diff options
Diffstat (limited to 'doc/sphinx/language')
| -rw-r--r-- | doc/sphinx/language/gallina-extensions.rst | 65 | ||||
| -rw-r--r-- | doc/sphinx/language/gallina-specification-language.rst | 94 |
2 files changed, 73 insertions, 86 deletions
diff --git a/doc/sphinx/language/gallina-extensions.rst b/doc/sphinx/language/gallina-extensions.rst index 8746897e75..53b993eddc 100644 --- a/doc/sphinx/language/gallina-extensions.rst +++ b/doc/sphinx/language/gallina-extensions.rst @@ -1175,52 +1175,53 @@ component is equal ``nat`` and hence ``M1.T`` as specified. If `qualid` denotes a valid basic module (i.e. its module type is a signature), makes its components available by their short names. -.. example:: + .. example:: - .. coqtop:: reset all + .. coqtop:: reset all - Module Mod. + Module Mod. - Definition T:=nat. + Definition T:=nat. - Check T. + Check T. - End Mod. + End Mod. - Check Mod.T. + Check Mod.T. - Fail Check T. + Fail Check T. - Import Mod. + Import Mod. - Check T. + Check T. -Some features defined in modules are activated only when a module is -imported. This is for instance the case of notations (see :ref:`Notations`). + Some features defined in modules are activated only when a module is + imported. This is for instance the case of notations (see :ref:`Notations`). -Declarations made with the Local flag are never imported by theImport -command. Such declarations are only accessible through their fully -qualified name. + Declarations made with the ``Local`` flag are never imported by the :cmd:`Import` + command. Such declarations are only accessible through their fully + qualified name. -.. example:: + .. example:: - .. coqtop:: all + .. coqtop:: all - Module A. + Module A. - Module B. + Module B. - Local Definition T := nat. + Local Definition T := nat. - End B. + End B. - End A. + End A. - Import A. + Import A. - Fail Check B.T. + Fail Check B.T. .. cmdv:: Export @qualid + :name: Export When the module containing the command Export qualid is imported, qualid is imported as well. @@ -1231,16 +1232,17 @@ qualified name. .. cmd:: Print Module @ident - Prints the module type and (optionally) the body of the module `ident`. + Prints the module type and (optionally) the body of the module :n:`@ident`. .. cmd:: Print Module Type @ident - Prints the module type corresponding to `ident`. + Prints the module type corresponding to :n:`@ident`. .. opt:: Short Module Printing - This option (off by default) disables the printing of the types of fields, - leaving only their names, for the commands ``Print Module`` and ``Print Module Type``. + This option (off by default) disables the printing of the types of fields, + leaving only their names, for the commands :cmd:`Print Module` and + :cmd:`Print Module Type`. Libraries and qualified names --------------------------------- @@ -1510,9 +1512,8 @@ implicitly applied to the implicit arguments it is waiting for: one says that the implicit argument is maximally inserted. Each implicit argument can be declared to have to be inserted maximally or non -maximally. This can be governed argument per argument by the command ``Implicit -Arguments`` (see Section :ref:`declare-implicit-args`) or globally by the -:opt:`Maximal Implicit Insertion` option. +maximally. This can be governed argument per argument by the command +:cmd:`Arguments (implicits)` or globally by the :opt:`Maximal Implicit Insertion` option. See also :ref:`displaying-implicit-args`. @@ -1565,7 +1566,7 @@ absent in every situation but still be able to specify it if needed: The syntax is supported in all top-level definitions: -``Definition``, ``Fixpoint``, ``Lemma`` and so on. For (co-)inductive datatype +:cmd:`Definition`, :cmd:`Fixpoint`, :cmd:`Lemma` and so on. For (co-)inductive datatype declarations, the semantics are the following: an inductive parameter declared as an implicit argument need not be repeated in the inductive definition but will become implicit for the constructors of the diff --git a/doc/sphinx/language/gallina-specification-language.rst b/doc/sphinx/language/gallina-specification-language.rst index 46e684b122..aa41f8058d 100644 --- a/doc/sphinx/language/gallina-specification-language.rst +++ b/doc/sphinx/language/gallina-specification-language.rst @@ -609,6 +609,7 @@ of any section is equivalent to using ``Local Parameter``. Adds blocks of variables with different specifications. .. cmdv:: Variables {+ ( {+ @ident } : @term) } + :name: Variables .. cmdv:: Hypothesis {+ ( {+ @ident } : @term) } :name: Hypothesis @@ -672,6 +673,7 @@ Section :ref:`typing-rules`. You have to explicitly give their fully qualified name to refer to them. .. cmdv:: Example @ident := @term + :name: Example .. cmdv:: Example @ident : @term := @term @@ -1243,37 +1245,37 @@ inhabitant of the type) is interactively built using tactics. The interactive proof mode is described in Chapter :ref:`proofhandling` and the tactics in Chapter :ref:`Tactics`. The basic assertion command is: -.. cmd:: Theorem @ident : @type +.. cmd:: Theorem @ident {? @binders } : @type -After the statement is asserted, Coq needs a proof. Once a proof of -:token:`type` under the assumptions represented by :token:`binders` is given and -validated, the proof is generalized into a proof of forall , :token:`type` and -the theorem is bound to the name :token:`ident` in the environment. + After the statement is asserted, Coq needs a proof. Once a proof of + :token:`type` under the assumptions represented by :token:`binders` is given and + validated, the proof is generalized into a proof of :n:`forall @binders, @type` and + the theorem is bound to the name :token:`ident` in the environment. -.. exn:: The term @term has type @type which should be Set, Prop or Type. + .. exn:: The term @term has type @type which should be Set, Prop or Type. -.. exn:: @ident already exists. - :name: @ident already exists. (Theorem) + .. exn:: @ident already exists. + :name: @ident already exists. (Theorem) - The name you provided is already defined. You have then to choose - another name. + The name you provided is already defined. You have then to choose + another name. -.. cmdv:: Lemma @ident : @type - :name: Lemma + The following commands are synonyms of :n:`Theorem @ident {? @binders } : type`: -.. cmdv:: Remark @ident : @type - :name: Remark + .. cmdv:: Lemma @ident {? @binders } : @type + :name: Lemma -.. cmdv:: Fact @ident : @type - :name: Fact + .. cmdv:: Remark @ident {? @binders } : @type + :name: Remark -.. cmdv:: Corollary @ident : @type - :name: Corollary + .. cmdv:: Fact @ident {? @binders } : @type + :name: Fact -.. cmdv:: Proposition @ident : @type - :name: Proposition + .. cmdv:: Corollary @ident {? @binders } : @type + :name: Corollary - These commands are synonyms of ``Theorem`` :token:`ident` : :token:`type`. + .. cmdv:: Proposition @ident {? @binders } : @type + :name: Proposition .. cmdv:: Theorem @ident : @type {* with @ident : @type} @@ -1300,13 +1302,13 @@ the theorem is bound to the name :token:`ident` in the environment. .. cmdv:: Definition @ident : @type This allows defining a term of type :token:`type` using the proof editing - mode. It behaves as Theorem but is intended to be used in conjunction with + mode. It behaves as :cmd:`Theorem` but is intended to be used in conjunction with :cmd:`Defined` in order to define a constant of which the computational behavior is relevant. The command can be used also with :cmd:`Example` instead of :cmd:`Definition`. - See also :cmd:`Opaque`, :cmd:`Transparent`, :tacn:`unfold`. + .. seealso:: :cmd:`Opaque`, :cmd:`Transparent`, :tacn:`unfold`. .. cmdv:: Let @ident : @type @@ -1326,21 +1328,14 @@ the theorem is bound to the name :token:`ident` in the environment. This generalizes the syntax of CoFixpoint so that one or more bodies can be defined interactively using the proof editing mode. -.. cmd:: Proof - - A proof starts by the keyword Proof. Then Coq enters the proof editing mode - until the proof is completed. The proof editing mode essentially contains - tactics that are described in chapter :ref:`Tactics`. Besides tactics, there - are commands to manage the proof editing mode. They are described in Chapter - :ref:`proofhandling`. - -.. cmd:: Qed - - When the proof is completed it should be validated and put in the environment - using the keyword Qed. +A proof starts by the keyword :cmd:`Proof`. Then Coq enters the proof editing mode +until the proof is completed. The proof editing mode essentially contains +tactics that are described in chapter :ref:`Tactics`. Besides tactics, there +are commands to manage the proof editing mode. They are described in Chapter +:ref:`proofhandling`. -.. exn:: @ident already exists. - :name: @ident already exists. (Qed) +When the proof is completed it should be validated and put in the environment +using the keyword :cmd:`Qed`. .. note:: @@ -1349,28 +1344,19 @@ the theorem is bound to the name :token:`ident` in the environment. #. Not only other assertions but any vernacular command can be given while in the process of proving a given assertion. In this case, the command is understood as if it would have been given before the - statements still to be proved. - - #. Proof is recommended but can currently be omitted. On the opposite - side, Qed (or Defined, see below) is mandatory to validate a proof. + statements still to be proved. Nonetheless, this practice is discouraged + and may stop working in future versions. - #. Proofs ended by Qed are declared opaque. Their content cannot be + #. Proofs ended by :cmd:`Qed` are declared opaque. Their content cannot be unfolded (see :ref:`performingcomputations`), thus realizing some form of *proof-irrelevance*. To be able to unfold a - proof, the proof should be ended by Defined (see below). - -.. cmdv:: Defined - :name: Defined - - Same as :cmd:`Qed` but the proof is then declared transparent, which means - that its content can be explicitly used for type-checking and that it can be - unfolded in conversion tactics (see :ref:`performingcomputations`, - :cmd:`Opaque`, :cmd:`Transparent`). + proof, the proof should be ended by :cmd:`Defined`. -.. cmdv:: Admitted - :name: Admitted + #. :cmd:`Proof` is recommended but can currently be omitted. On the opposite + side, :cmd:`Qed` (or :cmd:`Defined`) is mandatory to validate a proof. - Turns the current asserted statement into an axiom and exits the proof mode. + #. One can also use :cmd:`Admitted` in place of :cmd:`Qed` to turn the + current asserted statement into an axiom and exit the proof editing mode. .. [1] This is similar to the expression “*entry* :math:`\{` sep *entry* |