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Rice Wine
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1c14ae6f
Commit
1c14ae6f
authored
Mar 07, 2017
by
Robbert Krebbers
Browse files
Update star symbol in ProofMode docs.
parent
f870cdaf
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1
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ProofMode.md
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1c14ae6f
...
@@ 99,7 +99,7 @@ Separating logic specific tactics
...
@@ 99,7 +99,7 @@ Separating logic specific tactics
+
`%`
: repeatedly frame hypotheses from the Coq context.
+
`%`
: repeatedly frame hypotheses from the Coq context.
+
`#`
: repeatedly frame hypotheses from the persistent context.
+
`#`
: repeatedly frame hypotheses from the persistent context.
+
`
★
`
: frame as much of the spatial context as possible.
+
`
∗
`
: frame as much of the spatial context as possible.
Notice that framing spatial hypotheses makes them disappear, but framing Coq
Notice that framing spatial hypotheses makes them disappear, but framing Coq
or persistent hypotheses does not make them disappear.
or persistent hypotheses does not make them disappear.
...
@@ 107,7 +107,7 @@ Separating logic specific tactics
...
@@ 107,7 +107,7 @@ Separating logic specific tactics
This tactic finishes the goal in case everything in the conclusion has been
This tactic finishes the goal in case everything in the conclusion has been
framed.
framed.

`iCombine "H1" "H2" as "H"`
: turns
`H1 : P1`
and
`H2 : P2`
into

`iCombine "H1" "H2" as "H"`
: turns
`H1 : P1`
and
`H2 : P2`
into
`H : P1
★
P2`
.
`H : P1
∗
P2`
.
Modalities
Modalities


...
@@ 173,7 +173,7 @@ following _selection patterns_:
...
@@ 173,7 +173,7 @@ following _selection patterns_:

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

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

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

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

`#`
: select the entire persistent context.

`#`
: select the entire persistent context.

`
★
`
: select the entire spatial context.

`
∗
`
: select the entire spatial context.
Introduction patterns
Introduction patterns
=====================
=====================
...
@@ 208,7 +208,7 @@ appear at the top level:
...
@@ 208,7 +208,7 @@ appear at the top level:
For example, given:
For example, given:
∀ x, x = 0 ⊢ □ (P → False ∨ □ (Q ∧ ▷ R) 
★
P
★
▷ (R
★
Q ∧ x = pred 2)).
∀ x, x = 0 ⊢ □ (P → False ∨ □ (Q ∧ ▷ R) 
∗
P
∗
▷ (R
∗
Q ∧ x = pred 2)).
You can write
You can write
...
@@ 222,14 +222,14 @@ which results in:
...
@@ 222,14 +222,14 @@ which results in:
"HQ" : Q
"HQ" : Q
"HR" : R
"HR" : R
□
□
R
★
Q ∧ x = 1
R
∗
Q ∧ x = 1
Specialization patterns
Specialization patterns
=======================
=======================
Since we are reasoning in a spatial logic, when eliminating a lemma or
Since we are reasoning in a spatial logic, when eliminating a lemma or
hypothesis of type
``P_0 
★
... 
★
P_n 
★
R``
, one has to specify how the
hypothesis of type
``P_0 
∗
... 
∗
P_n 
∗
R``
, one has to specify how the
hypotheses are split between the premises. The proof mode supports the following
hypotheses are split between the premises. The proof mode supports the following
_specification patterns_
to express splitting of hypotheses:
_specification patterns_
to express splitting of hypotheses:
...
@@ 239,22 +239,22 @@ _specification patterns_ to express splitting of hypotheses:
...
@@ 239,22 +239,22 @@ _specification patterns_ to express splitting of hypotheses:
all persistent hypotheses. The spatial hypotheses among
`H1 ... Hn`
will be
all persistent hypotheses. The spatial hypotheses among
`H1 ... Hn`
will be
consumed. Hypotheses may be prefixed with a
`$`
, which results in them being
consumed. Hypotheses may be prefixed with a
`$`
, which results in them being
framed in the generated goal.
framed in the generated goal.

`[H1 ... Hn]`
: negated form of the above pattern.

`[H1 ... Hn]`
: negated form of the above pattern.

`>[H1 ... Hn]`
: same as the above pattern, but can only be used if the goal

`>[H1 ... Hn]`
: same as the above pattern, but can only be used if the goal
is a modality, in which case the modality will be kept in the generated goal
is a modality, in which case the modality will be kept in the generated goal
for the premise will be wrapped into the modality.
for the premise will be wrapped into the modality.

`>[H1 ... Hn]`
: negated form of the above pattern.

`>[H1 ... Hn]`
: negated form of the above pattern.

`>`
: shorthand for
`>[]`
(typically used for the last premise of an applied

`>`
: shorthand for
`>[]`
(typically used for the last premise of an applied
lemma).
lemma).

`[#]`
: This pattern can be used when eliminating
`P 
★
Q`
with
`P`

`[#]`
: This pattern can be used when eliminating
`P 
∗
Q`
with
`P`
persistent. Using this pattern, all hypotheses are available in the goal for
persistent. Using this pattern, all hypotheses are available in the goal for
`P`
, as well the remaining goal.
`P`
, as well the remaining goal.

`[%]`
: This pattern can be used when eliminating
`P 
★
Q`
when
`P`
is pure.

`[%]`
: This pattern can be used when eliminating
`P 
∗
Q`
when
`P`
is pure.
It will generate a Coq goal for
`P`
and does not consume any hypotheses.
It will generate a Coq goal for
`P`
and does not consume any hypotheses.
For example, given:
For example, given:
H : □ P 
★
P 2 
★
x = 0 
★
Q1 ∗ Q2
H : □ P 
∗
P 2 
∗
x = 0 
∗
Q1 ∗ Q2
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