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William Mansky
Iris
Commits
674fc37e
Commit
674fc37e
authored
8 years ago
by
Robbert Krebbers
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Make some iTactics local that are meant to be internal.
parent
d17a2e06
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proofmode/tactics.v
+26
-23
26 additions, 23 deletions
proofmode/tactics.v
with
26 additions
and
23 deletions
proofmode/tactics.v
+
26
−
23
View file @
674fc37e
...
...
@@ -17,17 +17,18 @@ Declare Reduction env_cbv := cbv [
Ltac
env_cbv
:=
match
goal
with
|
-
?u
=>
let
v
:=
eval
env_cbv
in
u
in
change
v
end
.
(** * Misc *)
Ltac
iFresh
:=
lazymatch
goal
with
|
-
of_envs
?Δ
⊢
_
=>
match
goal
with
|
_
=>
eval
vm_compute
in
(
fresh_string_of_set
"~"
(
dom
stringset
Δ
))
(* [vm_compute fails] if [Δ] contains evars, so fall-back to [cbv] *)
|
_
=>
eval
cbv
in
(
fresh_string_of_set
"~"
(
dom
stringset
Δ
))
end
|
_
=>
constr
:
"~"
end
.
(** * Misc *)
Tactic
Notation
"iTypeOf"
constr
(
H
)
tactic
(
tac
):=
let
Δ
:=
match
goal
with
|
-
of_envs
?Δ
⊢
_
=>
Δ
end
in
match
eval
env_cbv
in
(
envs_lookup
H
Δ
)
with
...
...
@@ -99,7 +100,7 @@ Tactic Notation "iAssumption" :=
Tactic
Notation
"iExFalso"
:=
apply
tac_ex_falso
.
(** * Pure introduction *)
Tactic
Notation
"iIntro"
"{"
simple_intropattern
(
x
)
"}"
:=
Local
Tactic
Notation
"iIntro"
"{"
simple_intropattern
(
x
)
"}"
:=
lazymatch
goal
with
|
|
-
_
⊢
(
∀
_,
_)
=>
apply
tac_forall_intro
;
intros
x
|
|
-
_
⊢
(
?P
→
_)
=>
...
...
@@ -112,7 +113,7 @@ Tactic Notation "iIntro" "{" simple_intropattern(x) "}" :=
end
.
(** * Introduction *)
Tactic
Notation
"iIntro"
constr
(
H
)
:=
Local
Tactic
Notation
"iIntro"
constr
(
H
)
:=
lazymatch
goal
with
|
|
-
_
⊢
(
?Q
→
_)
=>
eapply
tac_impl_intro
with
_
H
;
(* (i:=H) *)
...
...
@@ -125,7 +126,7 @@ Tactic Notation "iIntro" constr(H) :=
|
_
=>
fail
"iIntro: nothing to introduce"
end
.
Tactic
Notation
"iIntro"
"#"
constr
(
H
)
:=
Local
Tactic
Notation
"iIntro"
"#"
constr
(
H
)
:=
lazymatch
goal
with
|
|
-
_
⊢
(
?P
→
_)
=>
eapply
tac_impl_intro_persistent
with
_
H
_;
(* (i:=H) *)
...
...
@@ -165,7 +166,7 @@ Tactic Notation "iPure" constr(H) := iPure H as ?.
Tactic
Notation
"iPureIntro"
:=
apply
uPred
.
const_intro
.
(** * Specialize *)
Tactic
Notation
"iForallSpecialize"
constr
(
H
)
open_constr
(
x
)
:=
Local
Tactic
Notation
"iForallSpecialize"
constr
(
H
)
open_constr
(
x
)
:=
eapply
tac_forall_specialize
with
_
H
_
_
x
;
(* (i:=H) (a:=x) *)
[
env_cbv
;
reflexivity
||
fail
"iSpecialize:"
H
"not found"
|
env_cbv
;
reflexivity
|]
.
...
...
@@ -374,14 +375,14 @@ Tactic Notation "iApply" open_constr (H) "{" open_constr(x1) open_constr(x2)
(** * Revert *)
Tactic
Notation
"iRevert"
"★"
:=
eapply
tac_revert_spatial
;
env_cbv
.
Tactic
Notation
"iForallRevert"
ident
(
x
)
:=
Local
Tactic
Notation
"iForallRevert"
ident
(
x
)
:=
let
A
:=
type
of
x
in
lazymatch
type
of
A
with
|
Prop
=>
revert
x
;
apply
tac_pure_revert
|
_
=>
revert
x
;
apply
tac_forall_revert
end
||
fail
"iRevert: cannot revert"
x
.
Tactic
Notation
"iImplRevert"
constr
(
H
)
:=
Local
Tactic
Notation
"iImplRevert"
constr
(
H
)
:=
eapply
tac_revert
with
_
H
_
_;
(* (i:=H) *)
[
env_cbv
;
reflexivity
||
fail
"iRevert:"
H
"not found"
|
env_cbv
]
.
...
...
@@ -444,7 +445,7 @@ Tactic Notation "iRight" :=
[
let
P
:=
match
goal
with
|
-
OrSplit
?P
_
_
=>
P
end
in
apply
_
||
fail
"iRight:"
P
"not a disjunction"
|]
.
Tactic
Notation
"iOrDestruct"
constr
(
H
)
"as"
constr
(
H1
)
constr
(
H2
)
:=
Local
Tactic
Notation
"iOrDestruct"
constr
(
H
)
"as"
constr
(
H1
)
constr
(
H2
)
:=
eapply
tac_or_destruct
with
_
_
H
_
H1
H2
_
_
_;
(* (i:=H) (j1:=H1) (j2:=H2) *)
[
env_cbv
;
reflexivity
||
fail
"iOrDestruct:"
H
"not found"
|
let
P
:=
match
goal
with
|
-
OrDestruct
?P
_
_
=>
P
end
in
...
...
@@ -474,7 +475,7 @@ Tactic Notation "iSplitR" constr(Hs) :=
Tactic
Notation
"iSplitL"
:=
iSplitR
""
.
Tactic
Notation
"iSplitR"
:=
iSplitL
""
.
Tactic
Notation
"iSepDestruct"
constr
(
H
)
"as"
constr
(
H1
)
constr
(
H2
)
:=
Local
Tactic
Notation
"iSepDestruct"
constr
(
H
)
"as"
constr
(
H1
)
constr
(
H2
)
:=
eapply
tac_sep_destruct
with
_
H
_
H1
H2
_
_
_;
(* (i:=H) (j1:=H1) (j2:=H2) *)
[
env_cbv
;
reflexivity
||
fail
"iSepDestruct:"
H
"not found"
|
let
P
:=
match
goal
with
|
-
SepDestruct
_
?P
_
_
=>
P
end
in
...
...
@@ -531,7 +532,7 @@ Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) "," uconstr(x3) ","
uconstr
(
x8
)
:=
iExists
x1
;
iExists
x2
,
x3
,
x4
,
x5
,
x6
,
x7
,
x8
.
Tactic
Notation
"iExistDestruct"
constr
(
H
)
"as"
ident
(
x
)
constr
(
Hx
)
:=
Local
Tactic
Notation
"iExistDestruct"
constr
(
H
)
"as"
ident
(
x
)
constr
(
Hx
)
:=
eapply
tac_exist_destruct
with
H
_
Hx
_
_;
(* (i:=H) (j:=Hx) *)
[
env_cbv
;
reflexivity
||
fail
"iExistDestruct:"
H
"not found"
|
let
P
:=
match
goal
with
|
-
ExistDestruct
?P
_
=>
P
end
in
...
...
@@ -540,7 +541,7 @@ Tactic Notation "iExistDestruct" constr(H) "as" ident(x) constr(Hx) :=
[
env_cbv
;
reflexivity
||
fail
"iExistDestruct:"
Hx
"not fresh"
|]
.
(** * Destruct tactic *)
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
constr
(
pat
)
:=
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
constr
(
pat
)
:=
let
rec
go
Hz
pat
:=
lazymatch
pat
with
|
IAnom
=>
idtac
...
...
@@ -557,33 +558,33 @@ Tactic Notation "iDestructHyp" constr(H) "as" constr(pat) :=
end
in
let
pat
:=
intro_pat
.
parse_one
pat
in
go
H
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
"}"
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
@
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
x3
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
x3
x4
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
simple_intropattern
(
x5
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
x3
x4
x5
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
simple_intropattern
(
x5
)
simple_intropattern
(
x6
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
x3
x4
x5
x6
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
simple_intropattern
(
x5
)
simple_intropattern
(
x6
)
simple_intropattern
(
x7
)
"}"
constr
(
pat
)
:=
iExistDestruct
H
as
x1
H
;
iDestructHyp
H
as
{
x2
x3
x4
x5
x6
x7
}
pat
.
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
Local
Tactic
Notation
"iDestructHyp"
constr
(
H
)
"as"
"{"
simple_intropattern
(
x1
)
simple_intropattern
(
x2
)
simple_intropattern
(
x3
)
simple_intropattern
(
x4
)
simple_intropattern
(
x5
)
simple_intropattern
(
x6
)
simple_intropattern
(
x7
)
simple_intropattern
(
x8
)
"}"
constr
(
pat
)
:=
...
...
@@ -765,7 +766,7 @@ Tactic Notation "iIntros" "{" simple_intropattern(x1) simple_intropattern(x2)
(* This is pretty ugly, but without Ltac support for manipulating lists of
idents I do not know how to do this better. *)
Ltac
iLöbCore
IH
tac_before
tac_after
:=
Local
Ltac
iLöbCore
IH
tac_before
tac_after
:=
match
goal
with
|
|
-
of_envs
?Δ
⊢
_
=>
let
Hs
:=
constr
:(
rev
(
env_dom_list
(
env_spatial
Δ
)))
in
...
...
@@ -824,24 +825,25 @@ Tactic Notation "iAssert" constr(Q) "as" constr(pat) :=
iAssert
Q
as
pat
with
"[]"
.
(** * Rewrite *)
Ltac
iRewriteFindPred
:=
Local
Ltac
iRewriteFindPred
:=
match
goal
with
|
|
-
_
⊣⊢
?Φ
?x
=>
generalize
x
;
match
goal
with
|
-
(
∀
y
,
@
?Ψ
y
⊣⊢
_)
=>
unify
Φ
Ψ
;
reflexivity
end
end
.
Tactic
Notation
"iRewriteCore"
constr
(
lr
)
constr
(
Heq
)
:=
Local
Tactic
Notation
"iRewriteCore"
constr
(
lr
)
constr
(
Heq
)
:=
eapply
(
tac_rewrite
_
Heq
_
_
lr
);
[
env_cbv
;
reflexivity
||
fail
"iRewrite:"
Heq
"not found"
|
let
P
:=
match
goal
with
|
-
?P
⊢
_
=>
P
end
in
reflexivity
||
fail
"iRewrite:"
Heq
":"
P
"not an equality"
|
iRewriteFindPred
|
intros
???
->
;
reflexivity
|
lazy
beta
]
.
Tactic
Notation
"iRewrite"
constr
(
Heq
)
:=
iRewriteCore
false
Heq
.
Tactic
Notation
"iRewrite"
"-"
constr
(
Heq
)
:=
iRewriteCore
true
Heq
.
Tactic
Notation
"iRewriteCore"
constr
(
lr
)
constr
(
Heq
)
"in"
constr
(
H
)
:=
Local
Tactic
Notation
"iRewriteCore"
constr
(
lr
)
constr
(
Heq
)
"in"
constr
(
H
)
:=
eapply
(
tac_rewrite_in
_
Heq
_
_
H
_
_
lr
);
[
env_cbv
;
reflexivity
||
fail
"iRewrite:"
Heq
"not found"
|
env_cbv
;
reflexivity
||
fail
"iRewrite:"
H
"not found"
...
...
@@ -850,6 +852,7 @@ Tactic Notation "iRewriteCore" constr(lr) constr(Heq) "in" constr(H) :=
|
iRewriteFindPred
|
intros
???
->
;
reflexivity
|
env_cbv
;
reflexivity
|
lazy
beta
]
.
Tactic
Notation
"iRewrite"
constr
(
Heq
)
"in"
constr
(
H
)
:=
iRewriteCore
false
Heq
in
H
.
Tactic
Notation
"iRewrite"
"-"
constr
(
Heq
)
"in"
constr
(
H
)
:=
...
...
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