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AVA
FloVer
Commits
47a6769d
Commit
47a6769d
authored
Feb 22, 2019
by
Joachim Bard
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little work on inference
parent
a15083fd
Changes
2
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2 changed files
with
19 additions
and
31 deletions
+19
-31
coq/IntervalInference.v
coq/IntervalInference.v
+18
-30
coq/RealRangeArith.v
coq/RealRangeArith.v
+1
-1
No files found.
coq/IntervalInference.v
View file @
47a6769d
...
...
@@ -16,10 +16,10 @@ From Flover
From
Flover
Require
Export
IntervalArithQ
IntervalArith
ssaPrgs
RealRangeArith
.
Fixpoint
inferIntervalbounds
(
e
:
expr
Q
)
(
A
:
FloverMap
.
t
intv
)
(
*
(
P
:
FloverMap
.
t
intv
)
*
)
:
(
result
intv
*
FloverMap
.
t
intv
)
:=
Fixpoint
inferIntervalbounds
(
e
:
expr
Q
)
(
A
:
analysisResult
)
(
*
(
P
:
FloverMap
.
t
intv
)
*
)
:
(
result
intv
*
analysisResult
)
:=
match
FloverMap
.
find
e
A
with
|
Some
iv
=>
(
Succes
iv
,
A
)
|
Some
(
iv
,
_
)
=>
(
Succes
iv
,
A
)
|
None
=>
let
(
rIv
,
newA
)
:=
match
e
with
...
...
@@ -73,12 +73,12 @@ Fixpoint inferIntervalbounds (e:expr Q) (A: FloverMap.t intv) (* (P: FloverMap.t
|
Downcast
_
f1
=>
inferIntervalbounds
f1
A
|
Let
_
x
f1
f2
=>
match
inferIntervalbounds
f1
A
with
|
(
Succes
iv1
,
A1
)
=>
inferIntervalbounds
f2
(
FloverMap
.
add
(
Var
Q
x
)
iv1
A1
)
|
(
Succes
iv1
,
A1
)
=>
inferIntervalbounds
f2
(
FloverMap
.
add
(
Var
Q
x
)
(
iv1
,
0
)
A1
)
|
fail1
=>
fail1
end
end
in
match
rIv
with
|
Succes
iv
=>
(
rIv
,
FloverMap
.
add
e
iv
newA
)
|
Succes
iv
=>
(
rIv
,
FloverMap
.
add
e
(
iv
,
0
)
newA
)
|
failInfer
=>
(
failInfer
,
newA
)
end
end
.
...
...
@@ -95,38 +95,25 @@ Proof.
Qed
.
*
)
Theorem
inferIntervalbounds_sound
(
f
:
expr
Q
)
(
A
newA
:
FloverMap
.
t
intv
)
iv
Theorem
inferIntervalbounds_sound
(
f
:
expr
Q
)
(
A
newA
:
analysisResult
)
iv
inVars
outVars
(
E
:
env
)
Gamma
:
ssa
f
inVars
outVars
->
inferIntervalbounds
f
A
=
(
Succes
iv
,
newA
)
->
(
forall
e
iv
,
FloverMap
.
find
e
A
=
Some
iv
->
exists
v
,
eval_expr
E
(
toRTMap
(
toRExpMap
Gamma
))
DeltaMapR
(
toREval
(
toRExp
e
))
v
REAL
/
\
(
Q2R
(
fst
iv
)
<=
v
<=
Q2R
(
snd
iv
))
%
R
)
->
(
forall
e
r
,
FloverMap
.
find
e
A
=
Some
r
->
validRanges
e
A
E
(
toRTMap
(
toRExpMap
Gamma
)))
->
validTypes
f
Gamma
->
exists
(
iv
:
intv
)
(
vR
:
R
),
FloverMap
.
find
f
newA
=
Some
iv
/
\
eval_expr
E
(
toRTMap
(
toRExpMap
Gamma
))
DeltaMapR
(
toREval
(
toRExp
f
))
vR
REAL
/
\
(
Q2R
(
fst
iv
)
<=
vR
<=
Q2R
(
snd
iv
))
%
R
.
(
*
validRanges
f
newA
E
(
toRTMap
(
toRExpMap
Gamma
)).
*
)
validRanges
f
newA
E
(
toRTMap
(
toRExpMap
Gamma
)).
Proof
.
induction
f
in
E
,
inVars
,
A
,
newA
|-
*
;
intros
ssa_f
infer_success
init_valid
valid_types
;
cbn
in
*
.
-
Flover_compute
.
inversion
infer_success
;
subst
.
edestruct
init_valid
as
[
v
[
H1
H2
]];
eauto
.
-
Flover_compute
.
+
inversion
infer_success
;
subst
.
edestruct
init_valid
as
[
vR
[
H1
H2
]];
eauto
.
+
inversion
infer_success
;
subst
.
exists
(
v
,
v
),
(
Q2R
v
);
repeat
split
;
try
(
cbn
;
lra
).
*
rewrite
FloverMapFacts
.
P
.
F
.
add_o
.
admit
.
*
eapply
Const_dist
'
;
eauto
;
try
reflexivity
.
cbn
.
rewrite
Rabs_R0
.
lra
.
-
Flover_compute
.
+
inversion
infer_success
;
subst
.
edestruct
init_valid
as
[
vR
[
H1
H2
]];
eauto
.
+
destruct
r
;
inversion
infer_success
;
subst
.
unfold
inferIntervalbounds
in
infer_success
;
Flover_compute
;
inversion
infer_success
;
subst
;
try
eapply
init_valid
;
eauto
.
-
split
;
auto
.
exists
(
v
,
v
),
0
,
(
Q2R
v
);
repeat
split
;
try
(
cbn
;
lra
).
+
rewrite
FloverMapFacts
.
P
.
F
.
add_eq_o
;
auto
.
admit
.
+
eapply
Const_dist
'
;
eauto
;
try
reflexivity
.
cbn
.
rewrite
Rabs_R0
.
lra
.
-
destruct
r
;
inversion
infer_success
;
subst
.
(
*
-
destruct
(
NatSet
.
mem
n
dVars
)
eqn
:?
;
cbn
in
*
;
split
;
auto
.
+
destruct
(
valid_definedVars
n
)
...
...
@@ -415,6 +402,7 @@ Proof.
(
*
-
Flover_compute
.
congruence
.
*
)
Qed
.
*
)
Abort
.
(
*
Theorem
validIntervalboundsCmd_sound
(
f
:
cmd
Q
)
(
A
:
analysisResult
)
:
...
...
coq/RealRangeArith.v
View file @
47a6769d
...
...
@@ -497,4 +497,4 @@ Proof.
simpl
.
rewrite
!
freeVars_toREval_toRExp_compat
;
auto
.
*
)
A
dmitted
.
A
bort
.
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