diff options
Diffstat (limited to 'doc/sphinx/proof-engine')
| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 10 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/tactics.rst | 104 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/vernacular-commands.rst | 26 |
3 files changed, 37 insertions, 103 deletions
diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index b5d1e8bffd..28c5359a04 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -1624,9 +1624,15 @@ previous :token:`i_item` have been performed. The second entry in the :token:`i_view` grammar rule, ``/ltac:(`` :token:`tactic` ``)``, executes :token:`tactic`. -Notations can be used to name tactics, for example:: +Notations can be used to name tactics, for example - Notation myop := (ltac:(some ltac code)) : ssripat_scope. +.. coqtop:: none + + Tactic Notation "my" "ltac" "code" := idtac. + +.. coqtop:: in warn + + Notation "'myop'" := (ltac:(my ltac code)) : ssripat_scope. lets one write just ``/myop`` in the intro pattern. Note the scope annotation: views are interpreted opening the ``ssripat`` scope. diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst index 1ecfa05f99..7e6da490fb 100644 --- a/doc/sphinx/proof-engine/tactics.rst +++ b/doc/sphinx/proof-engine/tactics.rst @@ -1875,6 +1875,7 @@ analysis on inductive or co-inductive objects (see :ref:`inductive-definitions`) Lemma induction_test : forall n:nat, n = n -> n <= n. intros n H. induction n. + exact (le_n 0). .. exn:: Not an inductive product. :undocumented: @@ -2076,7 +2077,7 @@ analysis on inductive or co-inductive objects (see :ref:`inductive-definitions`) Now we are in a contradictory context and the proof can be solved. - .. coqtop:: all + .. coqtop:: all abort inversion H. @@ -2104,68 +2105,7 @@ analysis on inductive or co-inductive objects (see :ref:`inductive-definitions`) See also the larger example of :tacn:`dependent induction` and an explanation of the underlying technique. -.. tacn:: function induction (@qualid {+ @term}) - :name: function induction - - The tactic functional induction performs case analysis and induction - following the definition of a function. It makes use of a principle - generated by ``Function`` (see :ref:`advanced-recursive-functions`) or - ``Functional Scheme`` (see :ref:`functional-scheme`). - Note that this tactic is only available after a ``Require Import FunInd``. - -.. example:: - - .. coqtop:: reset all - - Require Import FunInd. - Functional Scheme minus_ind := Induction for minus Sort Prop. - Check minus_ind. - Lemma le_minus (n m:nat) : n - m <= n. - functional induction (minus n m) using minus_ind; simpl; auto. - Qed. - -.. note:: - :n:`(@qualid {+ @term})` must be a correct full application - of :n:`@qualid`. In particular, the rules for implicit arguments are the - same as usual. For example use :n:`@qualid` if you want to write implicit - arguments explicitly. - -.. note:: - Parentheses around :n:`@qualid {+ @term}` are not mandatory and can be skipped. - -.. note:: - :n:`functional induction (f x1 x2 x3)` is actually a wrapper for - :n:`induction x1, x2, x3, (f x1 x2 x3) using @qualid` followed by a cleaning - phase, where :n:`@qualid` is the induction principle registered for :g:`f` - (by the ``Function`` (see :ref:`advanced-recursive-functions`) or - ``Functional Scheme`` (see :ref:`functional-scheme`) - command) corresponding to the sort of the goal. Therefore - ``functional induction`` may fail if the induction scheme :n:`@qualid` is not - defined. See also :ref:`advanced-recursive-functions` for the function - terms accepted by ``Function``. - -.. note:: - There is a difference between obtaining an induction scheme - for a function by using :g:`Function` (see :ref:`advanced-recursive-functions`) - and by using :g:`Functional Scheme` after a normal definition using - :g:`Fixpoint` or :g:`Definition`. See :ref:`advanced-recursive-functions` - for details. - -.. seealso:: :ref:`advanced-recursive-functions`, :ref:`functional-scheme` and :tacn:`inversion` - -.. exn:: Cannot find induction information on @qualid. - :undocumented: - -.. exn:: Not the right number of induction arguments. - :undocumented: - -.. tacv:: functional induction (@qualid {+ @term}) as @simple_intropattern using @term with @bindings_list - - Similarly to :tacn:`induction` and :tacn:`elim`, this allows giving - explicitly the name of the introduced variables, the induction principle, and - the values of dependent premises of the elimination scheme, including - *predicates* for mutual induction when :n:`@qualid` is part of a mutually - recursive definition. +.. seealso:: :tacn:`functional induction` .. tacn:: discriminate @term :name: discriminate @@ -2672,6 +2612,8 @@ and an explanation of the underlying technique. assumption. Qed. +.. seealso:: :tacn:`functional inversion` + .. tacn:: fix @ident @num :name: fix @@ -4604,42 +4546,6 @@ symbol :g:`=`. Analogous to :tacn:`dependent rewrite ->` but uses the equality from right to left. -Inversion ---------- - -.. tacn:: functional inversion @ident - :name: functional inversion - - :tacn:`functional inversion` is a tactic that performs inversion on hypothesis - :n:`@ident` of the form :n:`@qualid {+ @term} = @term` or :n:`@term = @qualid - {+ @term}` where :n:`@qualid` must have been defined using Function (see - :ref:`advanced-recursive-functions`). Note that this tactic is only - available after a ``Require Import FunInd``. - - .. exn:: Hypothesis @ident must contain at least one Function. - :undocumented: - - .. exn:: Cannot find inversion information for hypothesis @ident. - - This error may be raised when some inversion lemma failed to be generated by - Function. - - - .. tacv:: functional inversion @num - - This does the same thing as :n:`intros until @num` followed by - :n:`functional inversion @ident` where :token:`ident` is the - identifier for the last introduced hypothesis. - - .. tacv:: functional inversion @ident @qualid - functional inversion @num @qualid - - If the hypothesis :token:`ident` (or :token:`num`) has a type of the form - :n:`@qualid__1 {+ @term__i } = @qualid__2 {+ @term__j }` where - :n:`@qualid__1` and :n:`@qualid__2` are valid candidates to - functional inversion, this variant allows choosing which :token:`qualid` - is inverted. - Classical tactics ----------------- diff --git a/doc/sphinx/proof-engine/vernacular-commands.rst b/doc/sphinx/proof-engine/vernacular-commands.rst index 7d031b9b7a..60fdbf0a9d 100644 --- a/doc/sphinx/proof-engine/vernacular-commands.rst +++ b/doc/sphinx/proof-engine/vernacular-commands.rst @@ -91,9 +91,15 @@ capital letter. This command supports the :attr:`local`, :attr:`global` and :attr:`export` attributes. They are described :ref:`here <set_unset_scope_qualifiers>`. - .. warn:: There is no option @setting_name. + .. warn:: There is no flag or option with this name: "@setting_name". - This message also appears for unknown flags. + This warning message can be raised by :cmd:`Set` and + :cmd:`Unset` when :n:`@setting_name` is unknown. It is a + warning rather than an error because this helps library authors + produce Coq code that is compatible with several Coq versions. + To preserve the same behavior, they may need to set some + compatibility flags or options that did not exist in previous + Coq versions. .. cmd:: Unset @setting_name :name: Unset @@ -119,6 +125,20 @@ capital letter. whether the table contains each specified value, otherise this is equivalent to :cmd:`Print Table`. The `for` clause is not valid for flags and options. + .. exn:: There is no flag, option or table with this name: "@setting_name". + + This error message is raised when calling the :cmd:`Test` + command (without the `for` clause), or the :cmd:`Print Table` + command, for an unknown :n:`@setting_name`. + + .. exn:: There is no qualid-valued table with this name: "@setting_name". + There is no string-valued table with this name: "@setting_name". + + These error messages are raised when calling the :cmd:`Add` or + :cmd:`Remove` commands, or the :cmd:`Test` command with the + `for` clause, if :n:`@setting_name` is unknown or does not have + the right type. + .. cmd:: Print Options Prints the current value of all flags and options, and the names of all tables. @@ -1076,6 +1096,8 @@ Controlling Typing Flags Print the status of the three typing flags: guard checking, positivity checking and universe checking. +See also :flag:`Cumulative StrictProp` in the |SProp| chapter. + .. example:: .. coqtop:: all reset |