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8c00cc65
Commit
8c00cc65
authored
Dec 25, 2018
by
Robbert Krebbers
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Update persistent → intuitionistic in ProofMode.md.
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ProofMode.md
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8c00cc65
...
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@@ 30,15 +30,15 @@ Context management
pattern
`selpat`
and the Coq level hypotheses/variables
`x1 ... xn`
.

`iRevert (x1 ... xn) "selpat"`
: revert the hypotheses given by the selection
pattern
`selpat`
into wands, and the Coq level hypotheses/variables
`x1 ... xn`
into universal quantifiers.
Persistent hypotheses are wrapped into
the persistence
modality.
`x1 ... xn`
into universal quantifiers.
Intuitionistic hypotheses are wrapped
into the intuitionistic
modality.

`iRename "H1" into "H2"`
: rename the hypothesis
`H1`
into
`H2`
.

`iSpecialize pm_trm`
: instantiate universal quantifiers and eliminate
implications/wands of a hypothesis
`pm_trm`
. See proof mode terms below.

`iSpecialize pm_trm as #`
: instantiate universal quantifiers and eliminate
implications/wands of a hypothesis
whose conclusion is persistent. In this
case, all hypotheses can be used for proving the premises, as well as for
the resulting
goal.
implications/wands of a hypothesis
`pm_trm`
whose conclusion is persistent.
All hypotheses can be used for proving the premises of
`pm_trm`
, as well as
for the resulting main
goal.

`iPoseProof pm_trm as (x1 ... xn) "ipat"`
: put
`pm_trm`
into the context and
eliminates it. This tactic is essentially the same as
`iDestruct`
with the
difference that when
`pm_trm`
is a nonuniversally quantified intuitionistic
...
...
@@ 48,9 +48,9 @@ Context management
specifies which hypotheses will be consumed by proving
`P`
. The introduction
pattern
`ipat`
specifies how to eliminate
`P`
.
In case all branches of
`ipat`
start with a
`#`
(which causes
`P`
to be moved
to the
persistent context) or with an
`%`
(which causes
`P`
to be moved to the
pure Coq context), then one can use all hypotheses for proving
`P`
as well as
for proving the current goal.
to the
intuitionistic context) or with an
`%`
(which causes
`P`
to be moved to
the pure Coq context), then one can use all hypotheses for proving
`P`
as well
as
for proving the current goal.

`iAssert P as %cpat`
: assert
`P`
and eliminate it using the Coq introduction
pattern
`cpat`
. All hypotheses can be used for proving
`P`
as well as for
proving the current goal.
...
...
@@ 68,8 +68,8 @@ Introduction of logical connectives
one of the operands is persistent.

`iSplitL "H1 ... Hn"`
: introduction of a separating conjunction. The
hypotheses
`H1 ... Hn`
are used for the left conjunct, and the remaining ones
for the right conjunct.
Persistent hypotheses are ignored, since these do not
need to be split.
for the right conjunct.
Intuitionistic hypotheses are ignored, since these do
n
ot n
eed to be split.

`iSplitR "H0 ... Hn"`
: symmetric version of the above.

`iExist t1, .., tn`
: introduction of an existential quantifier.
...
...
@@ 82,7 +82,7 @@ Elimination of logical connectives
elimination of an object level connective using the proof mode introduction
pattern
`ipat`
.
In case all branches of
`ipat`
start with a
`#`
(which causes the hypothesis
to be moved to the
persistent
context) or with an
`%`
(which causes the
to be moved to the
intuitionistic
context) or with an
`%`
(which causes the
hypothesis to be moved to the pure Coq context), then one can use all
hypotheses for proving the premises of
`pm_trm`
, as well as for proving the
resulting goal. Note that in this case the hypotheses still need to be
...
...
@@ 100,11 +100,11 @@ Separating logic specific tactics
of the selection pattern have the following meaning:
+
`%`
: repeatedly frame hypotheses from the Coq context.
+
`#`
: repeatedly frame hypotheses from the
persistent
context.
+
`#`
: repeatedly frame hypotheses from the
intuitionistic
context.
+
`∗`
: frame as much of the spatial context as possible.
Notice that framing spatial hypotheses makes them disappear, but framing Coq
or
persistent
hypotheses does not make them disappear.
or
intuitionistic
hypotheses does not make them disappear.
This tactic finishes the goal in case everything in the conclusion has been
framed.
...
...
@@ 117,9 +117,9 @@ Modalities

`iModIntro mod`
: introduction of a modality. The type class
`FromModal`
is
used to specify which modalities this tactic should introduce. Instances of
that type class include: later, except 0, basic update and fancy update,
persistently, affinely, plainly, absorbingly, objectively, and subjectively.
The optional argument
`mod`
can be used to specify what modality to introduce
in case of ambiguity, e.g.
`⎡==> P⎤`
.
intuitionistically, persistently, affinely, plainly, absorbingly, objectively,
and subjectively. The optional argument
`mod`
can be used to specify what
modality to introduce
in case of ambiguity, e.g.
`⎡==> P⎤`
.

`iAlways`
: a deprecated alias of
`iModIntro`
.

`iNext n`
: an alias of
`iModIntro (▷^n P)`
.

`iNext`
: an alias of
`iModIntro (▷^1 P)`
.
...
...
@@ 136,10 +136,10 @@ Induction
`selpat`
, and the spatial context.

`iInduction x as cpat "IH" forall (x1 ... xn) "selpat"`
: perform induction on
the Coq term
`x`
. The Coq introduction pattern is used to name the introduced
variables. The induction hypotheses are inserted into the
persistent context
and given fresh names prefixed
`IH`
. The tactic generalizes over the Coq level
variables
`x1 ... xn`
, the hypotheses given by the selection pattern
`selpat`
,
and the spatial context.
variables. The induction hypotheses are inserted into the
intuitionistic
context and given fresh names prefixed
`IH`
. The tactic generalizes over the
Coq level variables
`x1 ... xn`
, the hypotheses given by the selection pattern
`selpat`
,
and the spatial context.
Rewriting / simplification

...
...
@@ 186,7 +186,7 @@ following _selection patterns_:

`H`
: select the hypothesis named
`H`
.

`%`
: select the entire pure/Coq context.

`#`
: select the entire
persistent
context.

`#`
: select the entire
intuitionistic
context.

`∗`
: select the entire spatial context.
Introduction patterns
...
...
@@ 210,7 +210,7 @@ _introduction patterns_:

`[]`
: false elimination.

`%`
: move the hypothesis to the pure Coq context (anonymously).

`>`
and
`<`
: rewrite using a pure Coq equality

`# ipat`
: move the hypothesis
to the persistent
context.

`# ipat`
: move the hypothesis
into the intuitionistic
context.

`> ipat`
: eliminate a modality (if the goal permits).
Apart from this, there are the following introduction patterns that can only
...
...
@@ 259,11 +259,11 @@ _specification patterns_ to express splitting of hypotheses:
spatial, it will be consumed.

`[H1 .. Hn]`
and
`[H1 .. Hn //]`
: generate a goal for the premise with the
(spatial) hypotheses
`H1 ... Hn`
and all
persistent hypotheses. The spatial
hypotheses among
`H1 ... Hn`
will be consumed, and will not be available for
subsequent goals. Hypotheses prefixed with a
`$`
will be framed in the
goal for the premise. The pattern can be terminated with a
`//`
, which causes
`done`
to be called to close the goal (after framing).
(spatial) hypotheses
`H1 ... Hn`
and all
intuitionistic hypotheses. The
spatial hypotheses among
`H1 ... Hn`
will be consumed, and will not be
available for subsequent goals. Hypotheses prefixed with a
`$`
will be framed
in the goal for the premise. The pattern can be terminated with a
`//`
, which
causes
`done`
to be called to close the goal (after framing).

`[H1 ... Hn]`
and
`[H1 ... Hn //]`
: the negated forms of the above
patterns, where the goal for the premise will have all spatial premises except
`H1 .. Hn`
.
...
...
@@ 285,14 +285,14 @@ _specification patterns_ to express splitting of hypotheses:
which causes
`done`
to be called to close the goal.

`[$]`
: solve the premise by framing. It will first repeatedly frame the
spatial hypotheses, and then repeatedly frame the
persistent
hypotheses.
spatial hypotheses, and then repeatedly frame the
intuitionistic
hypotheses.
Spatial hypothesis that are not framed are carried over to the subsequent
goal.

`[> $]`
: like the above pattern, but this pattern can only be used if the
goal is a modality
`M`
, in which case the goal for the premise will be wrapped
in the modality
`M`
before framing.

`[# $]`
: solve the persistent premise by framing. It will first repeatedly
frame the spatial hypotheses, and then repeatedly frame the
persistent
frame the spatial hypotheses, and then repeatedly frame the
intuitionistic
hypotheses. This pattern does not consume any hypotheses.
For example, given:
...
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