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Simon Spies
Iris
Commits
6e697ccc
Commit
6e697ccc
authored
Dec 09, 2016
by
Robbert Krebbers
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Merge heap_lang/derived with other files.
parent
31818640
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_CoqProject
_CoqProject
+0
-1
heap_lang/derived.v
heap_lang/derived.v
+0
-77
heap_lang/lang.v
heap_lang/lang.v
+10
-0
heap_lang/notation.v
heap_lang/notation.v
+2
-2
heap_lang/rules.v
heap_lang/rules.v
+59
-0
heap_lang/wp_tactics.v
heap_lang/wp_tactics.v
+1
-1
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_CoqProject
View file @
6e697ccc
...
...
@@ -98,7 +98,6 @@ heap_lang/lang.v
heap_lang/tactics.v
heap_lang/wp_tactics.v
heap_lang/rules.v
heap_lang/derived.v
heap_lang/notation.v
heap_lang/lib/spawn.v
heap_lang/lib/par.v
...
...
heap_lang/derived.v
deleted
100644 → 0
View file @
31818640
From
iris
.
heap_lang
Require
Export
rules
.
Import
uPred
.
(** Define some derived forms, and derived lemmas about them. *)
Notation
Lam
x
e
:
=
(
Rec
BAnon
x
e
).
Notation
Let
x
e1
e2
:
=
(
App
(
Lam
x
e2
)
e1
).
Notation
Seq
e1
e2
:
=
(
Let
BAnon
e1
e2
).
Notation
LamV
x
e
:
=
(
RecV
BAnon
x
e
).
Notation
LetCtx
x
e2
:
=
(
AppRCtx
(
LamV
x
e2
)).
Notation
SeqCtx
e2
:
=
(
LetCtx
BAnon
e2
).
Notation
Skip
:
=
(
Seq
(
Lit
LitUnit
)
(
Lit
LitUnit
)).
Notation
Match
e0
x1
e1
x2
e2
:
=
(
Case
e0
(
Lam
x1
e1
)
(
Lam
x2
e2
)).
Section
derived
.
Context
`
{
heapG
Σ
}.
Implicit
Types
P
Q
:
iProp
Σ
.
Implicit
Types
Φ
:
val
→
iProp
Σ
.
(** Proof rules for the sugar *)
Lemma
wp_lam
E
x
elam
e1
e2
Φ
:
e1
=
Lam
x
elam
→
is_Some
(
to_val
e2
)
→
Closed
(
x
:
b
:
[])
elam
→
▷
WP
subst'
x
e2
elam
@
E
{{
Φ
}}
⊢
WP
App
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-(
wp_rec
_
BAnon
)
//.
Qed
.
Lemma
wp_let
E
x
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
(
x
:
b
:
[])
e2
→
▷
WP
subst'
x
e1
e2
@
E
{{
Φ
}}
⊢
WP
Let
x
e1
e2
@
E
{{
Φ
}}.
Proof
.
by
apply
wp_lam
.
Qed
.
Lemma
wp_seq
E
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
[]
e2
→
▷
WP
e2
@
E
{{
Φ
}}
⊢
WP
Seq
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
??.
by
rewrite
-
wp_let
.
Qed
.
Lemma
wp_skip
E
Φ
:
▷
Φ
(
LitV
LitUnit
)
⊢
WP
Skip
@
E
{{
Φ
}}.
Proof
.
rewrite
-
wp_seq
;
last
eauto
.
by
rewrite
-
wp_value
.
Qed
.
Lemma
wp_match_inl
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x1
:
b
:
[])
e1
→
▷
WP
subst'
x1
e0
e1
@
E
{{
Φ
}}
⊢
WP
Match
(
InjL
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inl
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
Lemma
wp_match_inr
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x2
:
b
:
[])
e2
→
▷
WP
subst'
x2
e0
e2
@
E
{{
Φ
}}
⊢
WP
Match
(
InjR
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inr
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
Lemma
wp_le
E
(
n1
n2
:
Z
)
P
Φ
:
(
n1
≤
n2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
n2
<
n1
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
LeOp
(
Lit
(
LitInt
n1
))
(
Lit
(
LitInt
n2
))
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
n1
≤
n2
))
;
by
eauto
with
omega
.
Qed
.
Lemma
wp_lt
E
(
n1
n2
:
Z
)
P
Φ
:
(
n1
<
n2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
n2
≤
n1
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
LtOp
(
Lit
(
LitInt
n1
))
(
Lit
(
LitInt
n2
))
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
n1
<
n2
))
;
by
eauto
with
omega
.
Qed
.
Lemma
wp_eq
E
e1
e2
v1
v2
P
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
(
v1
=
v2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
v1
≠
v2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
EqOp
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
v1
=
v2
))
;
by
eauto
.
Qed
.
End
derived
.
heap_lang/lang.v
View file @
6e697ccc
...
...
@@ -402,3 +402,13 @@ Canonical Structure heap_lang := ectx_lang (heap_lang.expr).
(* Prefer heap_lang names over ectx_language names. *)
Export
heap_lang
.
(** Define some derived forms *)
Notation
Lam
x
e
:
=
(
Rec
BAnon
x
e
).
Notation
Let
x
e1
e2
:
=
(
App
(
Lam
x
e2
)
e1
).
Notation
Seq
e1
e2
:
=
(
Let
BAnon
e1
e2
).
Notation
LamV
x
e
:
=
(
RecV
BAnon
x
e
).
Notation
LetCtx
x
e2
:
=
(
AppRCtx
(
LamV
x
e2
)).
Notation
SeqCtx
e2
:
=
(
LetCtx
BAnon
e2
).
Notation
Skip
:
=
(
Seq
(
Lit
LitUnit
)
(
Lit
LitUnit
)).
Notation
Match
e0
x1
e1
x2
e2
:
=
(
Case
e0
(
Lam
x1
e1
)
(
Lam
x2
e2
)).
heap_lang/notation.v
View file @
6e697ccc
From
iris
.
heap_lang
Require
Ex
port
derived
.
Export
heap_lang
.
From
iris
.
program_logic
Require
Im
port
language
.
From
iris
.
heap_lang
Require
Export
lang
tactics
.
Coercion
LitInt
:
Z
>->
base_lit
.
Coercion
LitBool
:
bool
>->
base_lit
.
...
...
heap_lang/rules.v
View file @
6e697ccc
...
...
@@ -214,4 +214,63 @@ Proof.
iMod
(@
gen_heap_update
with
"Hσ Hl"
)
as
"[$ Hl]"
.
iModIntro
.
iSplit
=>//.
by
iApply
"HΦ"
.
Qed
.
(** Proof rules for derived constructs *)
Lemma
wp_lam
E
x
elam
e1
e2
Φ
:
e1
=
Lam
x
elam
→
is_Some
(
to_val
e2
)
→
Closed
(
x
:
b
:
[])
elam
→
▷
WP
subst'
x
e2
elam
@
E
{{
Φ
}}
⊢
WP
App
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-(
wp_rec
_
BAnon
)
//.
Qed
.
Lemma
wp_let
E
x
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
(
x
:
b
:
[])
e2
→
▷
WP
subst'
x
e1
e2
@
E
{{
Φ
}}
⊢
WP
Let
x
e1
e2
@
E
{{
Φ
}}.
Proof
.
by
apply
wp_lam
.
Qed
.
Lemma
wp_seq
E
e1
e2
Φ
:
is_Some
(
to_val
e1
)
→
Closed
[]
e2
→
▷
WP
e2
@
E
{{
Φ
}}
⊢
WP
Seq
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
??.
by
rewrite
-
wp_let
.
Qed
.
Lemma
wp_skip
E
Φ
:
▷
Φ
(
LitV
LitUnit
)
⊢
WP
Skip
@
E
{{
Φ
}}.
Proof
.
rewrite
-
wp_seq
;
last
eauto
.
by
rewrite
-
wp_value
.
Qed
.
Lemma
wp_match_inl
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x1
:
b
:
[])
e1
→
▷
WP
subst'
x1
e0
e1
@
E
{{
Φ
}}
⊢
WP
Match
(
InjL
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inl
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
Lemma
wp_match_inr
E
e0
x1
e1
x2
e2
Φ
:
is_Some
(
to_val
e0
)
→
Closed
(
x2
:
b
:
[])
e2
→
▷
WP
subst'
x2
e0
e2
@
E
{{
Φ
}}
⊢
WP
Match
(
InjR
e0
)
x1
e1
x2
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
by
rewrite
-
wp_case_inr
//
-[
X
in
_
⊢
X
]
later_intro
-
wp_let
.
Qed
.
Lemma
wp_le
E
(
n1
n2
:
Z
)
P
Φ
:
(
n1
≤
n2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
n2
<
n1
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
LeOp
(
Lit
(
LitInt
n1
))
(
Lit
(
LitInt
n2
))
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
n1
≤
n2
))
;
by
eauto
with
omega
.
Qed
.
Lemma
wp_lt
E
(
n1
n2
:
Z
)
P
Φ
:
(
n1
<
n2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
n2
≤
n1
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
LtOp
(
Lit
(
LitInt
n1
))
(
Lit
(
LitInt
n2
))
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
n1
<
n2
))
;
by
eauto
with
omega
.
Qed
.
Lemma
wp_eq
E
e1
e2
v1
v2
P
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
(
v1
=
v2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
true
)))
→
(
v1
≠
v2
→
P
⊢
▷
Φ
(
LitV
(
LitBool
false
)))
→
P
⊢
WP
BinOp
EqOp
e1
e2
@
E
{{
Φ
}}.
Proof
.
intros
.
rewrite
-
wp_bin_op
//
;
[].
destruct
(
bool_decide_reflect
(
v1
=
v2
))
;
by
eauto
.
Qed
.
End
rules
.
heap_lang/wp_tactics.v
View file @
6e697ccc
From
iris
.
heap_lang
Require
Export
tactics
derived
.
From
iris
.
heap_lang
Require
Export
tactics
rules
.
Import
uPred
.
(** wp-specific helper tactics *)
...
...
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