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authorGravatar Théo Zimmermann <theo.zimmermann@univ-paris-diderot.fr>2018-05-05 12:02:16 +0200
committerGravatar Théo Zimmermann <theo.zimmermann@univ-paris-diderot.fr>2018-05-05 12:25:38 +0200
commit6f4c2fff85ecbf0462938fc94be61c6e09325073 (patch)
tree1506c1c5a2fbfb9af447fad1c49df3aef47839ae /doc
parent8cda6a9cd915e3d88e07a34d74e039c24d10ae55 (diff)
[sphinx] Fixes around refine, including indentation and a hard-coded ref.
Diffstat (limited to 'doc')
-rw-r--r--doc/sphinx/proof-engine/tactics.rst121
1 files changed, 61 insertions, 60 deletions
diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst
index 3470098ec..1ecd2bbfd 100644
--- a/doc/sphinx/proof-engine/tactics.rst
+++ b/doc/sphinx/proof-engine/tactics.rst
@@ -167,99 +167,100 @@ Applying theorems
.. tacn:: exact @term
:name: exact
-This tactic applies to any goal. It gives directly the exact proof
-term of the goal. Let ``T`` be our goal, let ``p`` be a term of type ``U`` then
-``exact p`` succeeds iff ``T`` and ``U`` are convertible (see
-:ref:`Conversion-rules`).
+ This tactic applies to any goal. It gives directly the exact proof
+ term of the goal. Let ``T`` be our goal, let ``p`` be a term of type ``U`` then
+ ``exact p`` succeeds iff ``T`` and ``U`` are convertible (see
+ :ref:`Conversion-rules`).
-.. exn:: Not an exact proof.
+ .. exn:: Not an exact proof.
-.. tacv:: eexact @term.
- :name: eexact
+ .. tacv:: eexact @term.
+ :name: eexact
-This tactic behaves like exact but is able to handle terms and goals with
-meta-variables.
+ This tactic behaves like exact but is able to handle terms and goals with
+ meta-variables.
.. tacn:: assumption
:name: assumption
-This tactic looks in the local context for an hypothesis which type is equal to
-the goal. If it is the case, the subgoal is proved. Otherwise, it fails.
+ This tactic looks in the local context for an hypothesis which type is equal to
+ the goal. If it is the case, the subgoal is proved. Otherwise, it fails.
-.. exn:: No such assumption.
+ .. exn:: No such assumption.
-.. tacv:: eassumption
- :name: eassumption
+ .. tacv:: eassumption
+ :name: eassumption
-This tactic behaves like assumption but is able to handle goals with
-meta-variables.
+ This tactic behaves like assumption but is able to handle goals with
+ meta-variables.
.. tacn:: refine @term
:name: refine
-This tactic applies to any goal. It behaves like exact with a big
-difference: the user can leave some holes (denoted by ``_`` or``(_:type)``) in
-the term. refine will generate as many subgoals as there are holes in
-the term. The type of holes must be either synthesized by the system
-or declared by an explicit cast like ``(_:nat->Prop)``. Any subgoal that
-occurs in other subgoals is automatically shelved, as if calling
-shelve_unifiable (see Section 8.17.4). This low-level tactic can be
-useful to advanced users.
+ This tactic applies to any goal. It behaves like :tacn:`exact` with a big
+ difference: the user can leave some holes (denoted by ``_`` or ``(_:type)``) in
+ the term. :tacn:`refine` will generate as many subgoals as there are holes in
+ the term. The type of holes must be either synthesized by the system
+ or declared by an explicit cast like ``(_:nat->Prop)``. Any subgoal that
+ occurs in other subgoals is automatically shelved, as if calling
+ :tacn:`shelve_unifiable`. This low-level tactic can be
+ useful to advanced users.
-.. example::
- .. coqtop:: reset all
+ .. example::
+ .. coqtop:: reset all
- Inductive Option : Set :=
- | Fail : Option
- | Ok : bool -> Option.
+ Inductive Option : Set :=
+ | Fail : Option
+ | Ok : bool -> Option.
- Definition get : forall x:Option, x <> Fail -> bool.
+ Definition get : forall x:Option, x <> Fail -> bool.
- refine
- (fun x:Option =>
- match x return x <> Fail -> bool with
- | Fail => _
- | Ok b => fun _ => b
- end).
+ refine
+ (fun x:Option =>
+ match x return x <> Fail -> bool with
+ | Fail => _
+ | Ok b => fun _ => b
+ end).
- intros; absurd (Fail = Fail); trivial.
+ intros; absurd (Fail = Fail); trivial.
- Defined.
+ Defined.
-.. exn:: Invalid argument.
+ .. exn:: Invalid argument.
- The tactic ``refine`` does not know what to do with the term you gave.
+ The tactic :tacn:`refine` does not know what to do with the term you gave.
-.. exn:: Refine passed ill-formed term.
+ .. exn:: Refine passed ill-formed term.
- The term you gave is not a valid proof (not easy to debug in general). This
- message may also occur in higher-level tactics that call ``refine``
- internally.
+ The term you gave is not a valid proof (not easy to debug in general). This
+ message may also occur in higher-level tactics that call :tacn:`refine`
+ internally.
-.. exn:: Cannot infer a term for this placeholder.
- :name: Cannot infer a term for this placeholder. (refine)
+ .. exn:: Cannot infer a term for this placeholder.
+ :name: Cannot infer a term for this placeholder. (refine)
- There is a hole in the term you gave whose type cannot be inferred. Put a
- cast around it.
+ There is a hole in the term you gave whose type cannot be inferred. Put a
+ cast around it.
-.. tacv:: simple refine @term
- :name: simple refine
+ .. tacv:: simple refine @term
+ :name: simple refine
- This tactic behaves like refine, but it does not shelve any subgoal. It does
- not perform any beta-reduction either.
+ This tactic behaves like refine, but it does not shelve any subgoal. It does
+ not perform any beta-reduction either.
-.. tacv:: notypeclasses refine @term
+ .. tacv:: notypeclasses refine @term
+ :name: notypeclasses refine
- This tactic behaves like ``refine`` except it performs typechecking without
- resolution of typeclasses.
+ This tactic behaves like :tacn:`refine` except it performs typechecking without
+ resolution of typeclasses.
-.. tacv:: simple notypeclasses refine @term
- :name: simple notypeclasses refine
+ .. tacv:: simple notypeclasses refine @term
+ :name: simple notypeclasses refine
- This tactic behaves like ``simple refine`` except it performs typechecking
- without resolution of typeclasses.
+ This tactic behaves like :tacn:`simple refine` except it performs typechecking
+ without resolution of typeclasses.
-.. tacv:: apply @term
+.. tacn:: apply @term
:name: apply
This tactic applies to any goal. The argument term is a term well-formed in the