diff options
Diffstat (limited to 'doc/sphinx')
| -rw-r--r-- | doc/sphinx/_templates/versions.html | 48 | ||||
| -rwxr-xr-x | doc/sphinx/conf.py | 22 | ||||
| -rw-r--r-- | doc/sphinx/language/cic.rst | 69 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/proof-handling.rst | 6 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 2 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/tactics.rst | 122 | ||||
| -rw-r--r-- | doc/sphinx/proof-engine/vernacular-commands.rst | 4 | ||||
| -rw-r--r-- | doc/sphinx/user-extensions/syntax-extensions.rst | 41 |
8 files changed, 297 insertions, 17 deletions
diff --git a/doc/sphinx/_templates/versions.html b/doc/sphinx/_templates/versions.html new file mode 100644 index 0000000000..967d00d2bf --- /dev/null +++ b/doc/sphinx/_templates/versions.html @@ -0,0 +1,48 @@ +{# Forked from versions.html in sphinx_rtd_theme 0.4.3 #} + +{# +The MIT License (MIT) + +Copyright (c) 2013-2018 Dave Snider, Read the Docs, Inc. & contributors + +Permission is hereby granted, free of charge, to any person obtaining a copy of +this software and associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of +the Software, and to permit persons to whom the Software is furnished to do so, +subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS +FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR +COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER +IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN +CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. +#} + +{% if not READTHEDOCS %} + <div class="rst-versions" data-toggle="rst-versions" role="note" aria-label="versions"> + <span class="rst-current-version" data-toggle="rst-current-version"> + <span class="fa fa-book"> Other versions</span> + v: {{ version }} + <span class="fa fa-caret-down"></span> + </span> + <div class="rst-other-versions"> + <dl> + <dt>{{ _('Versions') }}</dt> + {% for slug, url in versions %} + <dd><a href="{{ url }}">{{ slug }}</a></dd> + {% endfor %} + </dl> + <dl> + <dt>{{ _('Downloads') }}</dt> + {% for type, url in downloads %} + <dd><a href="{{ url }}">{{ type }}</a></dd> + {% endfor %} + </dl> + </div> + </div> +{% endif %} diff --git a/doc/sphinx/conf.py b/doc/sphinx/conf.py index dbe582df95..4136b406de 100755 --- a/doc/sphinx/conf.py +++ b/doc/sphinx/conf.py @@ -202,6 +202,7 @@ html_theme = 'sphinx_rtd_theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. +PDF_URL = "https://github.com/coq/coq/releases/download/V{version}/coq-{version}-reference-manual.pdf" html_theme_options = { 'collapse_navigation': False } @@ -210,7 +211,26 @@ html_context = { 'github_user': 'coq', 'github_repo': 'coq', 'github_version': 'master', - 'conf_py_path': '/doc/sphinx/' + 'conf_py_path': '/doc/sphinx/', + # Versions and downloads listed in the versions menu (see _templates/versions.html) + 'versions': [ + ("master", "https://coq.github.io/doc/master/refman/"), + ("stable", "https://coq.inria.fr/distrib/current/refman/"), + ("v8.11", "https://coq.github.io/doc/v8.11/refman/"), + ("v8.10", "https://coq.github.io/doc/v8.10/refman/"), + ("v8.9", "https://coq.github.io/doc/v8.9/refman/"), + ("8.8", "https://coq.inria.fr/distrib/V8.8.2/refman/"), + ("8.7", "https://coq.inria.fr/distrib/V8.7.2/refman/"), + ("8.6", "https://coq.inria.fr/distrib/V8.6.1/refman/"), + ("8.5", "https://coq.inria.fr/distrib/V8.5pl3/refman/"), + ("8.4", "https://coq.inria.fr/distrib/V8.4pl6/refman/"), + ("8.3", "https://coq.inria.fr/distrib/V8.3pl5/refman/"), + ("8.2", "https://coq.inria.fr/distrib/V8.2pl3/refman/"), + ("8.1", "https://coq.inria.fr/distrib/V8.1pl6/refman/"), + ("8.0", "https://coq.inria.fr/distrib/V8.0/doc/") + ], + 'downloads': ([("PDF", PDF_URL.format(version=version))] + if coq_config.is_a_released_version else []) } # Add any paths that contain custom themes here, relative to this directory. diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index e5af39c8fb..b125d21a3c 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -1108,6 +1108,75 @@ between universes for inductive types in the Type hierarchy. Check infinite_loop (lam (@id Lam)) : False. +.. example:: Non strictly positive occurrence + + It is less obvious why inductive type definitions with occurences + that are positive but not strictly positive are harmful. + We will see that in presence of an impredicative type they + are unsound: + + .. coqtop:: all + + Fail Inductive A: Type := introA: ((A -> Prop) -> Prop) -> A. + + If we were to accept this definition we could derive a contradiction + by creating an injective function from :math:`A → \Prop` to :math:`A`. + + This function is defined by composing the injective constructor of + the type :math:`A` with the function :math:`λx. λz. z = x` injecting + any type :math:`T` into :math:`T → \Prop`. + + .. coqtop:: none + + Unset Positivity Checking. + Inductive A: Type := introA: ((A -> Prop) -> Prop) -> A. + Set Positivity Checking. + + .. coqtop:: all + + Definition f (x: A -> Prop): A := introA (fun z => z = x). + + .. coqtop:: in + + Lemma f_inj: forall x y, f x = f y -> x = y. + Proof. + unfold f; intros ? ? H; injection H. + set (F := fun z => z = y); intro HF. + symmetry; replace (y = x) with (F y). + + unfold F; reflexivity. + + rewrite <- HF; reflexivity. + Qed. + + The type :math:`A → \Prop` can be understood as the powerset + of the type :math:`A`. To derive a contradiction from the + injective function :math:`f` we use Cantor's classic diagonal + argument. + + .. coqtop:: all + + Definition d: A -> Prop := fun x => exists s, x = f s /\ ~s x. + Definition fd: A := f d. + + .. coqtop:: in + + Lemma cantor: (d fd) <-> ~(d fd). + Proof. + split. + + intros [s [H1 H2]]; unfold fd in H1. + replace d with s. + * assumption. + * apply f_inj; congruence. + + intro; exists d; tauto. + Qed. + + Lemma bad: False. + Proof. + pose cantor; tauto. + Qed. + + This derivation was first presented by Thierry Coquand and Christine + Paulin in :cite:`CP90`. + .. _Template-polymorphism: Template polymorphism diff --git a/doc/sphinx/proof-engine/proof-handling.rst b/doc/sphinx/proof-engine/proof-handling.rst index 3b5233502d..cf4d432f64 100644 --- a/doc/sphinx/proof-engine/proof-handling.rst +++ b/doc/sphinx/proof-engine/proof-handling.rst @@ -90,9 +90,7 @@ list of assertion commands is given in :ref:`Assertions`. The command .. cmd:: Save @ident :name: Save - Forces the name of the original goal to be :token:`ident`. This - command can only be used if the original goal - was opened using the :cmd:`Goal` command. + Forces the name of the original goal to be :token:`ident`. .. cmd:: Admitted @@ -821,7 +819,7 @@ in compacted hypotheses: .. .. image:: ../_static/diffs-coqide-compacted.png - :alt: coqide with Set Diffs on with compacted hyptotheses + :alt: coqide with Set Diffs on with compacted hypotheses Controlling the effect of proof editing commands ------------------------------------------------ diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 28c5359a04..4be18ccda9 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -286,7 +286,7 @@ example, the null and all list function(al)s can be defined as follows: .. coqtop:: all Variable d: Set. - Fixpoint null (s : list d) := + Definition null (s : list d) := if s is nil then true else false. Variable a : d -> bool. Fixpoint all (s : list d) : bool := diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst index 8989dd29ab..bc2168411b 100644 --- a/doc/sphinx/proof-engine/tactics.rst +++ b/doc/sphinx/proof-engine/tactics.rst @@ -3355,6 +3355,128 @@ the conversion in hypotheses :n:`{+ @ident}`. This is the most general syntax that combines the different variants. +.. tacn:: with_strategy @strategy_level_or_var [ {+ @smart_qualid } ] @ltac_expr3 + :name: with_strategy + + Executes :token:`ltac_expr3`, applying the alternate unfolding + behavior that the :cmd:`Strategy` command controls, but only for + :token:`ltac_expr3`. This can be useful for guarding calls to + reduction in tactic automation to ensure that certain constants are + never unfolded by tactics like :tacn:`simpl` and :tacn:`cbn` or to + ensure that unfolding does not fail. + + .. note:: + + This tactic unfortunately does not yet play well with tactic + internalization, resulting in interpretation-time errors when + you try to use it directly with opaque identifiers, as seen in + the first (failing) use of :tacn:`with_strategy` in the + following example. This can be worked around by binding the + identifier to an |Ltac| variable, and this issue should + disappear in a future version of |Coq|; see `#12179 + <https://github.com/coq/coq/issues/12179>`_. + + .. example:: + + .. coqtop:: all reset abort + + Opaque id. + Goal id 10 = 10. + Fail unfold id. + Fail with_strategy transparent [id] unfold id. + let id' := id in with_strategy transparent [id] unfold id'. + + .. warning:: + + Use this tactic with care, as effects do not persist past the + end of the proof script. Notably, this fine-tuning of the + conversion strategy is not in effect during :cmd:`Qed` nor + :cmd:`Defined`, so this tactic is most useful either in + combination with :tacn:`abstract`, which will check the proof + early while the fine-tuning is still in effect, or to guard + calls to conversion in tactic automation to ensure that, e.g., + :tacn:`unfold` does not fail just because the user made a + constant :cmd:`Opaque`. + + This can be illustrated with the following example involving the + factorial function. + + .. coqtop:: in reset + + Fixpoint fact (n : nat) : nat := + match n with + | 0 => 1 + | S n' => n * fact n' + end. + + Suppose now that, for whatever reason, we want in general to + unfold the :g:`id` function very late during conversion: + + .. coqtop:: in + + Strategy 1000 [id]. + + If we try to prove :g:`id (fact n) = fact n` by + :tacn:`reflexivity`, it will now take time proportional to + :math:`n!`, because |Coq| will keep unfolding :g:`fact` and + :g:`*` and :g:`+` before it unfolds :g:`id`, resulting in a full + computation of :g:`fact n` (in unary, because we are using + :g:`nat`), which takes time :math:`n!`. We can see this cross + the relevant threshold at around :math:`n = 9`: + + .. coqtop:: all abort + + Goal True. + Time assert (id (fact 8) = fact 8) by reflexivity. + Time assert (id (fact 9) = fact 9) by reflexivity. + + Note that behavior will be the same if you mark :g:`id` as + :g:`Opaque` because while most reduction tactics refuse to + unfold :g:`Opaque` constants, conversion treats :g:`Opaque` as + merely a hint to unfold this constant last. + + We can get around this issue by using :tacn:`with_strategy`: + + .. coqtop:: all + + Goal True. + Fail Timeout 1 assert (id (fact 100) = fact 100) by reflexivity. + Time assert (id (fact 100) = fact 100) by with_strategy -1 [id] reflexivity. + + However, when we go to close the proof, we will run into + trouble, because the reduction strategy changes are local to the + tactic passed to :tacn:`with_strategy`. + + .. coqtop:: all abort fail + + exact I. + Timeout 1 Defined. + + We can fix this issue by using :tacn:`abstract`: + + .. coqtop:: all + + Goal True. + Time assert (id (fact 100) = fact 100) by with_strategy -1 [id] abstract reflexivity. + exact I. + Time Defined. + + On small examples this sort of behavior doesn't matter, but + because |Coq| is a super-linear performance domain in so many + places, unless great care is taken, tactic automation using + :tacn:`with_strategy` may not be robustly performant when + scaling the size of the input. + + .. warning:: + + In much the same way this tactic does not play well with + :cmd:`Qed` and :cmd:`Defined` without using :tacn:`abstract` as + an intermediary, this tactic does not play well with ``coqchk``, + even when used with :tacn:`abstract`, due to the inability of + tactics to persist information about conversion hints in the + proof term. See `#12200 + <https://github.com/coq/coq/issues/12200>`_ for more details. + Conversion tactics applied to hypotheses ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ diff --git a/doc/sphinx/proof-engine/vernacular-commands.rst b/doc/sphinx/proof-engine/vernacular-commands.rst index 1759264e87..7191444bac 100644 --- a/doc/sphinx/proof-engine/vernacular-commands.rst +++ b/doc/sphinx/proof-engine/vernacular-commands.rst @@ -817,13 +817,15 @@ described first. .. cmd:: Strategy {+ @strategy_level [ {+ @smart_qualid } ] } - .. insertprodn strategy_level strategy_level + .. insertprodn strategy_level strategy_level_or_var .. prodn:: strategy_level ::= opaque | @int | expand | transparent + strategy_level_or_var ::= @strategy_level + | @ident This command accepts the :attr:`local` attribute, which limits its effect to the current section or module, in which case the section and module diff --git a/doc/sphinx/user-extensions/syntax-extensions.rst b/doc/sphinx/user-extensions/syntax-extensions.rst index d72409e0d9..ea5ad79a80 100644 --- a/doc/sphinx/user-extensions/syntax-extensions.rst +++ b/doc/sphinx/user-extensions/syntax-extensions.rst @@ -1714,6 +1714,11 @@ Tactic notations allow customizing the syntax of tactics. - a global reference of term - :tacn:`unfold` + * - ``smart_global`` + - :token:`smart_qualid` + - a global reference of term + - :tacn:`with_strategy` + * - ``constr`` - :token:`term` - a term @@ -1734,6 +1739,16 @@ Tactic notations allow customizing the syntax of tactics. - an integer - :tacn:`do` + * - ``strategy_level`` + - :token:`strategy_level` + - a strategy level + - + + * - ``strategy_level_or_var`` + - :token:`strategy_level_or_var` + - a strategy level + - :tacn:`with_strategy` + * - ``tactic`` - :token:`ltac_expr` - a tactic @@ -1766,18 +1781,24 @@ Tactic notations allow customizing the syntax of tactics. .. todo: notation doesn't support italics - .. note:: In order to be bound in tactic definitions, each syntactic - entry for argument type must include the case of a simple |Ltac| - identifier as part of what it parses. This is naturally the case for - ``ident``, ``simple_intropattern``, ``reference``, ``constr``, ... but not for ``integer``. - This is the reason for introducing a special entry ``int_or_var`` which - evaluates to integers only but which syntactically includes + .. note:: In order to be bound in tactic definitions, each + syntactic entry for argument type must include the case + of a simple |Ltac| identifier as part of what it + parses. This is naturally the case for ``ident``, + ``simple_intropattern``, ``reference``, ``constr``, ... + but not for ``integer`` nor for ``strategy_level``. This + is the reason for introducing special entries + ``int_or_var`` and ``strategy_level_or_var`` which + evaluate to integers or strategy levels only, + respectively, but which syntactically includes identifiers in order to be usable in tactic definitions. - .. note:: The *entry*\ ``_list*`` and ``ne_``\ *entry*\ ``_list*`` entries can be used in - primitive tactics or in other notations at places where a list of the - underlying entry can be used: entry is either ``constr``, ``hyp``, ``integer`` - or ``int_or_var``. + .. note:: The *entry*\ ``_list*`` and ``ne_``\ *entry*\ ``_list*`` + entries can be used in primitive tactics or in other + notations at places where a list of the underlying entry + can be used: entry is either ``constr``, ``hyp``, + ``integer``, ``smart_qualid``, ``strategy_level``, + ``strategy_level_or_var``, or ``int_or_var``. .. rubric:: Footnotes |