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PierreMarie Pédrot
Iris
Commits
a64bb337
Commit
a64bb337
authored
May 12, 2017
by
Robbert Krebbers
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Have `iInduction x as ...` revert all proofmode hyps involving `x`.
parent
e98e4ccc
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1
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78 additions
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56 deletions
+78
56
theories/proofmode/tactics.v
theories/proofmode/tactics.v
+78
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theories/proofmode/tactics.v
View file @
a64bb337
...
...
@@ 1206,8 +1206,21 @@ Tactic Notation "iPoseProof" open_constr(lem) "as" "(" simple_intropattern(x1)
iPoseProofCore
lem
as
pat
false
(
fun
H
=>
iDestructHyp
H
as
(
x1
x2
x3
x4
x5
x6
x7
x8
)
pat
).
(** * Induction *)
Tactic
Notation
"iInductionCore"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:
=
(* An invocation of [iInduction (x) as pat IH forall (x1...xn) Hs] will
result in the following actions:
 Revert the proofmode hypotheses [Hs]
 Revert all remaining spatial hypotheses and the remaining persistent
hypotheses containing the induction variable [x]
 Revert the pure hypotheses [x1..xn]
 Actuall perform induction
 Introduce thee pure hypotheses [x1..xn]
 Introduce the spatial hypotheses and persistent hypotheses involving [x]
 Introduce the proofmode hypotheses [Hs]
*)
Tactic
Notation
"iInductionCore"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:
=
let
rec
fix_ihs
:
=
lazymatch
goal
with

H
:
coq_tactics
.
of_envs
_
⊢
_

_
=>
...
...
@@ 1220,75 +1233,88 @@ Tactic Notation "iInductionCore" constr(x)
end
in
induction
x
as
pat
;
fix_ihs
.
Ltac
iHypsContaining
x
:
=
let
rec
go
Γ
x
Hs
:
=
lazymatch
Γ
with

Enil
=>
constr
:
(
Hs
)

Esnoc
?
Γ
?H
?Q
=>
match
Q
with

context
[
x
]
=>
go
Γ
x
(
H
::
Hs
)

_
=>
go
Γ
x
Hs
end
end
in
let
Γ
p
:
=
lazymatch
goal
with

of_envs
(
Envs
?
Γ
p
_
)
⊢
_
=>
Γ
p
end
in
let
Γ
s
:
=
lazymatch
goal
with

of_envs
(
Envs
_
?
Γ
s
)
⊢
_
=>
Γ
s
end
in
let
Hs
:
=
go
Γ
p
x
(@
nil
string
)
in
go
Γ
s
x
Hs
.
Tactic
Notation
"iInductionRevert"
constr
(
x
)
constr
(
Hs
)
"with"
tactic
(
tac
)
:
=
iRevertIntros
Hs
with
(
iRevertIntros
"∗"
with
(
let
Hsx
:
=
iHypsContaining
x
in
iRevertIntros
Hsx
with
tac
)
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
:
=
i
RevertIntros
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
i
InductionRevert
x
""
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:
=
iRevertIntros
(
x1
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:
=
iRevertIntros
(
x1
x2
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:
=
iRevertIntros
(
x1
x2
x3
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
)
"
∗
"
with
(
iInductionCore
x
as
a
at
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
p
at
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
"
∗
"
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
x
as
pat
IH
)
)
.
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iInductionCore
x
as
pat
IH
).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
)
Hs
with
(
iInductionCore
x
as
aat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iInductionCore
x
as
pat
IH
)).
Tactic
Notation
"iInduction"
constr
(
x
)
"as"
simple_intropattern
(
pat
)
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
Hs
with
(
iInductionCore
x
as
pat
IH
).
iInductionRevert
x
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iInductionCore
x
as
pat
IH
)).
(** * Löb Induction *)
Tactic
Notation
"iLöbCore"
"as"
constr
(
IH
)
:
=
...
...
@@ 1297,65 +1323,61 @@ Tactic Notation "iLöbCore" "as" constr (IH) :=
[
reflexivity

fail
"iLöb: spatial context not empty, this should not happen"

env_reflexivity

fail
"iLöb:"
IH
"not fresh"
].
Tactic
Notation
"iLöbRevert"
constr
(
Hs
)
"with"
tactic
(
tac
)
:
=
iRevertIntros
Hs
with
(
iRevertIntros
"∗"
with
tac
).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
:
=
iRevert
Intros
"
∗
"
with
(
iL
ö
bCore
as
IH
).
i
L
ö
b
Revert
""
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
:
=
iRevertIntros
(
x1
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
:
=
iRevertIntros
(
x1
x2
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
:
=
iRevertIntros
(
x1
x2
x3
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
:
=
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
"
∗
"
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
""
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iL
ö
bCore
as
IH
)
)
.
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iL
ö
bCore
as
IH
).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
)
""
with
(
iL
ö
bCore
as
IH
)).
Tactic
Notation
"iLöb"
"as"
constr
(
IH
)
"forall"
"("
ident
(
x1
)
ident
(
x2
)
ident
(
x3
)
ident
(
x4
)
ident
(
x5
)
ident
(
x6
)
ident
(
x7
)
ident
(
x8
)
")"
constr
(
Hs
)
:
=
let
Hs
:
=
constr
:
(
Hs
+
:
+
"∗"
)
in
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
Hs
with
(
iL
ö
bCore
as
IH
).
iL
ö
bRevert
Hs
with
(
iRevertIntros
(
x1
x2
x3
x4
x5
x6
x7
x8
)
""
with
(
iL
ö
bCore
as
IH
)).
(** * Assert *)
(* The argument [p] denotes whether [Q] is persistent. It can either be a
...
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