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Diffstat (limited to 'doc/sphinx/proof-engine/tactics.rst')
| -rw-r--r-- | doc/sphinx/proof-engine/tactics.rst | 154 |
1 files changed, 66 insertions, 88 deletions
diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst index 08aa7110d..1868f4b9d 100644 --- a/doc/sphinx/proof-engine/tactics.rst +++ b/doc/sphinx/proof-engine/tactics.rst @@ -51,20 +51,15 @@ specified, the default selector is used. tactic_invocation : toplevel_selector : tactic. : |tactic . -.. cmd:: Set Default Goal Selector @toplevel_selector. +.. opt:: Default Goal Selector @toplevel_selector. -After using this command, the default selector – used when no selector -is specified when applying a tactic – is set to the chosen value. The -initial value is 1, hence the tactics are, by default, applied to the -first goal. Using Set Default Goal Selector ‘‘all’’ will make is so -that tactics are, by default, applied to every goal simultaneously. -Then, to apply a tactic tac to the first goal only, you can write -1:tac. Although more selectors are available, only ‘‘all’’ or a single -natural number are valid default goal selectors. - -.. cmd:: Test Default Goal Selector. - -This command displays the current default selector. + This option controls the default selector – used when no selector is + specified when applying a tactic – is set to the chosen value. The initial + value is 1, hence the tactics are, by default, applied to the first goal. + Using value ``all`` will make is so that tactics are, by default, applied to + every goal simultaneously. Then, to apply a tactic tac to the first goal + only, you can write ``1:tac``. Although more selectors are available, only + ``all`` or a single natural number are valid default goal selectors. .. _bindingslist: @@ -123,14 +118,12 @@ following syntax: The role of an occurrence clause is to select a set of occurrences of a term in a goal. In the first case, the :n:`@ident {? at {* num}}` parts indicate that -occurrences have to be selected in the hypotheses named :n:`@ident`. If no numbers -are given for hypothesis :n:`@ident`, then all the occurrences of `term` in the -hypothesis are selected. If numbers are given, they refer to occurrences of -`term` when the term is printed using option ``Set Printing All`` (see -:ref:`printing_constructions_full`), counting from left to right. In -particular, occurrences of `term` in implicit arguments (see -:ref:`ImplicitArguments`) or coercions (see :ref:`Coercions`) -are counted. +occurrences have to be selected in the hypotheses named :n:`@ident`. If no +numbers are given for hypothesis :n:`@ident`, then all the occurrences of `term` +in the hypothesis are selected. If numbers are given, they refer to occurrences +of `term` when the term is printed using option :opt:`Printing All`, counting +from left to right. In particular, occurrences of `term` in implicit arguments +(see :ref:`ImplicitArguments`) or coercions (see :ref:`Coercions`) are counted. If a minus sign is given between at and the list of occurrences, it negates the condition so that the clause denotes all the occurrences @@ -346,7 +339,7 @@ does. This summarizes the different syntaxes for ``apply`` and ``eapply``. .. tacv:: lapply @term - :name: `lapply + :name: lapply This tactic applies to any goal, say :g:`G`. The argument term has to be well-formed in the current context, its type being reducible to a non-dependent @@ -437,7 +430,7 @@ sequence ``cut B. 2:apply H.`` where ``cut`` is described below. ``forall A, ... -> A``. Excluding this kind of lemma can be avoided by setting the following option: -.. opt:: Set Universal Lemma Under Conjunction. +.. opt:: Universal Lemma Under Conjunction This option, which preserves compatibility with versions of Coq prior to 8.4 is also available for :n:`apply @term in @ident` (see :tacn:`apply ... in`). @@ -829,15 +822,10 @@ quantification or an implication. so that all the arguments of the i-th constructors of the corresponding inductive type are introduced can be controlled with the following option: - .. cmd:: Set Bracketing Last Introduction Pattern. - - Force completion, if needed, when the last introduction pattern is a - disjunctive or conjunctive pattern (this is the default). + .. opt:: Bracketing Last Introduction Pattern - .. cmd:: Unset Bracketing Last Introduction Pattern. - - Deactivate completion when the last introduction pattern is a disjunctive or - conjunctive pattern. + Force completion, if needed, when the last introduction pattern is a + disjunctive or conjunctive pattern (on by default). .. tacn:: clear @ident :name: clear @@ -1239,7 +1227,7 @@ name of the variable (here :g:`n`) is chosen based on :g:`T`. This is equivalent to :n:`generalize @term` but it generalizes only over the specified occurrences of :n:`@term` (counting from left to right on the - expression printed using option :g:`Set Printing All`). + expression printed using option :opt:`Printing All`). .. tacv:: generalize @term as @ident @@ -1964,13 +1952,13 @@ It is possible to ensure that :n:`injection @term` erases the original hypothesis and leaves the generated equalities in the context rather than putting them as antecedents of the current goal, as if giving :n:`injection @term as` (with an empty list of names). To obtain this -behavior, the option ``Set Structural Injection`` must be activated. This +behavior, the option :opt:`Structural Injection` must be activated. This option is off by default. -By default, ``injection`` only creates new equalities between :n:`@terms` whose +By default, :tacn:`injection` only creates new equalities between :n:`@terms` whose type is in sort :g:`Type` or :g:`Set`, thus implementing a special behavior for objects that are proofs of a statement in :g:`Prop`. This behavior can be -turned off by setting the option ``Set Keep Proof Equalities``. +turned off by setting the option :opt:`Keep Proof Equalities`. .. tacn:: inversion @ident :name: inversion @@ -1996,8 +1984,8 @@ turned off by setting the option ``Set Keep Proof Equalities``. equalities between expressions that appeared in the hypothesis that is being processed. By default, no equalities are generated if they relate two proofs (i.e. equalities between :n:`@terms` whose type is in sort - :g:`Prop`). This behavior can be turned off by using the option ``Set Keep - Proof Equalities``. + :g:`Prop`). This behavior can be turned off by using the option + :opt`Keep Proof Equalities`. .. tacv:: inversion @num @@ -2513,28 +2501,28 @@ unfolded and cleared. .. note:: - The behavior of subst can be controlled using option ``Set Regular Subst - Tactic.`` When this option is activated, subst also deals with the - following corner cases: - - + A context with ordered hypotheses :n:`@ident`:sub:`1` :n:`= @ident`:sub:`2` - and :n:`@ident`:sub:`1` :n:`= t`, or :n:`t′ = @ident`:sub:`1`` with `t′` not - a variable, and no other hypotheses of the form :n:`@ident`:sub:`2` :n:`= u` - or :n:`u = @ident`:sub:`2`; without the option, a second call to - subst would be necessary to replace :n:`@ident`:sub:`2` by `t` or - `t′` respectively. - + The presence of a recursive equation which without the option would - be a cause of failure of :tacn:`subst`. - + A context with cyclic dependencies as with hypotheses :n:`@ident`:sub:`1` :n:`= f @ident`:sub:`2` - and :n:`@ident`:sub:`2` :n:`= g @ident`:sub:`1` which without the - option would be a cause of failure of :tacn:`subst`. - - Additionally, it prevents a local definition such as :n:`@ident := t` to be - unfolded which otherwise it would exceptionally unfold in configurations - containing hypotheses of the form :n:`@ident = u`, or :n:`u′ = @ident` - with `u′` not a variable. Finally, it preserves the initial order of - hypotheses, which without the option it may break. The option is on by - default. + The behavior of subst can be controlled using option :opt:`Regular Subst + Tactic`. When this option is activated, subst also deals with the + following corner cases: + + + A context with ordered hypotheses :n:`@ident`:sub:`1` :n:`= @ident`:sub:`2` + and :n:`@ident`:sub:`1` :n:`= t`, or :n:`t′ = @ident`:sub:`1`` with `t′` not + a variable, and no other hypotheses of the form :n:`@ident`:sub:`2` :n:`= u` + or :n:`u = @ident`:sub:`2`; without the option, a second call to + subst would be necessary to replace :n:`@ident`:sub:`2` by `t` or + `t′` respectively. + + The presence of a recursive equation which without the option would + be a cause of failure of :tacn:`subst`. + + A context with cyclic dependencies as with hypotheses :n:`@ident`:sub:`1` :n:`= f @ident`:sub:`2` + and :n:`@ident`:sub:`2` :n:`= g @ident`:sub:`1` which without the + option would be a cause of failure of :tacn:`subst`. + + Additionally, it prevents a local definition such as :n:`@ident := t` to be + unfolded which otherwise it would exceptionally unfold in configurations + containing hypotheses of the form :n:`@ident = u`, or :n:`u′ = @ident` + with `u′` not a variable. Finally, it preserves the initial order of + hypotheses, which without the option it may break. The option is on by + default. .. tacn:: stepl @term @@ -3578,24 +3566,21 @@ We propose a smooth transitional path by providing the ``Loose Hint Behavior`` option which accepts three flags allowing for a fine-grained handling of non-imported hints. -**Variants:** - -.. cmd:: Set Loose Hint Behavior "Lax" +.. opt:: Loose Hint Behavior %( "Lax" %| "Warn" %| "Strict" %) - This is the default, and corresponds to the historical behavior, that - is, hints defined outside of a section have a global scope. + This option accepts three values, which control the behavior of hints w.r.t. + :cmd:`Import`: -.. cmd:: Set Loose Hint Behavior "Warn" + - "Lax": this is the default, and corresponds to the historical behavior, + that is, hints defined outside of a section have a global scope. - When set, it outputs a warning when a non-imported hint is used. Note that - this is an over-approximation, because a hint may be triggered by a run that - will eventually fail and backtrack, resulting in the hint not being actually - useful for the proof. + - "Warn": outputs a warning when a non-imported hint is used. Note that this + is an over-approximation, because a hint may be triggered by a run that + will eventually fail and backtrack, resulting in the hint not being + actually useful for the proof. -.. cmd:: Set Loose Hint Behavior "Strict" - - When set, it changes the behavior of an unloaded hint to a immediate fail - tactic, allowing to emulate an import-scoped hint mechanism. + - "Strict": changes the behavior of an unloaded hint to a immediate fail + tactic, allowing to emulate an import-scoped hint mechanism. .. _tactics-implicit-automation: @@ -3734,17 +3719,10 @@ some incompatibilities. Empty_set, unit, True``, :tacn:`dintuition` recognizes also all inductive types with one constructors and no indices, i.e. record-style connectives. -Some aspects of the tactic :tacn:`intuition` can be controlled using options. -To avoid that inner negations which do not need to be unfolded are -unfolded, use: - -.. cmd:: Unset Intuition Negation Unfolding - +.. opt:: Intuition Negation Unfolding -To do that all negations of the goal are unfolded even inner ones -(this is the default), use: - -.. cmd:: Set Intuition Negation Unfolding + Controls whether :tacn:`intuition` unfolds inner negations which do not need + to be unfolded. This option is on by default. .. tacn:: rtauto :name: rtauto @@ -3769,9 +3747,8 @@ usual logical connectives but instead may reason about any first-order class inductive definition. The default tactic used by :tacn:`firstorder` when no rule applies is :g:`auto -with \*`, it can be reset locally or globally using the ``Set Firstorder -Solver`` tactic vernacular command and printed using ``Print Firstorder -Solver``. +with \*`, it can be reset locally or globally using the :opt:`Firstorder Solver` +option and printed using :cmd:`Print Firstorder Solver`. .. tacv:: firstorder @tactic @@ -3792,8 +3769,9 @@ Solver``. This combines the effects of the different variants of :tacn:`firstorder`. -Proof-search is bounded by a depth parameter which can be set by -typing the ``Set Firstorder Depth n`` vernacular command. +.. opt:: Firstorder Depth @natural + + This option controls the proof-search depth bound. .. tacn:: congruence :name: congruence |