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authorThéo Zimmermann2019-02-13 11:49:29 +0100
committerThéo Zimmermann2019-02-13 11:49:29 +0100
commit90e2fa3344cff478a2ab23c0dbbb5eab5b4668e4 (patch)
tree7ad437364d4998e8a95ee8c0d1a1827099bd8084 /doc/sphinx/proof-engine
parent0b0fa735dc0da5660a870053a5a5f6fd1c5e22d1 (diff)
parentd638148dc3e0220ac99761cf9f2efa8284882c41 (diff)
Merge PR #9553: Sphinx various fixing of failing commands
Ack-by: Zimmi48
Diffstat (limited to 'doc/sphinx/proof-engine')
-rw-r--r--doc/sphinx/proof-engine/ltac.rst8
-rw-r--r--doc/sphinx/proof-engine/ssreflect-proof-language.rst192
-rw-r--r--doc/sphinx/proof-engine/tactics.rst2
3 files changed, 106 insertions, 96 deletions
diff --git a/doc/sphinx/proof-engine/ltac.rst b/doc/sphinx/proof-engine/ltac.rst
index 442077616f..4f486a777d 100644
--- a/doc/sphinx/proof-engine/ltac.rst
+++ b/doc/sphinx/proof-engine/ltac.rst
@@ -859,6 +859,10 @@ We can carry out pattern matching on terms with:
Goal True.
f (3+4).
+ .. coqtop:: none
+
+ Abort.
+
.. _ltac-match-goal:
Pattern matching on goals
@@ -1026,6 +1030,10 @@ Counting the goals
all:pr_numgoals.
+ .. coqtop:: none
+
+ Abort.
+
Testing boolean expressions
~~~~~~~~~~~~~~~~~~~~~~~~~~~
diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst
index 483dbd311d..ec97377128 100644
--- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst
+++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst
@@ -233,7 +233,7 @@ construct differs from the latter in that
.. coqtop:: reset all
- Definition f u := let (m, n) := u in m + n.
+ Fail Definition f u := let (m, n) := u in m + n.
The ``let:`` construct is just (more legible) notation for the primitive
@@ -413,7 +413,7 @@ each point of use, e.g., the above definition can be written:
Variable all : (T -> bool) -> list T -> bool.
- .. coqtop:: all undo
+ .. coqtop:: all
Prenex Implicits null.
Definition all_null (s : list T) := all null s.
@@ -436,7 +436,7 @@ The syntax of the new declaration is
a ``Set Printing All`` command). All |SSR| library files thus start
with the incantation
- .. coqtop:: all undo
+ .. coqdoc::
Set Implicit Arguments.
Unset Strict Implicit.
@@ -505,7 +505,7 @@ Definitions
|SSR| pose tactic supports *open syntax*: the body of the
definition does not need surrounding parentheses. For instance:
-.. coqtop:: in
+.. coqdoc::
pose t := x + y.
@@ -534,7 +534,7 @@ The |SSR| pose tactic also supports (co)fixpoints, by providing
the local counterpart of the ``Fixpoint f := …`` and ``CoFixpoint f := …``
constructs. For instance, the following tactic:
-.. coqtop:: in
+.. coqdoc::
pose fix f (x y : nat) {struct x} : nat :=
if x is S p then S (f p y) else 0.
@@ -544,7 +544,7 @@ on natural numbers.
Similarly, local cofixpoints can be defined by a tactic of the form:
-.. coqtop:: in
+.. coqdoc::
pose cofix f (arg : T) := … .
@@ -553,26 +553,26 @@ offers a smooth way of defining local abstractions. The type of
“holes” is guessed by type inference, and the holes are abstracted.
For instance the tactic:
-.. coqtop:: in
+.. coqdoc::
pose f := _ + 1.
is shorthand for:
-.. coqtop:: in
+.. coqdoc::
pose f n := n + 1.
When the local definition of a function involves both arguments and
holes, hole abstractions appear first. For instance, the tactic:
-.. coqtop:: in
+.. coqdoc::
pose f x := x + _.
is shorthand for:
-.. coqtop:: in
+.. coqdoc::
pose f n x := x + n.
@@ -580,13 +580,13 @@ The interaction of the pose tactic with the interpretation of implicit
arguments results in a powerful and concise syntax for local
definitions involving dependent types. For instance, the tactic:
-.. coqtop:: in
+.. coqdoc::
pose f x y := (x, y).
adds to the context the local definition:
-.. coqtop:: in
+.. coqdoc::
pose f (Tx Ty : Type) (x : Tx) (y : Ty) := (x, y).
@@ -766,7 +766,7 @@ Moreover:
.. coqtop:: all
Lemma test : forall x : nat, x + 1 = 0.
- set t := _ + 1.
+ Fail set t := _ + 1.
+ Typeclass inference should fill in any residual hole, but matching
should never assign a value to a global existential variable.
@@ -889,7 +889,7 @@ only one occurrence of the selected term.
.. coqtop:: all
Lemma test x y z : (x + y) + (z + z) = z + z.
- set a := {2}(_ + _).
+ Fail set a := {2}(_ + _).
.. _basic_localization_ssr:
@@ -1079,7 +1079,7 @@ constants to the goal.
Because they are tacticals, ``:`` and ``=>`` can be combined, as in
-.. coqtop:: in
+.. coqdoc::
move: m le_n_m => p le_n_p.
@@ -1139,7 +1139,7 @@ Basic tactics like apply and elim can also be used without the ’:’
tactical: for example we can directly start a proof of ``subnK`` by
induction on the top variable ``m`` with
-.. coqtop:: in
+.. coqdoc::
elim=> [|m IHm] n le_n.
@@ -1150,7 +1150,7 @@ explained in terms of the goal stack::
is basically equivalent to
-.. coqtop:: in
+.. coqdoc::
move: a H1 H2; tactic => a H1 H2.
@@ -1163,13 +1163,13 @@ temporary abbreviation to hide the statement of the goal from
The general form of the in tactical can be used directly with the
``move``, ``case`` and ``elim`` tactics, so that one can write
-.. coqtop:: in
+.. coqdoc::
elim: n => [|n IHn] in m le_n_m *.
instead of
-.. coqtop:: in
+.. coqdoc::
elim: n m le_n_m => [|n IHn] m le_n_m.
@@ -1398,7 +1398,7 @@ Switches affect the discharging of a :token:`d_item` as follows:
For example, the tactic:
-.. coqtop:: in
+.. coqdoc::
move: n {2}n (refl_equal n).
@@ -1409,7 +1409,7 @@ For example, the tactic:
Therefore this tactic changes any goal ``G`` into
-.. coqtop::
+.. coqdoc::
forall n n0 : nat, n = n0 -> G.
@@ -1843,7 +1843,7 @@ Generation of equations
The generation of named equations option stores the definition of a
new constant as an equation. The tactic:
-.. coqtop:: in
+.. coqdoc::
move En: (size l) => n.
@@ -1851,7 +1851,7 @@ where ``l`` is a list, replaces ``size l`` by ``n`` in the goal and
adds the fact ``En : size l = n`` to the context.
This is quite different from:
-.. coqtop:: in
+.. coqdoc::
pose n := (size l).
@@ -1936,7 +1936,7 @@ be substituted.
inferred looking at the type of the top assumption. This allows for the
compact syntax:
- .. coqtop:: in
+ .. coqdoc::
case: {2}_ / eqP.
@@ -2112,7 +2112,7 @@ In the script provided as example in section :ref:`indentation_ssr`, the
paragraph corresponding to each sub-case ends with a tactic line prefixed
with a ``by``, like in:
-.. coqtop:: in
+.. coqdoc::
by apply/eqP; rewrite -dvdn1.
@@ -2147,13 +2147,13 @@ A natural and common way of closing a goal is to apply a lemma which
is the exact one needed for the goal to be solved. The defective form
of the tactic:
-.. coqtop:: in
+.. coqdoc::
exact.
is equivalent to:
-.. coqtop:: in
+.. coqdoc::
do [done | by move=> top; apply top].
@@ -2161,13 +2161,13 @@ where ``top`` is a fresh name assigned to the top assumption of the goal.
This applied form is supported by the ``:`` discharge tactical, and the
tactic:
-.. coqtop:: in
+.. coqdoc::
exact: MyLemma.
is equivalent to:
-.. coqtop:: in
+.. coqdoc::
by apply: MyLemma.
@@ -2179,19 +2179,19 @@ is equivalent to:
follows the ``by`` keyword is considered to be a parenthesized block applied to
the current goal. Hence for example if the tactic:
- .. coqtop:: in
+ .. coqdoc::
by rewrite my_lemma1.
succeeds, then the tactic:
- .. coqtop:: in
+ .. coqdoc::
by rewrite my_lemma1; apply my_lemma2.
usually fails since it is equivalent to:
- .. coqtop:: in
+ .. coqdoc::
by (rewrite my_lemma1; apply my_lemma2).
@@ -2247,7 +2247,7 @@ Finally, the tactics ``last`` and ``first`` combine with the branching syntax
of Ltac: if the tactic generates n subgoals on a given goal,
then the tactic
-.. coqtop:: in
+.. coqdoc::
tactic ; last k [ tactic1 |…| tacticm ] || tacticn.
@@ -2262,7 +2262,6 @@ to the others.
.. coqtop:: reset
- Abort.
From Coq Require Import ssreflect.
Set Implicit Arguments.
Unset Strict Implicit.
@@ -2296,13 +2295,13 @@ Iteration
A tactic of the form:
-.. coqtop:: in
+.. coqdoc::
do [ tactic 1 | … | tactic n ].
is equivalent to the standard Ltac expression:
-.. coqtop:: in
+.. coqdoc::
first [ tactic 1 | … | tactic n ].
@@ -2327,14 +2326,14 @@ Their meaning is:
For instance, the tactic:
-.. coqtop:: in
+.. coqdoc::
tactic; do 1? rewrite mult_comm.
rewrites at most one time the lemma ``mult_comm`` in all the subgoals
generated by tactic , whereas the tactic:
-.. coqtop:: in
+.. coqdoc::
tactic; do 2! rewrite mult_comm.
@@ -2518,7 +2517,7 @@ tactics of the form:
which behave like:
-.. coqtop:: in
+.. coqdoc::
have: term ; first by tactic.
move=> clear_switch i_item.
@@ -2531,7 +2530,7 @@ to introduce the new assumption itself.
The ``by`` feature is especially convenient when the proof script of the
statement is very short, basically when it fits in one line like in:
-.. coqtop:: in
+.. coqdoc::
have H23 : 3 + 2 = 2 + 3 by rewrite addnC.
@@ -2559,7 +2558,7 @@ the further use of the intermediate step. For instance,
Thanks to the deferred execution of clears, the following idiom is
also supported (assuming x occurs in the goal only):
-.. coqtop:: in
+.. coqdoc::
have {x} -> : x = y.
@@ -2635,7 +2634,7 @@ Since the :token:`i_pattern` can be omitted, to avoid ambiguity,
bound variables can be surrounded
with parentheses even if no type is specified:
-.. coqtop:: in
+.. coqdoc::
have (x) : 2 * x = x + x by omega.
@@ -2816,7 +2815,7 @@ The
+ but the optional clear item is still performed in the *second*
branch. This means that the tactic:
- .. coqtop:: in
+ .. coqdoc::
suff {H} H : forall x : nat, x >= 0.
@@ -2888,7 +2887,7 @@ name of the local definition with the ``@`` character.
In the second subgoal, the tactic:
-.. coqtop:: in
+.. coqdoc::
move=> clear_switch i_item.
@@ -2995,10 +2994,13 @@ illustrated in the following example.
the pattern ``id (addx x)``, that would produce the following first
subgoal
- .. coqtop:: none
+ .. coqtop:: none reset
+
+ From Coq Require Import ssreflect Omega.
+ Set Implicit Arguments.
+ Unset Strict Implicit.
+ Unset Printing Implicit Defensive.
- Abort All.
- From Coq Require Import Omega.
Section Test.
Variable x : nat.
Definition addx z := z + x.
@@ -3153,7 +3155,7 @@ An :token:`r_item` can be:
Definition f := fun x y => x + y.
Lemma test x y : x + y = f y x.
- rewrite -[f y]/(y + _).
+ Fail rewrite -[f y]/(y + _).
but the following script succeeds
@@ -3192,7 +3194,7 @@ tactics.
In a rewrite tactic of the form:
-.. coqtop:: in
+.. coqdoc::
rewrite occ_switch [term1]term2.
@@ -3235,7 +3237,7 @@ Performing rewrite and simplification operations in a single tactic
enhances significantly the concision of scripts. For instance the
tactic:
-.. coqtop:: in
+.. coqdoc::
rewrite /my_def {2}[f _]/= my_eq //=.
@@ -3316,7 +3318,7 @@ the equality.
.. coqtop:: all
Lemma test (H : forall t u, t + u * 0 = t) x y : x + y * 4 + 2 * 0 = x + 2 * 0.
- rewrite [x + _]H.
+ Fail rewrite [x + _]H.
Indeed the left hand side of ``H`` does not match
the redex identified by the pattern ``x + y * 4``.
@@ -3498,7 +3500,7 @@ reasoning purposes. The library also provides one lemma per such
operation, stating that both versions return the same values when
applied to the same arguments:
-.. coqtop:: in
+.. coqdoc::
Lemma addE : add =2 addn.
Lemma doubleE : double =1 doublen.
@@ -3514,7 +3516,7 @@ hand side. In order to reason conveniently on expressions involving
the efficient operations, we gather all these rules in the definition
``trecE``:
-.. coqtop:: in
+.. coqdoc::
Definition trecE := (addE, (doubleE, oddE), (mulE, add_mulE, (expE, mul_expE))).
@@ -3572,14 +3574,14 @@ cases:
+ |SSR| never accepts to rewrite indeterminate patterns like:
- .. coqtop:: in
+ .. coqdoc::
Lemma foo (x : unit) : x = tt.
|SSR| will however accept the
ηζ expansion of this rule:
- .. coqtop:: in
+ .. coqdoc::
Lemma fubar (x : unit) : (let u := x in u) = tt.
@@ -3617,7 +3619,7 @@ cases:
.. coqtop:: all
- rewrite H.
+ Fail rewrite H.
Rewriting with ``H`` first requires unfolding the occurrences of
``f``
@@ -3729,7 +3731,7 @@ copy of any term t. However this copy is (on purpose) *not
convertible* to t in the |Coq| system [#8]_. The job is done by the
following construction:
-.. coqtop:: in
+.. coqdoc::
Lemma master_key : unit. Proof. exact tt. Qed.
Definition locked A := let: tt := master_key in fun x : A => x.
@@ -3793,14 +3795,14 @@ some functions by the partial evaluation switch ``/=``, unless this
allowed the evaluation of a condition. This is possible thanks to another
mechanism of term tagging, resting on the following *Notation*:
-.. coqtop:: in
+.. coqdoc::
Notation "'nosimpl' t" := (let: tt := tt in t).
The term ``(nosimpl t)`` simplifies to ``t`` *except* in a definition.
More precisely, given:
-.. coqtop:: in
+.. coqdoc::
Definition foo := (nosimpl bar).
@@ -3816,7 +3818,7 @@ Note that ``nosimpl bar`` is simply notation for a term that reduces to
The ``nosimpl`` trick only works if no reduction is apparent in
``t``; in particular, the declaration:
- .. coqtop:: in
+ .. coqdoc::
Definition foo x := nosimpl (bar x).
@@ -3824,14 +3826,14 @@ Note that ``nosimpl bar`` is simply notation for a term that reduces to
function, and to use the following definition, which blocks the
reduction as expected:
- .. coqtop:: in
+ .. coqdoc::
Definition foo x := nosimpl bar x.
A standard example making this technique shine is the case of
arithmetic operations. We define for instance:
-.. coqtop:: in
+.. coqdoc::
Definition addn := nosimpl plus.
@@ -3851,7 +3853,7 @@ Congruence
Because of the way matching interferes with parameters of type families,
the tactic:
-.. coqtop:: in
+.. coqdoc::
apply: my_congr_property.
@@ -4047,7 +4049,7 @@ For a quick glance at what can be expressed with the last
:token:`r_pattern`
consider the goal ``a = b`` and the tactic
-.. coqtop:: in
+.. coqdoc::
rewrite [in X in _ = X]rule.
@@ -4148,14 +4150,14 @@ patterns over simple terms, but to interpret a pattern with double
parentheses as a simple term. For example, the following tactic would
capture any occurrence of the term ``a in A``.
-.. coqtop:: in
+.. coqdoc::
set t := ((a in A)).
Contextual patterns can also be used as arguments of the ``:`` tactical.
For example:
-.. coqtop:: in
+.. coqdoc::
elim: n (n in _ = n) (refl_equal n).
@@ -4246,7 +4248,7 @@ context shortcuts.
The following example is taken from ``ssreflect.v`` where the
``LHS`` and ``RHS`` shortcuts are defined.
-.. coqtop:: in
+.. coqdoc::
Notation RHS := (X in _ = X)%pattern.
Notation LHS := (X in X = _)%pattern.
@@ -4254,7 +4256,7 @@ The following example is taken from ``ssreflect.v`` where the
Shortcuts defined this way can be freely used in place of the trailing
``ident in term`` part of any contextual pattern. Some examples follow:
-.. coqtop:: in
+.. coqdoc::
set rhs := RHS.
rewrite [in RHS]rule.
@@ -4287,13 +4289,13 @@ The view syntax combined with the ``elim`` tactic specifies an elimination
scheme to be used instead of the default, generated, one. Hence the
|SSR| tactic:
-.. coqtop:: in
+.. coqdoc::
elim/V.
is a synonym for:
-.. coqtop:: in
+.. coqdoc::
intro top; elim top using V; clear top.
@@ -4303,13 +4305,13 @@ Since an elimination view supports the two bookkeeping tacticals of
discharge and introduction (see section :ref:`basic_tactics_ssr`),
the |SSR| tactic:
-.. coqtop:: in
+.. coqdoc::
elim/V: x => y.
is a synonym for:
-.. coqtop:: in
+.. coqdoc::
elim x using V; clear x; intro y.
@@ -4367,13 +4369,13 @@ command) can be combined with the type family switches described
in section :ref:`type_families_ssr`.
Consider an eliminator ``foo_ind`` of type:
-.. coqtop:: in
+.. coqdoc::
foo_ind : forall …, forall x : T, P p1 … pm.
and consider the tactic:
-.. coqtop:: in
+.. coqdoc::
elim/foo_ind: e1 … / en.
@@ -4424,7 +4426,7 @@ Here is an example of a regular, but nontrivial, eliminator.
The following tactics are all valid and perform the same elimination
on this goal.
- .. coqtop:: in
+ .. coqdoc::
elim/plus_ind: z / (plus _ z).
elim/plus_ind: {z}(plus _ z).
@@ -4473,7 +4475,7 @@ Here is an example of a regular, but nontrivial, eliminator.
.. coqtop:: all
- elim/plus_ind: y / _.
+ Fail elim/plus_ind: y / _.
triggers an error: in the conclusion
of the ``plus_ind`` eliminator, the first argument of the predicate
@@ -4494,7 +4496,7 @@ Here is an example of a truncated eliminator:
Unset Printing Implicit Defensive.
Section Test.
- .. coqtop:: in
+ .. coqdoc::
Lemma test p n (n_gt0 : 0 < n) (pr_p : prime p) :
p %| \prod_(i <- prime_decomp n | i \in prime_decomp n) i.1 ^ i.2 ->
@@ -4505,7 +4507,7 @@ Here is an example of a truncated eliminator:
where the type of the ``big_prop`` eliminator is
- .. coqtop:: in
+ .. coqdoc::
big_prop: forall (R : Type) (Pb : R -> Type)
(idx : R) (op1 : R -> R -> R), Pb idx ->
@@ -4518,7 +4520,7 @@ Here is an example of a truncated eliminator:
inferred one is used instead: ``big[_/_]_(i <- _ | _ i) _ i``,
and after the introductions, the following goals are generated:
- .. coqtop:: in
+ .. coqdoc::
subgoal 1 is:
p %| 1 -> exists2 x : nat * nat, x \in prime_decomp n & p = x.1
@@ -4624,7 +4626,7 @@ equation name generation mechanism (see section :ref:`generation_of_equations_ss
This view tactic performs:
- .. coqtop:: in
+ .. coqdoc::
move=> HQ; case: {HQ}(Q2P HQ) => [HPa | HPb].
@@ -4661,14 +4663,14 @@ relevant for the current goal.
the double implication into the expected simple implication. The last
script is in fact equivalent to:
- .. coqtop:: in
+ .. coqdoc::
Lemma test a b : P (a || b) -> True.
move/(iffLR (PQequiv _ _)).
where:
- .. coqtop:: in
+ .. coqdoc::
Lemma iffLR P Q : (P <-> Q) -> P -> Q.
@@ -4810,7 +4812,7 @@ decidable predicate to its boolean version.
First, booleans are injected into propositions using the coercion
mechanism:
-.. coqtop:: in
+.. coqdoc::
Coercion is_true (b : bool) := b = true.
@@ -4827,7 +4829,7 @@ To get all the benefits of the boolean reflection, it is in fact
convenient to introduce the following inductive predicate ``reflect`` to
relate propositions and booleans:
-.. coqtop:: in
+.. coqdoc::
Inductive reflect (P: Prop): bool -> Type :=
| Reflect_true : P -> reflect P true
@@ -4838,7 +4840,7 @@ logically equivalent propositions.
For instance, the following lemma:
-.. coqtop:: in
+.. coqdoc::
Lemma andP: forall b1 b2, reflect (b1 /\ b2) (b1 && b2).
@@ -4853,20 +4855,20 @@ to the case analysis of |Coq|’s inductive types.
Since the equivalence predicate is defined in |Coq| as:
-.. coqtop:: in
+.. coqdoc::
Definition iff (A B:Prop) := (A -> B) /\ (B -> A).
where ``/\`` is a notation for ``and``:
-.. coqtop:: in
+.. coqdoc::
Inductive and (A B:Prop) : Prop := conj : A -> B -> and A B.
This make case analysis very different according to the way an
equivalence property has been defined.
-.. coqtop:: in
+.. coqdoc::
Lemma andE (b1 b2 : bool) : (b1 /\ b2) <-> (b1 && b2).
@@ -4950,13 +4952,13 @@ Specializing assumptions
The |SSR| tactic:
-.. coqtop:: in
+.. coqdoc::
move/(_ term1 … termn).
is equivalent to the tactic:
-.. coqtop:: in
+.. coqdoc::
intro top; generalize (top term1 … termn); clear top.
@@ -5013,13 +5015,13 @@ If ``term`` is a double implication, then the view hint will be one of
the defined view hints for implication. These hints are by default the
ones present in the file ``ssreflect.v``:
-.. coqtop:: in
+.. coqdoc::
Lemma iffLR : forall P Q, (P <-> Q) -> P -> Q.
which transforms a double implication into the left-to-right one, or:
-.. coqtop:: in
+.. coqdoc::
Lemma iffRL : forall P Q, (P <-> Q) -> Q -> P.
@@ -5123,7 +5125,7 @@ equality, while the second term is the one applied to the right hand side.
In this context, the identity view can be used when no view has to be applied:
-.. coqtop:: in
+.. coqdoc::
Lemma idP : reflect b1 b1.
@@ -5198,7 +5200,7 @@ in sequence. Both move and apply can be followed by an arbitrary
number of ``/term``. The main difference between the following two
tactics
-.. coqtop:: in
+.. coqdoc::
apply/v1/v2/v3.
apply/v1; apply/v2; apply/v3.
@@ -5210,7 +5212,7 @@ line would apply the view ``v2`` to all the goals generated by ``apply/v1``.
Note that the NO-OP intro pattern ``-`` can be used to separate two views,
making the two following examples equivalent:
-.. coqtop:: in
+.. coqdoc::
move=> /v1; move=> /v2.
move=> /v1 - /v2.
diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst
index 66d510bc0e..0bcfce2322 100644
--- a/doc/sphinx/proof-engine/tactics.rst
+++ b/doc/sphinx/proof-engine/tactics.rst
@@ -2493,7 +2493,7 @@ and an explanation of the underlying technique.
Let us consider the relation Le over natural numbers and the following
variables:
- .. coqtop:: all
+ .. coqtop:: all reset
Inductive Le : nat -> nat -> Set :=
| LeO : forall n:nat, Le 0 n