blob: e202412fc5096686a4d98641c865e7a78875ca86 (
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
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
|
class IntList {
ghost var Repr: set<object>;
ghost var list: seq<int>;
var root: IntNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(root != null ==> root in Repr && root.Repr <= Repr && this !in root.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(root == null ==> |list| == 0) &&
(root != null ==> |list| == |root.succ| + 1 && (list[0] == root.data && (forall i: int :: 0 < i && i <= |root.succ| ==> root.succ[i - 1] != null && list[i] == root.succ[i - 1].data)))
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(root != null ==> root.Valid())
}
method Empty()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [];
{
this.list := [];
this.root := null;
// repr stuff
this.Repr := {this};
}
method SingletonTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [2];
{
var gensym65 := new IntNode;
gensym65.data := 2;
gensym65.next := null;
gensym65.succ := [];
this.list := [2];
this.root := gensym65;
// repr stuff
gensym65.Repr := {gensym65};
this.Repr := {this} + this.root.Repr;
}
method OneTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [1] + [2];
{
var gensym63 := new IntNode;
var gensym75 := new IntNode;
gensym63.data := 1;
gensym63.next := gensym75;
gensym63.succ := [gensym75];
gensym75.data := 2;
gensym75.next := null;
gensym75.succ := [];
this.list := [1, 2];
this.root := gensym63;
// repr stuff
gensym75.Repr := {gensym75};
gensym63.Repr := {gensym63} + gensym63.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Singleton(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p];
{
var gensym66 := new IntNode;
gensym66.data := p;
gensym66.next := null;
gensym66.succ := [];
this.list := [p];
this.root := gensym66;
// repr stuff
gensym66.Repr := {gensym66};
this.Repr := {this} + this.root.Repr;
}
method TwoConsecutive(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [p + 1];
{
var gensym64 := new IntNode;
var gensym75 := new IntNode;
gensym64.data := p;
gensym64.next := gensym75;
gensym64.succ := [gensym75];
gensym75.data := p + 1;
gensym75.next := null;
gensym75.succ := [];
this.list := [p] + [p + 1];
this.root := gensym64;
// repr stuff
gensym75.Repr := {gensym75};
gensym64.Repr := {gensym64} + gensym64.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Double(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p] + [q];
{
var gensym65 := new IntNode;
var gensym77 := new IntNode;
gensym65.data := p;
gensym65.next := gensym77;
gensym65.succ := [gensym77];
gensym77.data := q;
gensym77.next := null;
gensym77.succ := [];
this.list := [p] + [q];
this.root := gensym65;
// repr stuff
gensym77.Repr := {gensym77};
gensym65.Repr := {gensym65} + gensym65.next.Repr;
this.Repr := {this} + this.root.Repr;
}
method Sum(p: int, q: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures list == [p + q];
{
var gensym67 := new IntNode;
gensym67.data := p + q;
gensym67.next := null;
gensym67.succ := [];
this.list := [p + q];
this.root := gensym67;
// repr stuff
gensym67.Repr := {gensym67};
this.Repr := {this} + this.root.Repr;
}
}
class IntNode {
ghost var Repr: set<object>;
ghost var succ: seq<IntNode>;
ghost var data: int;
var next: IntNode;
function Valid_repr(): bool
reads *;
{
this in Repr &&
null !in Repr &&
(next != null ==> next in Repr && next.Repr <= Repr && this !in next.Repr)
}
function Valid_self(): bool
reads *;
{
Valid_repr() &&
(next == null ==> |succ| == 0) &&
(next != null ==> succ == [next] + next.succ) &&
(!(null in succ))
}
function Valid(): bool
reads *;
{
this.Valid_self() &&
(next != null ==> next.Valid_self() && (next.next != null ==> next.next.Valid_self()))
}
method Zero()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures data == 0;
ensures succ == [];
{
this.data := 0;
this.next := null;
this.succ := [];
// repr stuff
this.Repr := {this};
}
method OneTwo()
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures data == 1;
ensures |succ| == 1;
ensures succ[0] != null;
ensures succ[0].data == 2;
{
var gensym71 := new IntNode;
gensym71.data := 2;
gensym71.next := null;
gensym71.succ := [];
this.data := 1;
this.next := gensym71;
this.succ := [gensym71];
// repr stuff
gensym71.Repr := {gensym71};
this.Repr := {this} + this.next.Repr;
}
method Init(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures data == p;
{
this.data := p;
this.next := null;
this.succ := [];
// repr stuff
this.Repr := {this};
}
method InitInc(p: int)
modifies this;
ensures fresh(Repr - {this});
ensures Valid();
ensures data == p + 1;
{
this.data := p + 1;
this.next := null;
this.succ := [];
// repr stuff
this.Repr := {this};
}
}
|
