Vernacular commands¶
Displaying¶
This command displays on the screen information about the declared or
defined object referred by qualid
.
Error messages:
-
Error
Universe instance should have length :n:`num`.
¶
-
Error
This object does not support universe names.
¶
Variants:
-
Variant
Print Term qualid.
This is a synonym to Print
qualid
when qualid
denotes a global constant.
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.
This locally renames the polymorphic universes of qualid
.
An underscore means the raw universe is printed.
This form can be used with Print Term
and About
.
-
Command
Print All.
¶
This command displays information about the current state of the environment, including sections and modules.
Variants:
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 configurability is based on flags (e.g. Printing All
), options
(e.g. Printing Width
), or tables (e.g. Add Printing Record
). The
names of flags, options and tables are made of non-empty sequences of
identifiers (conventionally with capital initial letter). The general commands
handling flags, options and tables are given below.
-
Command
Set flag.
¶
This command switches flag
on. The original state of flag
is restored
when the current module ends.
Variants:
-
Variant
Local Set flag.
This command switches flag
on. The original state
of flag
is restored when the current section ends.
-
Variant
Global Set flag.
This command switches flag
on. The original state
of flag
is not restored at the end of the module. Additionally, if
set in a file, flag
is switched on when the file is Require-d.
-
Variant
Export Set flag.
This command switches
flag
on. The original state offlag
is restored at the end of the current module, butflag
is switched on when this module is imported.
-
Command
Unset flag.
¶
This command switches flag
off. The original state of flag
is restored
when the current module ends.
Variants:
-
Variant
Local Unset flag.
This command switches flag
off. The original
state of flag
is restored when the current section ends.
-
Variant
Global Unset flag.
This command switches flag
off. The original
state of flag
is not restored at the end of the module. Additionally,
if set in a file, flag
is switched off when the file is Require-d.
-
Variant
Export Unset flag.
This command switches
flag
off. The original state offlag
is restored at the end of the current module, butflag
is switched off when this module is imported.
-
Command
Test flag.
¶
This command prints whether flag
is on or off.
-
Command
Set option value.
This command sets option
to value
. The original value of ` option` is
restored when the current module ends.
Variants:
-
Variant
Local Set option value.
This command sets option
to value
. The
original value of option
is restored at the end of the module.
-
Variant
Global Set option value.
This command sets option
to value
. The
original value of option
is not restored at the end of the module.
Additionally, if set in a file, option
is set to value when the file
is Require-d.
-
Variant
Export Set option.
This command set
option
tovalue
. The original state ofoption
is restored at the end of the current module, butoption
is set tovalue
when this module is imported.
-
Command
Unset option.
This command turns off
option
.
Variants:
-
Variant
Local Unset option.
This command turns off
option
. The original state ofoption
is restored when the current section ends.
-
Variant
Global Unset option.
This command turns off
option
. The original state ofoption
is not restored at the end of the module. Additionally, if unset in a file,option
is reset to its default value when the file is Require-d.
-
Variant
Export Unset option.
This command turns off
option
. The original state ofoption
is restored at the end of the current module, butoption
is set to its default value when this module is imported.
-
Command
Test option.
This command prints the current value of option
.
-
Command
Add table value.
¶
-
Command
Remove table value.
¶
-
Command
Test table value.
¶
-
Command
Test table for value.
¶
-
Command
Print Table table.
¶
These are general commands for tables.
-
Command
Print Options.
¶
This command lists all available flags, options and tables.
Variants:
-
Variant
Print Tables.
This is a synonymous of Print Options
.
Requests to the environment¶
This command displays the type of term
. When called in proof mode, the
term is checked in the local context of the current subgoal.
Variants:
specifies on which subgoal to perform typing (see Section Invocation of tactics).
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.
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.
This command displays the extracted term from term
. The extraction is
processed according to the distinction between Set
and Prop
; that is
to say, between logical and computational content (see Section Sorts).
The extracted term is displayed in OCaml syntax, where global identifiers are
still displayed as in Coq terms.
Variants:
-
Variant
Recursive Extraction qualid+.
Recursively extracts all the material needed for the extraction of the qualified identifiers.
See also: Chapter Extraction of programs in OCaml and Haskell.
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.
Variants:
-
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.
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 messages:
There is no constant in the environment named qualid.
Variants:
-
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
.
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.
- 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
Note
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.
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.
- SearchHead 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
- SearchHead (@eq bool).
- andb_true_intro: forall b1 b2 : bool, b1 = true /\ b2 = true -> (b1 && b2)%bool = true
Variants:
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 messages:
No module qualid
has been required
(see Section Compiled files).
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
.
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.
- Require Import Arith.
- SearchPattern (_ + _ = _ + _).
- 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)
- SearchPattern (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
- SearchPattern (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.
- SearchPattern (?X1 + _ = _ + ?X1).
- Nat.add_comm: forall n m : nat, n + m = m + n
Variants:
This restricts the search to constructions defined in the modules named by the given qualid
sequence.
This restricts the search to constructions not defined in the modules named by the given qualid
sequence.
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.
-
Variant
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 “_”.
- 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))
Variants:
-
Variant
SearchRewrite term inside qualid+.
This restricts the search to constructions defined in the modules named by the given qualid
sequence.
This restricts the search to constructions not defined in the modules named by the given qualid
sequence.
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
For the Search
, SearchHead
, SearchPattern
and SearchRewrite
queries, it
is possible to globally filter the search results via the command
Add Search Blacklist
substring
. A lemma whose fully-qualified name
contains any of the declared substrings will be removed from the
search results. The default blacklisted substrings are _subproof
Private_
. The command Remove Search Blacklist ...
allows expunging
this blacklist.
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 name spaces of Coq: terms, modules, Ltac, etc.
- Set Printing Depth 50.
- 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
Variants:
-
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.
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.
Variants:
-
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 messages:
-
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.
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.
Variants:
-
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 messages:
-
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).
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.
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).
Variants:
-
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 messages:
-
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.
This command changes the current directory according to string
which
can be any valid path.
Variants:
-
Variant
Cd.
Is equivalent to Pwd.
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.
Variants:
-
Variant
Add LoadPath string.
Performs as Add LoadPath string
as dirpath
but
for the empty directory path.
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.
Variants:
-
Variant
Add Rec LoadPath string.
Works as Add Rec LoadPath
string
as dirpath
but for the empty
logical directory path.
This command removes the path string
from the current Coq loadpath.
-
Command
Print LoadPath.
¶
This command displays the current Coq loadpath.
Variants:
-
Variant
Print LoadPath dirpath.
Works as Print LoadPath
but displays only
the paths that extend the dirpath
prefix.
This command adds the path string
to the current OCaml
loadpath (see the command Declare ML Module` in Section Compiled files).
This command adds the directory string
and all its subdirectories to
the current OCaml loadpath (see the command Declare ML Module
in Section Compiled files).
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).
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
.
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 messages:
Variants:
-
Command
Reset Initial.
¶
Goes back to the initial state, just after the start of the interactive session.
-
Command
Back.
¶
This commands 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.
Variants:
-
Variant
Back num.
Undoes 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 messages:
-
Error
Invalid backtrack
¶
The user wants to undo more commands than available in the history.
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.
Variants:
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 messages:
-
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 implementors 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).
-
Command
Time command.
¶
This command executes the vernacular command command
and displays the
time needed to execute it.
This command executes the vernacular command command
, redirecting its
output to “string
.out”.
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 aTimeout
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 messages:
-
Error
The command has not failed!
¶
Controlling display¶
-
Option
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.
-
Option
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 integer
¶ 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 integer
¶ 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.
-
Option
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.
-
Option
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.
-
Option
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.
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.
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, Automatizing, Switching on/off the proof editing mode
Error messages:
-
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.
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.
The scope of Transparent is limited to the current section, or current
file, unless the variant Global Transparent
is
used.
Error messages:
-
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, Automatizing, Switching on/off the proof editing mode
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 −∞)
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.
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 messages:
-
Error
The reference is not unfoldable.
¶
Variants:
-
Variant
Print Strategies.
Print all the currently non-transparent strategies.
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: sections 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
(see Section Coercions) andStrategy
(see here) 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 extent 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
Implicit Arguments
,Ltac
orNotation
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 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
occurs in. The
Transparent
andOpaque
(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
andUnset
commands belong to this category.