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3f9e2ea5
Commit
3f9e2ea5
authored
Aug 12, 2019
by
Rodolphe Lepigre
Committed by
Robbert
Aug 12, 2019
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Add some trivial but useful heaplang libraries.
parent
6c620a09
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_CoqProject
_CoqProject
+2
0
theories/heap_lang/lib/arith.v
theories/heap_lang/lib/arith.v
+43
0
theories/heap_lang/lib/diverge.v
theories/heap_lang/lib/diverge.v
+27
0
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_CoqProject
View file @
3f9e2ea5
...
...
@@ 116,6 +116,8 @@ theories/heap_lang/lib/clairvoyant_coin.v
theories/heap_lang/lib/counter.v
theories/heap_lang/lib/atomic_heap.v
theories/heap_lang/lib/increment.v
theories/heap_lang/lib/diverge.v
theories/heap_lang/lib/arith.v
theories/proofmode/base.v
theories/proofmode/tokens.v
theories/proofmode/coq_tactics.v
...
...
theories/heap_lang/lib/arith.v
0 → 100644
View file @
3f9e2ea5
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
heap_lang
Require
Import
proofmode
notation
.
Set
Default
Proof
Using
"Type"
.
(** A library defining binary [minimum] and [maximum] functions, together with
their expected specs. These operations come up often when working manipulating
array indices (checking for bounds). *)
Definition
minimum
:
val
:
=
λ
:
"m"
"n"
,
if
:
"m"
<
"n"
then
"m"
else
"n"
.
Definition
maximum
:
val
:
=
λ
:
"m"
"n"
,
if
:
"m"
<
"n"
then
"n"
else
"m"
.
Lemma
minimum_spec
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
Z
)
:
▷
Φ
#(
m
`
min
`
n
)

∗
WP
minimum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
wp_lam
.
wp_pures
.
case_bool_decide
;
wp_pures
.

rewrite
Z
.
min_l
;
[
done

by
lia
].

rewrite
Z
.
min_r
;
[
done

by
lia
].
Qed
.
Lemma
minimum_spec_nat
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
nat
)
:
▷
Φ
#(
m
`
min
`
n
)%
nat

∗
WP
minimum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
iApply
minimum_spec
.
by
rewrite
Nat2Z
.
inj_min
.
Qed
.
Lemma
maximum_spec
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
Z
)
:
▷
Φ
#(
m
`
max
`
n
)

∗
WP
maximum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
wp_lam
.
wp_pures
.
case_bool_decide
;
wp_pures
.

rewrite
Z
.
max_r
;
[
done

by
lia
].

rewrite
Z
.
max_l
;
[
done

by
lia
].
Qed
.
Lemma
maximum_spec_nat
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
nat
)
:
▷
Φ
#(
m
`
max
`
n
)%
nat

∗
WP
maximum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
iApply
maximum_spec
.
by
rewrite
Nat2Z
.
inj_max
.
Qed
.
theories/heap_lang/lib/diverge.v
0 → 100644
View file @
3f9e2ea5
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
heap_lang
Require
Import
proofmode
notation
.
Set
Default
Proof
Using
"Type"
.
(** This library provides a [diverge] function that goes into an infinite loop
when provided with an (arbitrary) argument value. This function can be used to
let the program diverge in corner cases that one wants to omit in proofs. This
mechanism should be used with care and communicated clearly, obviously.
Note that this mechanism only works when establishing partial correctness with
the ordinary version of weakest preconditions, and not when establishing total
correctness using the total version of weakest preconditions.
A typical application for [diverge] is insertion functions for data structures
having a fixed capacity. In such cases, we can choose divergence instead of an
explicit error handling when the full capacity has already been reached. *)
Definition
diverge
:
val
:
=
rec
:
"diverge"
"v"
:
=
"diverge"
"v"
.
Lemma
wp_diverge
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
v
:
val
)
:
WP
diverge
v
@
s
;
E
{{
Φ
}}%
I
.
Proof
.
iL
ö
b
as
"IH"
.
wp_lam
.
iApply
"IH"
.
Qed
.
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