop, unless stated otherwise: -I directory, -include directory Add physical path directory to the OCaml loadpath, which is needed to load OCaml object code files (.cmo or .cmxs). Subdirectories are not included. See the command Declare ML Module. Directories added with -I are searched after the current directory, in the order in which they were given on the command line -Q directory dirpath Makes the .vo files in a package available for loading with the Require command by adding new entries to the load path. The entries map the logical path dirpath to the physical path directory. Then Coq recursively adds load path entries for subdirectories. For example, -Q . Lib may add the logical path Lib.SubDir.File, which maps to the file ./SubDir/File.vo. Only subdirectories and files that follow the lexical conventions for idents are included. Subdirectories named CVS or _darcs are excluded. Some operating systems or file systems are more restrictive. For example, Linux’s ext4 file system limits filenames to 255 bytes. The default on NTFS (Windows) and HFS+ (MacOS X) file systems is to disallow two files in the same directory with names that differ only in their case. Loading files from packages made available with -Q must include the logical name of the package in From clause of the Require command or provide a fully qualified name. -R directory dirpath Similar to -Q directory dirpath, but allows using Require with a partially qualified name (i.e. without a From clause). -top dirpath Set the logical module name to dirpath for the coqtop interactive session. If no module name is specified, coqtop will default to Top. coqc does not accept this option because the logical module name is inferred from the name of the input file and the corresponding -R / -Q options. -exclude-dir directory Exclude any subdirectory named directory while processing options such as -R and -Q. By default, only the conventional version control management directories named CVS and_darcs are excluded. -nois, -noinit Start from an empty state instead of loading the Init.Prelude module. -init-file file Load file as the resource file instead of loading the default resource file from the standard configuration directories. -q Do not to load the default resource file. -l file, -load-vernac-source file Load and execute the Coq script from file.v. -lv file, -load-vernac-source-verbose file Load and execute the Coq script from file.v. Write its contents to the standard output as it is executed. -require qualid Load Coq compiled library qualid. This is equivalent to running Require qualid (note: the short form -r *qualid* is intentionally not provided to prevent the risk of collision with -R). Note Note that the relative order of this command-line option and its variants (-ri, -re, -rfrom, -refrom, -rifrom) and of the -set and -unset options matters since the various Require, Require Import, Require Export, Set and Unset commands will be executed in the order specified on the command-line. -ri qualid, -require-import qualid Load Coq compiled library qualid and import it. This is equivalent to running Require Import qualid. See the note above regarding the order of command-line options. -re qualid, -require-export qualid Load Coq compiled library qualid and transitively import it. This is equivalent to running Require Export qualid. See the note above regarding the order of command-line options. -rfrom dirpath qualid, -require-from dirpath qualid Load Coq compiled library qualid. This is equivalent to running From dirpath Require qualid. See the note above regarding the order of command-line options. -rifrom dirpath qualid, -require-import-from dirpath qualid Load Coq compiled library qualid and import it. This is equivalent to running From dirpath Require Import qualid. See the note above regarding the order of command-line options. -refrom dirpath qualid, -require-export-from dirpath qualid Load Coq compiled library qualid and transitively import it. This is equivalent to running From dirpath Require Export qualid. See the note above regarding the order of command-line options. -load-vernac-object qualid Obsolete synonym of -require qualid. -batch Exit just after argument parsing. Available for coqtop only. -verbose Output the content of the input file as it is compiled. This option is available for coqc only. -native-compiler (yes|no|ondemand) Enable the native_compute reduction machine and precompilation to .cmxs files for future use by native_compute. Setting yes enables native_compute; it also causes Coq to precompile the native code for future use; all dependencies need to have been precompiled beforehand. Setting no disables native_compute which defaults back to vm_compute; no files are precompiled. Setting ondemand enables native_compute but disables precompilation; all missing dependencies will be recompiled every time native_compute is called. Deprecated since version 8.14: This flag has been deprecated in favor of the Split compilation of native computation files binary. The toolchain has been adapted to transparently rely on the latter, so if you use Building a Coq project with coq_makefile (details) there is nothing to do. Otherwise you should substitute calls to coqc -native-compiler yes to calls to coqc followed by coqnative on the resulting vo file. Changed in version 8.13: The default value is set at configure time, -config can be used to retrieve it. All this can be summarized in the following table: configure coqc native_compute outcome requirements yes yes (default) native_compute .cmxs .cmxs of deps yes no vm_compute none none yes ondemand native_compute none none no yes, no, ondemand vm_compute none none ondemand yes native_compute .cmxs .cmxs of deps ondemand no vm_compute none none ondemand ondemand (default) native_compute none none -native-output-dir dir Set the directory in which to put the aforementioned .cmxs for native_compute. Defaults to .coq-native. -vos Indicate Coq to skip the processing of opaque proofs (i.e., proofs ending with Qed or Admitted), output a .vos files instead of a .vo file, and to load .vos files instead of .vo files when interpreting Require commands. -vok Indicate Coq to check a file completely, to load .vos files instead of .vo files when interpreting Require commands, and to output an empty .vok files upon success instead of writing a .vo file. -w (all|none|w₁,…,wₙ) Configure the display of warnings. This option expects all, none or a comma-separated list of warning names or categories (see Section Controlling display). -color (on|off|auto) Coqtop only. Enable or disable color output. Default is auto, meaning color is shown only if the output channel supports ANSI escape sequences. -diffs (on|off|removed) Coqtop only. Controls highlighting of differences between proof steps. on highlights added tokens, removed highlights both added and removed tokens. Requires that -color is enabled. (see Section Showing differences between proof steps). -beautify Pretty-print each command to file.beautified when compiling file.v, in order to get old-fashioned syntax/definitions/notations. -emacs, -ide-slave Start a special toplevel to communicate with a specific IDE. -impredicative-set Change the logical theory of Coq by declaring the sort Set impredicative. Warning This is known to be inconsistent with some standard axioms of classical mathematics such as the functional axiom of choice or the principle of description. -type-in-type Collapse the universe hierarchy of Coq. Warning This makes the logic inconsistent. -mangle-names ident Experimental. Do not depend on this option. Replace Coq's auto-generated name scheme with names of the form ident0, ident1, etc. Within Coq, the Mangle Names flag turns this behavior on, and the Mangle Names Prefix option sets the prefix to use. This feature is intended to be used as a linter for developments that want to be robust to changes in the auto-generated name scheme. The options are provided to facilitate tracking down problems. -set string Enable flags and set options. string should be setting_name=value, the value is interpreted according to the type of the option. For flags setting_name is equivalent to setting_name=true. For instance -set "Universe Polymorphism" will enable Universe Polymorphism. Note that the quotes are shell syntax, Coq does not see them. See the note above regarding the order of command-line options. -unset string As -set but used to disable options and flags. string must be . See the note above regarding the order of command-line options. -compat version Load a file that sets a few options to maintain partial backward-compatibility with a previous version. This is equivalent to Require Import Coq.Compat.CoqXXX with XXX one of the last three released versions (including the current version). Note that the explanations above regarding the order of command-line options apply, and this could be relevant if you are resetting some of the compatibility options. -dump-glob file Dump references for global names in file file (to be used by coqdoc, see Documenting Coq files with coqdoc). By default, if file.v is being compiled, file.glob is used. -no-glob Disable the dumping of references for global names. -image file Set the binary image to be used by coqc to be file instead of the standard one. Not of general use. -bindir directory Set the directory containing Coq binaries to be used by coqc. It is equivalent to doing export COQBIN= directory before launching coqc. -where Print the location of Coq’s standard library and exit. -config Print the locations of Coq’s binaries, dependencies, and libraries, then exit. -filteropts Print the list of command line arguments that coqtop has recognized as options and exit. -v Print Coq’s version and exit. -list-tags Print the highlight tags known by Coq as well as their currently associated color and exit. -h, --help Print a short usage and exit. -time Output timing information for each command to standard output. -time-file file Output timing information for each command to the given file. -profile file Output Profiling information to the given file. ## Profiling¶ Use the coqc command line argument -profile or the environment variable PROFILE in coq_makefile, to generate profiling information in Google trace format <https://docs.google.com/document/d/1CvAClvFfyA5R-PhYUmn5OOQtYMH4h6I0nSsKchNAySU/edit>. The output gives the duration and event counts for the execution of components of Coq (for instance process for the whole file, command for each command, pretyping for elaboration). Environment variable COQ_PROFILE_COMPONENTS can be used to filter which components produce events. This may be needed to reduce the size of the generated file. The generated file can be visualized with <https://ui.perfetto.dev> (which can directly load the .gz compressed file produced by coq_makefile) or processed using any JSON-capable system. Events are annotated with additional information in the args field (either on the beginning B or end E event): • major and minor indicate how many major and minor words were allocated during the event. • subtimes indicates how much time was spent in sub-components and how many times each subcomponent was profiled during the event (including subcomponents which do not appear in COQ_PROFILE_COMPONENTS). • for the command event, cmd displays the precise location of the command and a compressed representation of it (like the -time header), and line is the start line of the command. ## Compiled interfaces (produced using -vos)¶ Compiled interfaces help saving time while developing Coq formalizations, by compiling the formal statements exported by a library independently of the proofs that it contains. Warning Compiled interfaces should only be used for development purposes. At the end of the day, one still needs to proof check all files by producing standard .vo files. (Technically, when using -vos, fewer universe constraints are collected.) Moreover, this feature is still experimental, it may be subject to change without prior notice. Principle. The compilation using coqc -vos foo.v produces a file called foo.vos, which is similar to foo.vo except that all opaque proofs are skipped in the compilation process. The compilation using coqc -vok foo.v checks that the file foo.v correctly compiles, including all its opaque proofs. If the compilation succeeds, then the output is a file called foo.vok, with empty contents. This file is only a placeholder indicating that foo.v has been successfully compiled. (This placeholder is useful for build systems such as make.) When compiling a file bar.v that depends on foo.v (for example via a Require Foo. command), if the compilation command is coqc -vos bar.v or coqc -vok bar.v, then the file foo.vos gets loaded (instead of foo.vo). A special case is if file foo.vos exists and has empty contents, and foo.vo exists, then foo.vo is loaded. Appart from the aforementioned case where foo.vo can be loaded in place of foo.vos, in general the .vos and .vok files live totally independently from the .vo files. Dependencies generated by coq_makefile. The files foo.vos and foo.vok both depend on foo.v. Furthermore, if a file foo.v requires bar.v, then foo.vos and foo.vok also depend on bar.vos. Note, however, that foo.vok does not depend on bar.vok. Hence, as detailed further, parallel compilation of proofs is possible. In addition, coq_makefile generates for a file foo.v a target foo.required_vos which depends on the list of .vos files that foo.vos depends upon (excluding foo.vos itself). As explained next, the purpose of this target is to be able to request the minimal working state for editing interactively the file foo.v. Warning When writing a custom build system, be aware that coqdep only produces dependencies related to .vos and .vok if the -vos command line flag is passed. This is to maintain compatibility with dune (see ocaml/dune#2642 on github). Typical compilation of a set of file using a build system. Assume a file foo.v that depends on two files f1.v and f2.v. The command make foo.required_vos will compile f1.v and f2.v using the option -vos to skip the proofs, producing f1.vos and f2.vos. At this point, one is ready to work interactively on the file foo.v, even though it was never needed to compile the proofs involved in the files f1.v and f2.v. Assume a set of files f1.v ... fn.v with linear dependencies. The command make vos enables compiling the statements (i.e. excluding the proofs) in all the files. Next, make -j vok enables compiling all the proofs in parallel. Thus, calling make -j vok directly enables taking advantage of a maximal amount of parallelism during the compilation of the set of files. Note that this comes at the cost of parsing and typechecking all definitions twice, once for the .vos file and once for the .vok file. However, if files contain nontrivial proofs, or if the files have many linear chains of dependencies, or if one has many cores available, compilation should be faster overall. Need for Proof using When a theorem is in a section, typechecking the statement of the theorem may be insufficient to deduce the type of the statement at the end of the section. For example, the proof of the theorem may make use of section variables or section hypotheses that are not mentioned in the statement of the theorem. For this reason, proofs in sections should begin with Proof using instead of Proof. The using clause should give the names of the section variables that are required for the proof that are not involved in the typechecking of the statement. See Suggest Proof Using. (Note it's fine to use Proof using. instead of Proof. for proofs that are not in a section.) When using -vos, proofs in sections with Proof using are skipped. Proofs in sections without Proof using are fully processed (much slower). Interaction with standard compilation When compiling a file foo.v using coqc in the standard way (i.e., without -vos nor -vok), an empty file foo.vos and an empty file foo.vok are created in addition to the regular output file foo.vo. If coqc is subsequently invoked on some other file bar.v using option -vos or -vok, and that bar.v requires foo.v, if Coq finds an empty file foo.vos, then it will load foo.vo instead of foo.vos. The purpose of this feature is to allow users to benefit from the -vos option even if they depend on libraries that were compiled in the traditional manner (i.e., never compiled using the -vos option). ## Compiled libraries checker (coqchk)¶ The coqchk command takes a list of library paths as argument, described either by their logical name or by their physical filename, which must end in .vo. The corresponding compiled libraries (.vo files) are searched in the path, recursively processing the libraries they depend on. The content of all these libraries is then type checked. The effect of coqchk is only to return with normal exit code in case of success, and with positive exit code if an error has been found. Error messages are not deemed to help the user understand what is wrong. In the current version, it does not modify the compiled libraries to mark them as successfully checked. Note that non-logical information is not checked. By logical information, we mean the type and optional body associated with names. It excludes for instance anything related to the concrete syntax of objects (customized syntax rules, association between short and long names), implicit arguments, etc. This tool can be used for several purposes. One is to check that a compiled library provided by a third-party has not been forged and that loading it cannot introduce inconsistencies 1. Another point is to get an even higher level of security. Since coqtop can be extended with custom tactics, possibly ill-typed code, it cannot be guaranteed that the produced compiled libraries are correct. coqchk is a standalone verifier, and thus it cannot be tainted by such malicious code. Command-line options -Q, -R, -where and -impredicative-set are supported by coqchk and have the same meaning as for coqtop. As there is no notion of relative paths in object files -Q and -R have exactly the same meaning. -norec module Check module but do not check its dependencies. -admit module Do not check module and any of its dependencies, unless explicitly required. -o At exit, print a summary about the context. List the names of all assumptions and variables (constants without a body). -silent Do not write progress information to the standard output. Environment variable$COQLIB can be set to override the location of the standard library.

The algorithm for deciding which modules are checked or admitted is the following: assuming that coqchk is called with argument M, option -norec N, and -admit A. Let us write $$\overline{S}$$ for the set of reflexive transitive dependencies of set $$S$$. Then:

• Modules $$C = \overline{M} \backslash \overline{A} \cup M \cup N$$ are loaded and type checked before being added to the context.

• And $$M \cup N \backslash C$$ is the set of modules that are loaded and added to the context without type checking. Basic integrity checks (checksums) are nonetheless performed.

As a rule of thumb, -admit can be used to tell Coq that some libraries have already been checked. So coqchk A B can be split in coqchk A && coqchk B -admit A without type checking any definition twice. Of course, the latter is slightly slower since it makes more disk access. It is also less secure since an attacker might have replaced the compiled library A after it has been read by the first command, but before it has been read by the second command.

1

Ill-formed non-logical information might for instance bind Coq.Init.Logic.True to short name False, so apparently False is inhabited, but using fully qualified names, Coq.Init.Logic.False will always refer to the absurd proposition, what we guarantee is that there is no proof of this latter constant.