summaryrefslogtreecommitdiff
path: root/Test/VSI-Benchmarks/b8.dfy
blob: 34e0cfef25f011db70a87831e6510087719e74bc (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
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
// Benchmark 8

// A dictionary is a mapping between words and sequences of words
// to set up the dictionary in main we will read a stream of words and put them into the mapping - the first element of the stream is the term, 
// the following words (until we read null) form the terms definition. Then the stream provides the next term etc.

class Queue<T> {
  var contents: seq<T>;
  method Init();
    modifies this;
    ensures |contents| == 0;
  method Enqueue(x: T);
    modifies this;
    ensures contents == old(contents) + [x];
  method Dequeue() returns (x: T);
    requires 0 < |contents|;
    modifies this;
    ensures contents == old(contents)[1..] && x == old(contents)[0];
  function Head(): T
    requires 0 < |contents|;
    reads this;
  { contents[0] }
  function Get(i: int): T
    requires 0 <= i && i < |contents|;
    reads this;
  { contents[i] }
}


class Glossary {
  method Sort(q: Queue<Word>) returns (r: Queue<Word>, perm:seq<int>);
    requires q != null;
    modifies q;
    ensures r != null && fresh(r);
    ensures |r.contents| == |old(q.contents)|;
    ensures (forall i, j :: 0 <= i && i < j && j < |r.contents| ==>
                r.Get(i) != null &&
                r.Get(i).AtMost(r.Get(j)));
    //perm is a permutation
    ensures |perm| == |r.contents|; // ==|pperm|
    ensures (forall i: int :: 0 <= i && i < |perm|==> 0 <= perm[i] && perm[i] < |perm| );
    ensures (forall i, j: int :: 0 <= i && i < j && j < |perm| ==> perm[i] != perm[j]); 
    // the final Queue is a permutation of the input Queue
    ensures (forall i: int :: 0 <= i && i < |perm| ==> r.contents[i] == old(q.contents)[perm[i]]);

  method Main()
  {
    var rs:= new ReaderStream;
    call rs.Open();
    var glossary := new Map<Word,seq<Word>>;
    call glossary.Init();
    var q:= new Queue<Word>;
    call q.Init();
    
    while (true)
      invariant rs.Valid() && fresh(rs.footprint);
      invariant glossary.Valid();
      invariant glossary !in rs.footprint;
      invariant null !in glossary.keys;
      invariant (forall d :: d in glossary.values ==> null !in d);
      invariant q !in rs.footprint;
      invariant q.contents == glossary.keys;
      decreases *;  // we leave out the decreases clause - unbounded stream
    {
      call term,definition := readDefinition(rs);
      if (term == null) {
        break;
      }
      call present, d := glossary.Find(term);
      if (!present) {
        call glossary.Add(term,definition);
        call q.Enqueue(term);
      }
    }    
    
    call rs.Close();
    call q,p := Sort(q);
    var wr := new WriterStream;
    call wr.Create();
    
    while (0<|q.contents|)
      invariant wr.Valid() && fresh(wr.footprint);
      invariant glossary.Valid();
      invariant glossary !in wr.footprint && null !in glossary.keys;
      invariant (forall d :: d in glossary.values ==> null !in d);
      invariant q !in wr.footprint;
      invariant (forall k :: k in q.contents ==> k in glossary.keys);
      decreases |q.contents|;
    {
      call term := q.Dequeue();
      call present,definition := glossary.Find(term);
      assert present;
      
      // write term with a html anchor
      call wr.PutWordInsideTag(term, term);
      var i := 0;

      var qcon := q.contents;
      while (i < |definition|)
        invariant wr.Valid() && fresh(wr.footprint);
        invariant glossary.Valid();
        invariant glossary !in wr.footprint && null !in glossary.keys;
        invariant (forall d :: d in glossary.values ==> null !in d);
        invariant q !in wr.footprint;
        invariant qcon == q.contents;
        invariant (forall k :: k in q.contents ==> k in glossary.keys);
      {
        var w := definition[i];
        call present, d := glossary.Find(w);
        if (present)
        {
          call wr. PutWordInsideHyperlink(w, w);
        }
        else 
        {
          call wr. PutWord(w);
        }
        i:= i +1;
      }
    }
    call wr.Close();          
  }
    

  method readDefinition(rs:ReaderStream) returns (term:Word, definition:seq<Word>)
    requires rs != null && rs.Valid();
    modifies rs.footprint;
    ensures rs.Valid() && fresh(rs.footprint - old(rs.footprint));
    ensures term != null ==> null !in definition;
  {
    call term := rs.GetWord();
    if (term != null)
    {
      definition := [];
      while (true)
        invariant rs.Valid() && fresh(rs.footprint - old(rs.footprint));
        invariant null !in definition;
        decreases *;  // we leave out the decreases clause - unbounded stream
      {
        call w := rs.GetWord();
        if (w == null)
        {
          break;
        }
        definition := definition + [w];
      }
    }
  }
}
  
class Word
{
  function AtMost(w:Word) :bool;
}
  
class ReaderStream {
  ghost var footprint:set<object>;
  var isOpen:bool;
  
  function Valid():bool
  reads this, footprint;
  {
    null !in footprint && this in footprint && isOpen
  }
  
  method Open() //reading
  modifies this;
  ensures Valid() && fresh(footprint -{this});
  {
    footprint := {this}; 
    isOpen :=true;
  }
  
  method GetWord()returns(x:Word)
    requires Valid() ;
    modifies footprint;
    ensures Valid() && fresh(footprint - old(footprint));
  {
  }
  
  method Close() 
    requires Valid();
    modifies footprint;
  {
    isOpen := false;
  }
}

class WriterStream {
  ghost var footprint:set<object>;
  var stream:seq<int>; 
  var isOpen:bool;
  
  function Valid():bool
  reads this, footprint;
  {
    null !in footprint && this in footprint && isOpen
  }
  
  method Create() //writing
    modifies this;
    ensures Valid() && fresh(footprint -{this});
    ensures stream == [];
  {
    stream := [];
    footprint := {this}; 
    isOpen:= true;
  }
  method GetCount() returns (c:int)
    requires Valid();
    ensures 0<=c;
  {
    c:=|stream|;
  }
  
  method PutWord(w:Word )
    requires Valid();
    requires  w != null; 
    modifies footprint;
    ensures Valid() && fresh(footprint - old(footprint));
    ensures old(stream)<= stream;
  {
  }

  method PutWordInsideTag(tag:Word,w:Word )
    requires Valid();
    requires tag != null && w != null;
    modifies footprint;
    ensures Valid() && fresh(footprint - old(footprint));
    ensures old(stream)<= stream;
  {
  }
  
  method PutWordInsideHyperlink(tag:Word,w:Word )
    requires Valid();
    requires tag != null && w != null;
    modifies footprint;
    ensures Valid() && fresh(footprint - old(footprint));
    ensures old(stream)<= stream;
  {
  }
   
  method Close() 
    requires Valid();
    modifies footprint;
  {
    isOpen := false;
  }
}

  
  
  
class Map<Key,Value> {
  var keys: seq<Key>;
  var values: seq<Value>;
  
  function Valid(): bool
    reads this;
  {
    |keys| == |values| &&
    (forall i, j :: 0 <= i && i < j && j < |keys| ==> keys[i] != keys[j])
  }

  method Init()
    modifies this;
    ensures Valid() && |keys| == 0;
  {
    keys := [];
    values := [];
  }

  method Find(key: Key) returns (present: bool, val: Value)
    requires Valid();
    ensures !present ==> key !in keys;
    ensures present ==> (exists i :: 0 <= i && i < |keys| &&
                                     keys[i] == key && values[i] == val);
  {
    call j := FindIndex(key);
    if (j == -1) {
      present := false;
    } else {
      present := true;
      val := values[j];
    }
  }

  method Add(key: Key, val: Value)
    requires Valid();
    modifies this;
    ensures Valid();
    ensures (forall i :: 0 <= i && i < |old(keys)| && old(keys)[i] == key ==>
              |keys| == |old(keys)| &&
              keys[i] == key && values[i] == val &&
              (forall j :: 0 <= j && j < |values| && i != j ==> keys[j] == old(keys)[j] && values[j] == old(values)[j]));
    ensures key !in old(keys) ==> keys == old(keys) + [key] && values == old(values) + [val];
  {
    call j := FindIndex(key);
    if (j == -1) {
      keys := keys + [key];
      values := values + [val];
    } else {
      values := values[j := val];
    }
  }

  method Remove(key: Key)
    requires Valid();
    modifies this;
    ensures Valid();
    // no key is introduced:
    ensures (forall k :: k in keys ==> k in old(keys));
    // at most one key is removed:
    ensures (forall k :: k in old(keys) ==> k in keys || k == key);
    // the given key is not there:
    // other values don't change:
    ensures key !in old(keys) ==> keys == old(keys) && values == old(values);
    ensures key in old(keys) ==>
            |keys| == |old(keys)| - 1 && key !in keys &&
            (exists h ::
              0 <= h && h <= |keys| &&
              keys[..h] == old(keys)[..h] &&
              values[..h] == old(values)[..h] &&
              keys[h..] == old(keys)[h+1..] &&
              values[h..] == old(values)[h+1..]);
  {
    call j := FindIndex(key);
    if (0 <= j) {
      keys := keys[..j] + keys[j+1..];
      values := values[..j] + values[j+1..];
    }
  }

  method FindIndex(key: Key) returns (idx: int)
    requires Valid();
    ensures -1 <= idx && idx < |keys|;
    ensures idx == -1 ==> key !in keys;
    ensures 0 <= idx ==> keys[idx] == key;
  {
    var j := 0;
    while (j < |keys|)
      invariant j <= |keys|;
      invariant key !in keys[..j];
    {
      if (keys[j] == key) {
        idx := j;
        return;
      }
      j := j + 1;
    }
    idx := -1;
  }
}