diff options
author | Théo Zimmermann <theo.zimmermann@univ-paris-diderot.fr> | 2018-04-24 11:59:51 +0200 |
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committer | Théo Zimmermann <theo.zimmermann@univ-paris-diderot.fr> | 2018-05-05 11:54:05 +0200 |
commit | 5e22cf0783c9272158df92b90faedc37f6e47066 (patch) | |
tree | 9d67460206e7ba3f6547a4603ab0745eceea2c4a /doc/sphinx/language/gallina-specification-language.rst | |
parent | 10bc91ad4d3bc63618e6d5756d4dec2117059c45 (diff) |
Clean-up around cmd documentation.
In particular, remove trailing dots.
Diffstat (limited to 'doc/sphinx/language/gallina-specification-language.rst')
-rw-r--r-- | doc/sphinx/language/gallina-specification-language.rst | 80 |
1 files changed, 40 insertions, 40 deletions
diff --git a/doc/sphinx/language/gallina-specification-language.rst b/doc/sphinx/language/gallina-specification-language.rst index 44bf255bb..46e684b12 100644 --- a/doc/sphinx/language/gallina-specification-language.rst +++ b/doc/sphinx/language/gallina-specification-language.rst @@ -551,7 +551,7 @@ has type :token:`type`. .. _Axiom: -.. cmd:: Axiom @ident : @term. +.. cmd:: Axiom @ident : @term This command links *term* to the name *ident* as its specification in the global context. The fact asserted by *term* is thus assumed as a @@ -560,24 +560,24 @@ has type :token:`type`. .. exn:: @ident already exists. :name: @ident already exists. (Axiom) -.. cmdv:: Parameter @ident : @term. +.. cmdv:: Parameter @ident : @term :name: Parameter Is equivalent to ``Axiom`` :token:`ident` : :token:`term` -.. cmdv:: Parameter {+ @ident } : @term. +.. cmdv:: Parameter {+ @ident } : @term Adds parameters with specification :token:`term` -.. cmdv:: Parameter {+ ( {+ @ident } : @term ) }. +.. cmdv:: Parameter {+ ( {+ @ident } : @term ) } Adds blocks of parameters with different specifications. -.. cmdv:: Parameters {+ ( {+ @ident } : @term ) }. +.. cmdv:: Parameters {+ ( {+ @ident } : @term ) } Synonym of ``Parameter``. -.. cmdv:: Local Axiom @ident : @term. +.. cmdv:: Local Axiom @ident : @term Such axioms are never made accessible through their unqualified name by :cmd:`Import` and its variants. You have to explicitly give their fully @@ -588,7 +588,7 @@ has type :token:`type`. Is equivalent to ``Axiom`` :token:`ident` : :token:`term`. -.. cmd:: Variable @ident : @term. +.. cmd:: Variable @ident : @term This command links :token:`term` to the name :token:`ident` in the context of the current section (see Section :ref:`section-mechanism` for a description of @@ -600,20 +600,20 @@ of any section is equivalent to using ``Local Parameter``. .. exn:: @ident already exists. :name: @ident already exists. (Variable) -.. cmdv:: Variable {+ @ident } : @term. +.. cmdv:: Variable {+ @ident } : @term Links :token:`term` to each :token:`ident`. -.. cmdv:: Variable {+ ( {+ @ident } : @term) }. +.. cmdv:: Variable {+ ( {+ @ident } : @term) } Adds blocks of variables with different specifications. -.. cmdv:: Variables {+ ( {+ @ident } : @term) }. +.. cmdv:: Variables {+ ( {+ @ident } : @term) } -.. cmdv:: Hypothesis {+ ( {+ @ident } : @term) }. +.. cmdv:: Hypothesis {+ ( {+ @ident } : @term) } :name: Hypothesis -.. cmdv:: Hypotheses {+ ( {+ @ident } : @term) }. +.. cmdv:: Hypotheses {+ ( {+ @ident } : @term) } Synonyms of ``Variable``. @@ -643,7 +643,7 @@ type which is the type of its body. A formal presentation of constants and environments is given in Section :ref:`typing-rules`. -.. cmd:: Definition @ident := @term. +.. cmd:: Definition @ident := @term This command binds :token:`term` to the name :token:`ident` in the environment, provided that :token:`term` is well-typed. @@ -651,31 +651,31 @@ Section :ref:`typing-rules`. .. exn:: @ident already exists. :name: @ident already exists. (Definition) -.. cmdv:: Definition @ident : @term := @term. +.. cmdv:: Definition @ident : @term := @term It checks that the type of :token:`term`:math:`_2` is definitionally equal to :token:`term`:math:`_1`, and registers :token:`ident` as being of type :token:`term`:math:`_1`, and bound to value :token:`term`:math:`_2`. -.. cmdv:: Definition @ident {* @binder } : @term := @term. +.. cmdv:: Definition @ident {* @binder } : @term := @term This is equivalent to ``Definition`` :token:`ident` : :g:`forall` :token:`binder`:math:`_1` … :token:`binder`:math:`_n`, :token:`term`:math:`_1` := fun :token:`binder`:math:`_1` … :token:`binder`:math:`_n` => :token:`term`:math:`_2`. -.. cmdv:: Local Definition @ident := @term. +.. cmdv:: Local Definition @ident := @term Such definitions are never made accessible through their unqualified name by :cmd:`Import` and its variants. You have to explicitly give their fully qualified name to refer to them. -.. cmdv:: Example @ident := @term. +.. cmdv:: Example @ident := @term -.. cmdv:: Example @ident : @term := @term. +.. cmdv:: Example @ident : @term := @term -.. cmdv:: Example @ident {* @binder } : @term := @term. +.. cmdv:: Example @ident {* @binder } : @term := @term These are synonyms of the Definition forms. @@ -683,7 +683,7 @@ These are synonyms of the Definition forms. See also :cmd:`Opaque`, :cmd:`Transparent`, :tacn:`unfold`. -.. cmd:: Let @ident := @term. +.. cmd:: Let @ident := @term This command binds the value :token:`term` to the name :token:`ident` in the environment of the current section. The name :token:`ident` disappears when the @@ -696,11 +696,11 @@ prefixed by the let-in definition ``let`` :token:`ident` ``:=`` :token:`term` .. exn:: @ident already exists. :name: @ident already exists. (Let) -.. cmdv:: Let @ident : @term := @term. +.. cmdv:: Let @ident : @term := @term -.. cmdv:: Let Fixpoint @ident @fix_body {* with @fix_body}. +.. cmdv:: Let Fixpoint @ident @fix_body {* with @fix_body} -.. cmdv:: Let CoFixpoint @ident @cofix_body {* with @cofix_body}. +.. cmdv:: Let CoFixpoint @ident @cofix_body {* with @cofix_body} See also Sections :ref:`section-mechanism`, commands :cmd:`Opaque`, :cmd:`Transparent`, and tactic :tacn:`unfold`. @@ -916,7 +916,7 @@ Mutually defined inductive types The definition of a block of mutually inductive types has the form: -.. cmdv:: Inductive @ident : @term := {? | } @ident : @type {* | @ident : @type } {* with @ident : @term := {? | } @ident : @type {* | @ident : @type }}. +.. cmdv:: Inductive @ident : @term := {? | } @ident : @type {* | @ident : @type } {* with @ident : @term := {? | } @ident : @type {* | @ident : @type }} It has the same semantics as the above ``Inductive`` definition for each :token:`ident` All :token:`ident` are simultaneously added to the environment. @@ -928,7 +928,7 @@ parameters correspond to a local context in which the whole set of inductive declarations is done. For this reason, the parameters must be strictly the same for each inductive types The extended syntax is: -.. cmdv:: Inductive @ident {+ @binder} : @term := {? | } @ident : @type {* | @ident : @type } {* with @ident {+ @binder} : @term := {? | } @ident : @type {* | @ident : @type }}. +.. cmdv:: Inductive @ident {+ @binder} : @term := {? | } @ident : @type {* | @ident : @type } {* with @ident {+ @binder} : @term := {? | } @ident : @type {* | @ident : @type }} The typical example of a mutual inductive data type is the one for trees and forests. We assume given two types :g:`A` and :g:`B` as variables. It can @@ -1041,7 +1041,7 @@ constructions. .. _Fixpoint: -.. cmd:: Fixpoint @ident @params {struct @ident} : @type := @term. +.. cmd:: Fixpoint @ident @params {struct @ident} : @type := @term This command allows defining functions by pattern-matching over inductive objects using a fixed point construction. The meaning of this declaration is to @@ -1155,7 +1155,7 @@ The ``Fixpoint`` construction enjoys also the with extension to define functions over mutually defined inductive types or more generally any mutually recursive definitions. -.. cmdv:: Fixpoint @ident @params {struct @ident} : @type := @term {* with @ident {+ @params} : @type := @term}. +.. cmdv:: Fixpoint @ident @params {struct @ident} : @type := @term {* with @ident {+ @params} : @type := @term} allows to define simultaneously fixpoints. @@ -1182,7 +1182,7 @@ induction principles. It is described in Section Definitions of recursive objects in co-inductive types ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -.. cmd:: CoFixpoint @ident : @type := @term. +.. cmd:: CoFixpoint @ident : @type := @term introduces a method for constructing an infinite object of a coinductive type. For example, the stream containing all natural numbers can be @@ -1243,7 +1243,7 @@ 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 : @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 @@ -1258,24 +1258,24 @@ the theorem is bound to the name :token:`ident` in the environment. The name you provided is already defined. You have then to choose another name. -.. cmdv:: Lemma @ident : @type. +.. cmdv:: Lemma @ident : @type :name: Lemma -.. cmdv:: Remark @ident : @type. +.. cmdv:: Remark @ident : @type :name: Remark -.. cmdv:: Fact @ident : @type. +.. cmdv:: Fact @ident : @type :name: Fact -.. cmdv:: Corollary @ident : @type. +.. cmdv:: Corollary @ident : @type :name: Corollary -.. cmdv:: Proposition @ident : @type. +.. cmdv:: Proposition @ident : @type :name: Proposition These commands are synonyms of ``Theorem`` :token:`ident` : :token:`type`. -.. cmdv:: Theorem @ident : @type {* with @ident : @type}. +.. cmdv:: Theorem @ident : @type {* with @ident : @type} This command is useful for theorems that are proved by simultaneous induction over a mutually inductive assumption, or that assert mutually dependent @@ -1297,7 +1297,7 @@ the theorem is bound to the name :token:`ident` in the environment. The command can be used also with :cmd:`Lemma`, :cmd:`Remark`, etc. instead of :cmd:`Theorem`. -.. cmdv:: Definition @ident : @type. +.. 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 @@ -1308,20 +1308,20 @@ the theorem is bound to the name :token:`ident` in the environment. See also :cmd:`Opaque`, :cmd:`Transparent`, :tacn:`unfold`. -.. cmdv:: Let @ident : @type. +.. cmdv:: Let @ident : @type Like Definition :token:`ident` : :token:`type`. except that the definition is turned into a let-in definition generalized over the declarations depending on it after closing the current section. -.. cmdv:: Fixpoint @ident @binders with . +.. cmdv:: Fixpoint @ident @binders with This generalizes the syntax of Fixpoint so that one or more bodies can be defined interactively using the proof editing mode (when a body is omitted, its type is mandatory in the syntax). When the block of proofs is completed, it is intended to be ended by Defined. -.. cmdv:: CoFixpoint @ident with. +.. cmdv:: CoFixpoint @ident with This generalizes the syntax of CoFixpoint so that one or more bodies can be defined interactively using the proof editing mode. @@ -1367,7 +1367,7 @@ the theorem is bound to the name :token:`ident` in the environment. unfolded in conversion tactics (see :ref:`performingcomputations`, :cmd:`Opaque`, :cmd:`Transparent`). -.. cmdv:: Admitted. +.. cmdv:: Admitted :name: Admitted Turns the current asserted statement into an axiom and exits the proof mode. |