\[\begin{split}\newcommand{\alors}{\textsf{then}} \newcommand{\alter}{\textsf{alter}} \newcommand{\as}{\kw{as}} \newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)} \newcommand{\bool}{\textsf{bool}} \newcommand{\case}{\kw{case}} \newcommand{\conc}{\textsf{conc}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} \newcommand{\conshl}{\textsf{cons\_hl}} \newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)} \newcommand{\emptyf}{\textsf{emptyf}} \newcommand{\End}{\kw{End}} \newcommand{\kwend}{\kw{end}} \newcommand{\EqSt}{\textsf{EqSt}} \newcommand{\even}{\textsf{even}} \newcommand{\evenO}{\textsf{even}_\textsf{O}} \newcommand{\evenS}{\textsf{even}_\textsf{S}} \newcommand{\false}{\textsf{false}} \newcommand{\filter}{\textsf{filter}} \newcommand{\Fix}{\kw{Fix}} \newcommand{\fix}{\kw{fix}} \newcommand{\for}{\textsf{for}} \newcommand{\forest}{\textsf{forest}} \newcommand{\from}{\textsf{from}} \newcommand{\Functor}{\kw{Functor}} \newcommand{\haslength}{\textsf{has\_length}} \newcommand{\hd}{\textsf{hd}} \newcommand{\ident}{\textsf{ident}} \newcommand{\In}{\kw{in}} \newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)} \newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)} \newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}} \newcommand{\injective}{\kw{injective}} \newcommand{\kw}[1]{\textsf{#1}} \newcommand{\lb}{\lambda} \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{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} \newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} \newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} \newcommand{\mto}{.\;} \newcommand{\Nat}{\mathbb{N}} \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{\Prod}{\textsf{prod}} \newcommand{\Prop}{\textsf{Prop}} \newcommand{\return}{\kw{return}} \newcommand{\Set}{\textsf{Set}} \newcommand{\si}{\textsf{if}} \newcommand{\sinon}{\textsf{else}} \newcommand{\Sort}{\cal S} \newcommand{\Str}{\textsf{Stream}} \newcommand{\Struct}{\kw{Struct}} \newcommand{\subst}[3]{#1\{#2/#3\}} \newcommand{\tl}{\textsf{tl}} \newcommand{\tree}{\textsf{tree}} \newcommand{\true}{\textsf{true}} \newcommand{\Type}{\textsf{Type}} \newcommand{\unfold}{\textsf{unfold}} \newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} \newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} \newcommand{\WF}[2]{{\cal W\!F}(#1)[#2]} \newcommand{\WFE}[1]{\WF{E}{#1}} \newcommand{\WFT}[2]{#1[] \vdash {\cal W\!F}(#2)} \newcommand{\WFTWOLINES}[2]{{\cal 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}]} \newcommand{\zeros}{\textsf{zeros}} \end{split}\]

# Vernacular commands

## Displaying

Command `Print qualid`

  This command displays on the screen information about the declared or defined object referred by `qualid`.

  Error messages:

  Error `qualid not a defined object.`
  Error `Universe instance should have length num.`
  Error `This object does not support universe names.`
  Variant `Print Term qualid`

    This is a synonym of `Print` `qualid` when `qualid` denotes a global constant.

  Variant `Print Term? qualid@name`

    This locally renames the polymorphic universes of `qualid`. An underscore means the raw universe is printed.

Command `About qualid`

  This displays various information about the object denoted by `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.

  Variant `About qualid@name`

    This locally renames the polymorphic universes of `qualid`. An underscore means the raw universe is printed.

Command `Print All`

  This command displays information about the current state of the environment, including sections and modules.

  Variant `Inspect num`

    This command displays the `num` last objects of the current environment, including sections and modules.

  Variant `Print Section ident`

    The name `ident` should correspond to a currently open section, this command displays the objects defined since the beginning of this section.

## Flags, Options and Tables

Coq has many settings to control its behavior. Setting types include flags, options and tables:

- A `flag` has a boolean value, such as `Asymmetric Patterns`.
- An `option` generally has a numeric or string value, such as `Firstorder Depth`.
- A `table` contains a set of strings or qualids.
- In addition, some commands provide settings, such as `Extraction Language OCaml`.

Flags, options and tables are identified by a series of identifiers, each with an initial capital letter.

Command `Local | Global | Export? Set flag`

  Sets `flag` on. Scoping qualifiers are described here.

Command `Local | Global | Export? Unset flag`

  Sets `flag` off. Scoping qualifiers are described here.

Command `Test flag`

  Prints the current value of `flag`.

Command `Local | Global | Export? Set option ( num | string )`

  Sets `option` to the specified value. Scoping qualifiers are described here.

Command `Local | Global | Export? Unset option`

  Sets `option` to its default value. Scoping qualifiers are described here.

Command `Test option`

  Prints the current value of `option`.

Command `Print Options`

  Prints the current value of all flags and options, and the names of all tables.

Command `Add table ( string | qualid )`

  Adds the specified value to `table`.

Command `Remove table ( string | qualid )`

  Removes the specified value from `table`.

Command `Test table for ( string | qualid )`

  Reports whether `table` contains the specified value.

Command `Print Table table`

  Prints the values in `table`.

Command `Test table`

  A synonym for `Print Table @table`.

Command `Print Tables`

  A synonym for `Print Options`.

### Scope qualifiers for `Set` and `Unset`

`Local | Global | Export?`

Flag and option settings can be global in scope or local to nested scopes created by `Module` and `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 `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 `Import`-ing the file sets the option.

Newly opened scopes inherit the current settings.

## Requests to the environment

Command `Check term`

  This command displays the type of `term`. When called in proof mode, the term is checked in the local context of the current subgoal.

  Variant `selector: Check term`

    This variant specifies on which subgoal to perform typing (see Section Invocation of tactics).

Command `Eval convtactic in term`

  This command performs the specified reduction on `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).

  See also

  Section Performing computations.

Command `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` `term`.

  See also

  Section Performing computations.

Command `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.

  Variant `Print Opaque Dependencies qualid`

    Displays the set of opaque constants `qualid` relies on in addition to the assumptions.

  Variant `Print Transparent Dependencies qualid`

    Displays the set of transparent constants `qualid` relies on in addition to the assumptions.

  Variant `Print All Dependencies qualid`

    Displays all assumptions and constants `qualid` relies on.

Command `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 `qualid`. This command is useful to remind the user of the name of library lemmas.

  Error `The reference qualid was not found in the current environment.`

    There is no constant in the environment named qualid.

  Variant `Search string`

    If `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 `qualid` (referred to by its main symbol as in "+" or by its notation’s string as in "_ + _" or "_ 'U' _", see Section Notations), the command works like `Search` `qualid`.

  Variant `Search string%key`

    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 `key` (see Section Local interpretation rules for notations).

  Variant `Search term_pattern`

    This searches for all statements or types of definition that contains a subterm that matches the pattern term_pattern (holes of the pattern are either denoted by _ or by ?ident when non linear patterns are expected).

  Variant `Search { + [-]term_pattern_string }`

    where `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 `term_pattern` (or `qualid` if `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.

  Variant `Search term_pattern_string … term_pattern_string inside qualid+`

    This restricts the search to constructions defined in the modules named by the given `qualid` sequence.

  Variant `Search term_pattern_string … term_pattern_string outside qualid+`

    This restricts the search to constructions not defined in the modules named by the given `qualid` sequence.

  Variant `selector: Search [-]term_pattern_string … [-]term_pattern_string`

    This specifies the goal on which to search hypothesis (see Section Invocation of tactics). By default the 1st goal is searched. This variant can be combined with other variants presented here.

    Example

    Require Import ZArith.
      [Loading ML file z_syntax_plugin.cmxs ... done] [Loading ML file quote_plugin.cmxs ... done] [Loading ML file newring_plugin.cmxs ... done] [Loading ML file omega_plugin.cmxs ... done]
    Search Z.mul Z.add "distr".
      Z.mul_add_distr_l: forall n m p : Z, (n * (m + p))%Z = (n * m + n * p)%Z Z.mul_add_distr_r: forall n m p : Z, ((n + m) * p)%Z = (n * p + m * p)%Z fast_Zmult_plus_distr_l: forall (n m p : Z) (P : Z -> Prop), P (n * p + m * p)%Z -> P ((n + m) * p)%Z
    Search "+"%Z "*"%Z "distr" -positive -Prop.
      Z.mul_add_distr_l: forall n m p : Z, (n * (m + p))%Z = (n * m + n * p)%Z Z.mul_add_distr_r: forall n m p : Z, ((n + m) * p)%Z = (n * p + m * p)%Z
    Search (?x * _ + ?x * _)%Z outside OmegaLemmas.
      Z.mul_add_distr_l: forall n m p : Z, (n * (m + p))%Z = (n * m + n * p)%Z
  Variant `SearchAbout`

    Deprecated since version 8.5.

    Up to Coq version 8.4, `Search` had the behavior of current `SearchHead` and the behavior of current `Search` was obtained with command `SearchAbout`. For compatibility, the deprecated name `SearchAbout` can still be used as a synonym of `Search`. For compatibility, the list of objects to search when using `SearchAbout` may also be enclosed by optional `[ ]` delimiters.

Command `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

  Search Head le.
    le_n: forall n : nat, n <= n le_0_n: forall n : nat, 0 <= n le_S: forall n m : nat, n <= m -> n <= S m le_pred: forall n m : nat, n <= m -> Nat.pred n <= Nat.pred m le_n_S: forall n m : nat, n <= m -> S n <= S m le_S_n: forall n m : nat, S n <= S m -> n <= m
  Search Head (@eq bool).
    andb_true_intro: forall b1 b2 : bool, b1 = true /\ b2 = true -> (b1 && b2)%bool = true
  Variant `SearchHead term inside qualid+`

    This restricts the search to constructions defined in the modules named by the given `qualid` sequence.

  Variant `SearchHead term outside qualid+`

    This restricts the search to constructions not defined in the modules named by the given `qualid` sequence.

  Error `Module/section qualid not found.`

    No module `qualid` has been required (see Section Compiled files).

  Variant `selector: SearchHead term`

    This specifies the goal on which to search hypothesis (see Section 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`.

Command `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 `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

  Require Import Arith.
  Search Pattern (_ + _ = _ + _).
    Nat.add_comm: forall n m : nat, n + m = m + n plus_Snm_nSm: forall n m : nat, S n + m = n + S m Nat.add_succ_comm: forall n m : nat, S n + m = n + S m Nat.add_shuffle3: forall n m p : nat, n + (m + p) = m + (n + p) plus_assoc_reverse: forall n m p : nat, n + m + p = n + (m + p) Nat.add_assoc: forall n m p : nat, n + (m + p) = n + m + p Nat.add_shuffle0: forall n m p : nat, n + m + p = n + p + m f_equal2_plus: forall x1 y1 x2 y2 : nat, x1 = y1 -> x2 = y2 -> x1 + x2 = y1 + y2 Nat.add_shuffle2: forall n m p q : nat, n + m + (p + q) = n + q + (m + p) Nat.add_shuffle1: forall n m p q : nat, n + m + (p + q) = n + p + (m + q)
  Search Pattern (nat -> bool).
    Nat.odd: nat -> bool Init.Nat.odd: nat -> bool Nat.even: nat -> bool Init.Nat.even: nat -> bool Init.Nat.testbit: nat -> nat -> bool Nat.leb: nat -> nat -> bool Nat.eqb: nat -> nat -> bool Init.Nat.eqb: nat -> nat -> bool Nat.ltb: nat -> nat -> bool Nat.testbit: nat -> nat -> bool Init.Nat.leb: nat -> nat -> bool Init.Nat.ltb: nat -> nat -> bool BinNat.N.testbit_nat: BinNums.N -> nat -> bool BinPosDef.Pos.testbit_nat: BinNums.positive -> nat -> bool BinPos.Pos.testbit_nat: BinNums.positive -> nat -> bool BinNatDef.N.testbit_nat: BinNums.N -> nat -> bool
  Search Pattern (forall l : list _, _ l l).
    List.incl_refl: forall (A : Type) (l : list A), List.incl l l List.lel_refl: forall (A : Type) (l : list A), List.lel 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

  Search Pattern (?X1 + _ = _ + ?X1).
    Nat.add_comm: forall n m : nat, n + m = m + n
  Variant `SearchPattern term inside qualid+`

    This restricts the search to constructions defined in the modules named by the given `qualid` sequence.

  Variant `SearchPattern term outside qualid+`

    This restricts the search to constructions not defined in the modules named by the given `qualid` sequence.

  Variant `selector: SearchPattern term`

    This specifies the goal on which to search hypothesis (see Section Invocation of tactics). By default the 1st goal is searched. This variant can be combined with other variants presented here.

Command `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

  Require Import Arith.
  SearchRewrite (_ + _ + _).
    Nat.add_shuffle0: forall n m p : nat, n + m + p = n + p + m plus_assoc_reverse: forall n m p : nat, n + m + p = n + (m + p) Nat.add_assoc: forall n m p : nat, n + (m + p) = n + m + p Nat.add_shuffle1: forall n m p q : nat, n + m + (p + q) = n + p + (m + q) Nat.add_shuffle2: forall n m p q : nat, n + m + (p + q) = n + q + (m + p) Nat.add_carry_div2: forall (a b : nat) (c0 : bool), (a + b + Nat.b2n c0) / 2 = a / 2 + b / 2 + Nat.b2n (Nat.testbit a 0 && Nat.testbit b 0 || c0 && (Nat.testbit a 0 || Nat.testbit b 0))
  Variant `SearchRewrite term inside qualid+`

    This restricts the search to constructions defined in the modules named by the given `qualid` sequence.

  Variant `SearchRewrite term outside qualid+`

    This restricts the search to constructions not defined in the modules named by the given `qualid` sequence.

  Variant `selector: SearchRewrite term`

    This specifies the goal on which to search hypothesis (see Section 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`

  Specifies a set of strings used to exclude lemmas from the results of `Search`, `SearchHead`, `SearchPattern` and `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 `Add @table` and `Remove @table` commands to update the set of blacklisted strings.

Command `Locate qualid`

  This command displays the full name of objects whose name is a prefix of the qualified identifier `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

  Locate nat.
    Inductive Coq.Init.Datatypes.nat
  Locate Datatypes.O.
    Constructor Coq.Init.Datatypes.O (shorter name to refer to it in current context is O)
  Locate Init.Datatypes.O.
    Constructor Coq.Init.Datatypes.O (shorter name to refer to it in current context is O)
  Locate Coq.Init.Datatypes.O.
    Constructor Coq.Init.Datatypes.O (shorter name to refer to it in current context is O)
  Locate I.Dont.Exist.
    No object of suffix I.Dont.Exist
  Variant `Locate Term qualid`

    As Locate but restricted to terms.

  Variant `Locate Module qualid`

    As Locate but restricted to modules.

  Variant `Locate Ltac qualid`

    As Locate but restricted to tactics.

See also

Section Locating notations

## 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.

Command `Load ident`

  This command loads the file named `ident`.v, searching successively in each of the directories specified in the loadpath. (see Section Libraries and filesystem)

  Files loaded this way cannot leave proofs open, and the `Load` command cannot be used inside a proof either.

  Variant `Load string`

    Loads the file denoted by the string `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`.

  Variant `Load Verbose ident`
  Variant `Load Verbose string`

    Display, while loading, the answers of Coq to each command (including tactics) contained in the loaded file.

    See also

    Section Controlling display.

  Error `Can’t find file ident on loadpath.`
  Error `Load is not supported inside proofs.`
  Error `Files processed by Load cannot leave open proofs.`

## Compiled files

This section describes the commands used to load compiled files (see Chapter The Coq commands for documentation on how to compile a file). A compiled file is a particular case of module called library file.

Command `Require qualid`

  This command looks in the loadpath for a file containing module `qualid` and adds the corresponding module to the environment of Coq. As library files have dependencies in other library files, the command `Require` `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, `qualid` is decomposed under the form dirpath.ident and the file 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 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.

  Variant `Require Import qualid`

    This loads and declares the module `qualid` and its dependencies then imports the contents of `qualid` as described here. It does not import the modules on which qualid depends unless these modules were themselves required in module `qualid` using `Require Export`, as described below, or recursively required through a sequence of `Require Export`. If the module required has already been loaded, `Require Import` `qualid` simply imports it, as `Import` `qualid` would.

  Variant `Require Export qualid`

    This command acts as `Require Import` `qualid`, but if a further module, say A, contains a command `Require Export` B, then the command `Require Import` A also imports the module B.

  Variant `Require [Import | Export] qualid+`

    This loads the modules named by the `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`.

  Variant `From dirpath Require qualid`

    This command acts as `Require`, but picks any library whose absolute name is of the form dirpath.dirpath’.qualid for some dirpath’. This is useful to ensure that the `qualid` library comes from a given package by making explicit its absolute root.

  Error `Cannot load qualid: no physical path bound to dirpath.`
  Error `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 Libraries and filesystem).

  Error `Compiled library ident.vo makes inconsistent assumptions over library qualid.`

    The command tried to load library file `ident`.vo that depends on some specific version of library `qualid` which is not the one already loaded in the current Coq session. Probably ident.v was not properly recompiled with the last version of the file containing module `qualid`.

  Error `Bad magic number.`

    The file ident.vo was found but either it is not a Coq compiled module, or it was compiled with an incompatible version of Coq.

  Error `The file `ident.vo` contains library dirpath and not library dirpath’.`

    The library file dirpath’ is indirectly required by the `Require` command but it is bound in the current loadpath to the file ident.vo which was bound to a different library name dirpath at the time it was compiled.

  Error `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 Import).

    See also

    Chapter The Coq commands

Command `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.

Command `Declare ML Module string+`

  This commands loads the OCaml compiled files with names given by the `string` sequence (dynamic link). It is mainly used to load tactics dynamically. The files are searched into the current OCaml loadpath (see the command `Add ML Path` in Section Libraries and filesystem). Loading of OCaml files is only possible under the bytecode version of `coqtop` (i.e. `coqtop` called with option `-byte`, see chapter The Coq commands), or when Coq has been compiled with a version of OCaml that supports native Dynlink (≥ 3.11).

  Variant `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.

  Error `File not found on loadpath: string.`
  Error `Loading of ML object file forbidden in a native Coq.`

Command `Print ML Modules`

  This prints the name of all OCaml modules loaded with `Declare ML Module`. To know from where these module were loaded, the user should use the command `Locate File` (see here)

## 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.

Command `Pwd`

  This command displays the current working directory.

Command `Cd string`

  This command changes the current directory according to `string` which can be any valid path.

  Variant `Cd`

    Is equivalent to Pwd.

Command `Add LoadPath string as dirpath`

  This command is equivalent to the command line option `-Q` `string` `dirpath`. It adds the physical directory string to the current Coq loadpath and maps it to the logical directory dirpath.

  Variant `Add LoadPath string`

    Performs as Add LoadPath `string` as `dirpath` but for the empty directory path.

Command `Add Rec LoadPath string as dirpath`

  This command is equivalent to the command line option `-R` `string` `dirpath`. It adds the physical directory string and all its subdirectories to the current Coq loadpath.

  Variant `Add Rec LoadPath string`

    Works as `Add Rec LoadPath` `string` as `dirpath` but for the empty logical directory path.

Command `Remove LoadPath string`

  This command removes the path `string` from the current Coq loadpath.

Command `Print LoadPath`

  This command displays the current Coq loadpath.

  Variant `Print LoadPath dirpath`

    Works as `Print LoadPath` but displays only the paths that extend the `dirpath` prefix.

Command `Add ML Path string`

  This command adds the path `string` to the current OCaml loadpath (see the command Declare ML Module` in Section Compiled files).

Command `Add Rec ML Path string`

  This command adds the directory `string` and all its subdirectories to the current OCaml loadpath (see the command `Declare ML Module`).

Command `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 Compiled files).

Command `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.

Command `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 `dirpath`.

## 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`.

Command `Reset ident`

  This command removes all the objects in the environment since `ident` was introduced, including `ident`. `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.

  Error `ident: no such entry.`
  Variant `Reset Initial`

    Goes back to the initial state, just after the start of the interactive session.

Command `Back`

  This command undoes all the effects of the last vernacular command. Commands read from a vernacular file via a `Load` are considered as a single command. Proof management commands are also handled by this command (see Chapter Proof handling). 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 `Qed`, the management information about the closed proof has been discarded. In this case, `Back` will then undo all the proof steps up to the statement of this proof.

  Variant `Back num`

    Undo `num` vernacular commands. As for Back, some extra commands may be undone in order to reach an adequate state. For instance Back `num` will not re-enter a closed proof, but rather go just before that proof.

  Error `Invalid backtrack.`

    The user wants to undo more commands than available in the history.

Command `BackTo num`

  This command brings back the system to the state labeled `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 `Back` (see above), the `BackTo` command now handles proof states. For that, it may have to undo some extra commands and end on a state num′ ≤ num if necessary.

  Variant `Backtrack num num num`

    Deprecated since version 8.4.

    `Backtrack` is a deprecated form of `BackTo` which allows explicitly manipulating the proof environment. The three numbers represent the following:

    - first number : State label to reach, as for `BackTo`.
    - second number : Proof state number to unbury once aborts have been done. Coq will compute the number of `Undo` to perform (see Chapter Proof handling).
    - third number : Number of `Abort` to perform, i.e. the number of currently opened nested proofs that must be canceled (see Chapter Proof handling).
  Error `Invalid backtrack.`

    The destination state label is unknown.

## Quitting and debugging

Command `Quit`

  This command permits to quit Coq.

Command `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

  1. It only works with the bytecode version of Coq (i.e. coqtop.byte, see Section interactive-use).
  2. 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).

Command `Time command`

  This command executes the vernacular command `command` and displays the time needed to execute it.

Command `Redirect string command`

  This command executes the vernacular command `command`, redirecting its output to "`string`.out".

Command `Timeout num command`

  This command executes the vernacular command `command`. If the command has not terminated after the time specified by the `num` (time expressed in seconds), then it is interrupted and an error message is displayed.

  Option `Default Timeout num`

    This option controls a default timeout for subsequent commands, as if they were passed to a `Timeout` command. Commands already starting by a `Timeout` are unaffected.

Command `Fail command`

  For debugging scripts, sometimes it is desirable to know whether a command or a tactic fails. If the given `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 `command` succeeds, the statement is an error, and it prints a message indicating that the failure did not occur.

  Error `The command has not failed!`

## Controlling display

Flag `Silent`

  This option controls the normal displaying.

Option `Warnings "( - | + )? ident+,"`

  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 `Search`, `SearchHead`, `SearchPattern`, `SearchRewrite` etc. to omit types from their output, printing only identifiers.

Option `Printing Width num`

  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.

Option `Printing Depth num`

  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 `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 Bullets or 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.

## 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 [Ler90]. 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.

Command `Opaque qualid+`

  This command has an effect on unfoldable constants, i.e. on constants defined by `Definition` or `Let` (with an explicit body), or by a command assimilated to a definition such as `Fixpoint`, `Program Definition`, etc, or by a proof ended by `Defined`. The command tells not to unfold the constants in the `qualid` sequence in tactics using δ-conversion (unfolding a constant is replacing it by its definition).

  `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 Conversion rules) of two distinct applied constants.

  Variant `Global Opaque qualid+`

    The scope of `Opaque` is limited to the current section, or current file, unless the variant `Global Opaque` is used.

  See also

  Sections Performing computations, Automating, Switching on/off the proof editing mode

  Error `The reference qualid was not found in the current environment.`

    There is no constant referred by `qualid` in the environment. Nevertheless, if you asked `Opaque` foo bar and if bar does not exist, foo is set opaque.

Command `Transparent qualid+`

  This command is the converse of `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.

  Variant `Global Transparent qualid+`

    The scope of Transparent is limited to the current section, or current file, unless the variant `Global Transparent` is used.

  Error `The reference qualid was not found in the current environment.`

    There is no constant referred by `qualid` in the environment.

    See also

    Sections Performing computations, Automating, Switching on/off the proof editing mode

Command `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 `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.

  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).
  > - `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 −∞)
  > Variant `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 `Transparent` and `Opaque` commands.

Command `Print Strategy qualid`

  This command prints the strategy currently associated to `qualid`. It fails if `qualid` is not an unfoldable reference, that is, neither a variable nor a constant.

  Error `The reference is not unfoldable.`
  Variant `Print Strategies`

    Print all the currently non-transparent strategies.

Command `Declare Reduction ident := convtactic`

  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 `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 cannot be qualified. In particular declaring the same name in several modules or in several functor applications will be refused if these declarations are not local. The name `ident` cannot be used directly as an Ltac tactic, but nothing prevents the user to also perform a `Ltac` ident `:=` convtactic.

  See also

  Performing computations

## Controlling the locality of commands

Command `Local command`

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 `Coercion` and `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 `Arguments`, `Ltac` or `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 `Transparent` and `Opaque` (see Section Controlling the reduction strategies and the conversion algorithm) 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 `Set` and `Unset` commands belong to this category.