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Rodolphe Lepigre
Iris
Commits
876e9848
Commit
876e9848
authored
Jun 20, 2014
by
Ralf Jung
Browse files
update to the current set of axioms
parent
97c0889d
Changes
3
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core_lang.v
View file @
876e9848
...
...
@@ -40,6 +40,8 @@ Module Type CORE_LANG.
K1
[[
e
]]
=
K2
[[
e
]]
->
K1
=
K2
.
Axiom
fill_inj2
:
forall
K
e1
e2
,
K
[[
e1
]]
=
K
[[
e2
]]
->
e1
=
e2
.
Axiom
fill_noinv
:
forall
K1
K2
,
(* Interestingly, it seems impossible to derive this *)
K1
∘
K2
=
ε
->
K1
=
ε
/\
K2
=
ε
.
Axiom
fill_value
:
forall
K
e
,
is_value
(
K
[[
e
]])
->
K
=
ε
.
...
...
@@ -56,10 +58,14 @@ Module Type CORE_LANG.
(** The primitive atomic stepping relation **)
Parameter
prim_step
:
prim_cfg
->
prim_cfg
->
Prop
.
Definition
reducible
e
:
Prop
:
=
exists
sigma
cfg'
,
prim_step
(
e
,
sigma
)
cfg'
.
Definition
stuck
(
e
:
expr
)
:
Prop
:
=
forall
σ
c
K
e'
,
forall
K
e'
,
e
=
K
[[
e'
]]
->
~
prim_step
(
e'
,
σ
)
c
.
~
reducible
e'
.
Axiom
fork_stuck
:
forall
K
e
,
stuck
(
K
[[
fork
e
]]).
...
...
@@ -71,9 +77,9 @@ Module Type CORE_LANG.
sub-context of K' - in other words, e also contains the reducible
expression *)
Axiom
step_by_value
:
forall
K
K'
e
e'
sigma
cfg
,
forall
K
K'
e
e'
,
K
[[
e
]]
=
K'
[[
e'
]]
->
prim_step
(
e'
,
sigma
)
cfg
->
reducible
e'
->
~
is_value
e
->
exists
K''
,
K'
=
K
∘
K''
.
(* Similar to above, buth with a fork instead of a reducible
...
...
@@ -87,13 +93,13 @@ Module Type CORE_LANG.
(** Atomic expressions **)
Parameter
atomic
:
expr
->
Prop
.
Axiom
atomic_not_stuck
:
forall
e
,
atomic
e
->
~stuck
e
.
Axiom
atomic_reducible
:
forall
e
,
atomic
e
->
reducible
e
.
Axiom
atomic_step
:
forall
eR
K
e
e'
σ
σ
'
,
atomic
eR
->
eR
=
K
[[
e
]]
->
prim_step
(
e
,
σ
)
(
e'
,
σ
'
)
->
K
=
ε
/\
is_value
e'
.
Axiom
atomic_step
:
forall
e
σ
e'
σ
'
,
atomic
e
->
prim_step
(
e
,
σ
)
(
e'
,
σ
'
)
->
is_value
e'
.
End
CORE_LANG
.
iris.v
View file @
876e9848
...
...
@@ -589,7 +589,7 @@ Module Iris (RL : PCM_T) (C : CORE_LANG).
-
intros
w
n
r
;
apply
Hp
;
exact
I
.
Qed
.
Lemma
vsFalse
m1
m2
:
Lemma
vsFalse
m1
m2
:
(* TODO move to derived rules *)
valid
(
vs
m1
m2
⊥
⊥
).
Proof
.
rewrite
valid_iff
,
box_top
.
...
...
@@ -745,7 +745,7 @@ Qed.
(* XXX missing statements:
GhostUpd,
VSTimeless *)
(* XXX missing statements: VSTimeless *)
End
ViewShiftProps
.
...
...
@@ -1163,7 +1163,7 @@ Qed.
Qed
.
(** Framing **)
(* TODO: mask framing *)
Lemma
htFrame
m
P
R
e
φ
:
ht
m
P
e
φ
⊑
ht
m
(
P
*
R
)
e
(
lift_bin
sc
φ
(
umconst
R
)).
Proof
.
...
...
@@ -1270,8 +1270,6 @@ Qed.
eapply
fork_not_value
;
eassumption
.
Qed
.
(** Not stated: the Shift (timeless) rule *)
End
HoareTripleProperties
.
End
Iris
.
lang.v
View file @
876e9848
...
...
@@ -89,7 +89,48 @@ Module Lang (C : CORE_LANG).
apply
comp_ctx_inj1
in
HEq
;
congruence
.
Qed
.
(* atomic expressions *)
(* Lemmas about expressions *)
Lemma
reducible_not_value
e
:
reducible
e
->
~is_value
e
.
Proof
.
intros
H_red
H_val
.
eapply
values_stuck
;
try
eassumption
.
now
erewrite
fill_empty
.
Qed
.
Lemma
step_same_ctx
:
forall
K
K'
e
e'
,
fill
K
e
=
fill
K'
e'
->
reducible
e
->
reducible
e'
->
K
=
K'
.
Proof
.
intros
K
K'
e
e'
H_fill
H_red
H_red'
.
edestruct
(
step_by_value
K
K'
e
e'
)
as
[
K''
H_K''
].
-
assumption
.
-
assumption
.
-
now
apply
reducible_not_value
.
-
edestruct
(
step_by_value
K'
K
e'
e
)
as
[
K'''
H_K'''
].
+
now
symmetry
.
+
assumption
.
+
now
apply
reducible_not_value
.
+
subst
K
.
rewrite
comp_ctx_assoc
in
H_K''
.
assert
(
H_emp
:
=
comp_ctx_neut_emp_r
_
_
H_K''
).
apply
fill_noinv
in
H_emp
.
destruct
H_emp
as
[
H_K'''_emp
H_K''_emp
].
subst
K''
K'''
.
now
rewrite
comp_ctx_emp_r
.
Qed
.
Lemma
atomic_not_stuck
e
:
atomic
e
->
~stuck
e
.
Proof
.
intros
H_atomic
H_stuck
.
eapply
H_stuck
.
-
now
erewrite
fill_empty
.
-
now
eapply
atomic_reducible
.
Qed
.
Lemma
fork_not_atomic
K
e
:
~atomic
(
K
[[
fork
e
]]).
Proof
.
...
...
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