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fbd0f2b1
Commit
fbd0f2b1
authored
Jan 27, 2016
by
Ralf Jung
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unicodify heap_lang
parent
c02ea520
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barrier/heap_lang.v
barrier/heap_lang.v
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barrier/heap_lang.v
View file @
fbd0f2b1
...
...
@@ -30,8 +30,8 @@ Inductive expr :=
|
App
(
e1
e2
:
expr
)
(* Embedding of Coq values and operations *)
|
Lit
{
T
:
Type
}
(
t
:
T
)
(* arbitrary Coq values become literals *)
|
Op1
{
T1
To
:
Type
}
(
f
:
T1
->
To
)
(
e1
:
expr
)
|
Op2
{
T1
T2
To
:
Type
}
(
f
:
T1
->
T2
->
To
)
(
e1
:
expr
)
(
e2
:
expr
)
|
Op1
{
T1
To
:
Type
}
(
f
:
T1
→
To
)
(
e1
:
expr
)
|
Op2
{
T1
T2
To
:
Type
}
(
f
:
T1
→
T2
→
To
)
(
e1
:
expr
)
(
e2
:
expr
)
(* Products *)
|
Pair
(
e1
e2
:
expr
)
|
Fst
(
e
:
expr
)
...
...
@@ -106,7 +106,7 @@ Qed.
Section
e2e
.
(* To get local tactics. *)
Lemma
e2e
e
v
:
e2v
e
=
Some
v
->
v2e
v
=
e
.
e2v
e
=
Some
v
→
v2e
v
=
e
.
Proof
.
Ltac
case0
:
=
case
=><-
;
simpl
;
eauto
using
f_equal
,
f_equal2
.
Ltac
case1
e1
:
=
destruct
(
e2v
e1
)
;
simpl
;
[|
discriminate
]
;
...
...
@@ -121,7 +121,7 @@ Qed.
End
e2e
.
Lemma
v2e_inj
v1
v2
:
v2e
v1
=
v2e
v2
->
v1
=
v2
.
v2e
v1
=
v2e
v2
→
v1
=
v2
.
Proof
.
revert
v2
;
induction
v1
=>
v2
;
destruct
v2
;
simpl
;
try
discriminate
;
first
[
case_depeq1
|
case
]
;
eauto
using
f_equal
,
f_equal2
.
...
...
@@ -215,27 +215,27 @@ Proof.
Qed
.
Lemma
fill_inj_r
K
e1
e2
:
fill
K
e1
=
fill
K
e2
->
e1
=
e2
.
fill
K
e1
=
fill
K
e2
→
e1
=
e2
.
Proof
.
revert
e1
e2
;
induction
K
=>
el
er
/=
;
(
move
=><-
;
reflexivity
)
||
(
case
=>
/
IHK
<-
;
reflexivity
).
Qed
.
Lemma
fill_value
K
e
v'
:
e2v
(
fill
K
e
)
=
Some
v'
->
is_Some
(
e2v
e
).
e2v
(
fill
K
e
)
=
Some
v'
→
is_Some
(
e2v
e
).
Proof
.
revert
v'
;
induction
K
=>
v'
/=
;
try
discriminate
;
try
destruct
(
e2v
(
fill
K
e
))
;
rewrite
?v2v
;
eauto
.
Qed
.
Lemma
fill_not_value
e
K
:
e2v
e
=
None
->
e2v
(
fill
K
e
)
=
None
.
e2v
e
=
None
→
e2v
(
fill
K
e
)
=
None
.
Proof
.
intros
Hnval
.
induction
K
=>/=
;
by
rewrite
?v2v
/=
?IHK
/=.
Qed
.
Lemma
fill_not_value2
e
K
v
:
e2v
e
=
None
->
e2v
(
fill
K
e
)
=
Some
v
->
False
.
e2v
e
=
None
→
e2v
(
fill
K
e
)
=
Some
v
->
False
.
Proof
.
intros
Hnval
Hval
.
erewrite
fill_not_value
in
Hval
by
assumption
.
discriminate
.
Qed
.
...
...
@@ -309,10 +309,10 @@ Section step_by_value.
sub-context of K' - in other words, e also contains the reducible
expression *)
Lemma
step_by_value
{
K
K'
e
e'
σ
}
:
fill
K
e
=
fill
K'
e'
->
reducible
e'
σ
->
e2v
e
=
None
->
exists
K''
,
K'
=
comp_ctx
K
K''
.
fill
K
e
=
fill
K'
e'
→
reducible
e'
σ
→
e2v
e
=
None
→
∃
K''
,
K'
=
comp_ctx
K
K''
.
Proof
.
Ltac
bad_fill
:
=
intros
;
exfalso
;
subst
;
(
eapply
values_stuck
;
eassumption
)
||
...
...
@@ -375,8 +375,8 @@ Definition atomic (e: expr) :=
match
e
with
|
Alloc
e
=>
is_Some
(
e2v
e
)
|
Load
e
=>
is_Some
(
e2v
e
)
|
Store
e1
e2
=>
is_Some
(
e2v
e1
)
/\
is_Some
(
e2v
e2
)
|
Cas
e0
e1
e2
=>
is_Some
(
e2v
e0
)
/\
is_Some
(
e2v
e1
)
/\
is_Some
(
e2v
e2
)
|
Store
e1
e2
=>
is_Some
(
e2v
e1
)
∧
is_Some
(
e2v
e2
)
|
Cas
e0
e1
e2
=>
is_Some
(
e2v
e0
)
∧
is_Some
(
e2v
e1
)
∧
is_Some
(
e2v
e2
)
|
_
=>
False
end
.
...
...
@@ -387,8 +387,8 @@ Proof.
Qed
.
Lemma
atomic_step
e1
σ
1 e2
σ
2
ef
:
atomic
e1
->
prim_step
e1
σ
1 e2
σ
2
ef
->
atomic
e1
→
prim_step
e1
σ
1 e2
σ
2
ef
→
is_Some
(
e2v
e2
).
Proof
.
destruct
e1
;
simpl
;
intros
Hatomic
Hstep
;
inversion
Hstep
;
...
...
@@ -397,8 +397,8 @@ Qed.
(* Atomics must not contain evaluation positions. *)
Lemma
atomic_fill
e
K
:
atomic
(
fill
K
e
)
->
e2v
e
=
None
->
atomic
(
fill
K
e
)
→
e2v
e
=
None
→
K
=
EmptyCtx
.
Proof
.
destruct
K
;
simpl
;
first
reflexivity
;
unfold
is_Some
;
intros
Hatomic
Hnval
;
...
...
@@ -412,8 +412,8 @@ Qed.
Section
Language
.
Definition
ectx_step
e1
σ
1 e2
σ
2
(
ef
:
option
expr
)
:
=
exists
K
e1'
e2'
,
e1
=
fill
K
e1'
/\
e2
=
fill
K
e2'
/\
prim_step
e1'
σ
1 e2
'
σ
2
ef
.
∃
K
e1'
e2'
,
e1
=
fill
K
e1'
∧
e2
=
fill
K
e2'
∧
prim_step
e1'
σ
1 e2
'
σ
2
ef
.
Global
Program
Instance
heap_lang
:
Language
expr
value
state
:
=
{|
of_val
:
=
v2e
;
...
...
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