blob: 5262e462dd7a5ebecc07905f655766dd9bfd568e (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
|
class RingBuffer<T>
{
// public fields that are used to define the abstraction:
ghost var Contents: seq<T>; // the contents of the ring buffer
ghost var N: nat; // the capacity of the ring buffer
ghost var Repr: set<object>; // the set of objects used in the implementation
// Valid encodes the consistency of RingBuffer objects (think, invariant).
// An explanation of this idiom is explained in the README file.
function Valid(): bool
reads this, Repr;
{
this in Repr && null !in Repr &&
data != null && data in Repr &&
data.Length == N &&
(N == 0 ==> len == first == 0 && Contents == []) &&
(N != 0 ==> len <= N && first < N) &&
Contents == if first + len <= N then data[first..first+len]
else data[first..] + data[..first+len-N]
}
// private implementation:
var data: array<T>;
var first: nat;
var len: nat;
constructor Create(n: nat)
modifies this;
ensures Valid() && fresh(Repr - {this});
ensures Contents == [] && N == n;
{
Repr := {this};
data := new T[n];
Repr := Repr + {data};
first, len := 0, 0;
Contents, N := [], n;
}
method Clear()
requires Valid();
modifies Repr;
ensures Valid() && fresh(Repr - old(Repr));
ensures Contents == [] && N == old(N);
{
len := 0;
Contents := [];
}
method Head() returns (x: T)
requires Valid();
requires Contents != [];
ensures x == Contents[0];
{
x := data[first];
}
method Push(x: T)
requires Valid();
requires |Contents| != N;
modifies Repr;
ensures Valid() && fresh(Repr - old(Repr));
ensures Contents == old(Contents) + [x] && N == old(N);
{
var nextEmpty := if first + len < data.Length
then first + len else first + len - data.Length;
data[nextEmpty] := x;
len := len + 1;
Contents := Contents + [x];
}
method Pop() returns (x: T)
requires Valid();
requires Contents != [];
modifies Repr;
ensures Valid() && fresh(Repr - old(Repr));
ensures x == old(Contents)[0] && Contents == old(Contents)[1..] && N == old(N);
{
x := data[first];
first, len := if first + 1 == data.Length then 0 else first + 1, len - 1;
Contents := Contents[1..];
}
}
method TestHarness(x: int, y: int, z: int)
{
var b := new RingBuffer<int>.Create(2);
b.Push(x);
b.Push(y);
var h := b.Pop(); assert h == x;
b.Push(z);
h := b.Pop(); assert h == y;
h := b.Pop(); assert h == z;
}
|
