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PierreMarie Pédrot
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1c14ae6f
Commit
1c14ae6f
authored
Mar 07, 2017
by
Robbert Krebbers
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Update star symbol in ProofMode docs.
parent
f870cdaf
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ProofMode.md
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1c14ae6f
...
...
@@ 99,7 +99,7 @@ Separating logic specific tactics
+
`%`
: repeatedly frame hypotheses from the Coq 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
or persistent hypotheses does not make them disappear.
...
...
@@ 107,7 +107,7 @@ Separating logic specific tactics
This tactic finishes the goal in case everything in the conclusion has been
framed.

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

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

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

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

`#`
: select the entire persistent context.

`
★
`
: select the entire spatial context.

`
∗
`
: select the entire spatial context.
Introduction patterns
=====================
...
...
@@ 208,7 +208,7 @@ appear at the top level:
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
...
...
@@ 222,14 +222,14 @@ which results in:
"HQ" : Q
"HR" : R
□
R
★
Q ∧ x = 1
R
∗
Q ∧ x = 1
Specialization patterns
=======================
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
_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
consumed. Hypotheses may be prefixed with a
`$`
, which results in them being
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
is a modality, in which case the modality will be kept in the generated goal
for the premise will be wrapped into the modality.

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

`>`
: shorthand for
`>[]`
(typically used for the last premise of an applied
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
`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.
For example, given:
H : □ P 
★
P 2 
★
x = 0 
★
Q1 ∗ Q2
H : □ P 
∗
P 2 
∗
x = 0 
∗
Q1 ∗ Q2
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