summaryrefslogtreecommitdiff
path: root/Test/dafny0/Parallel.dfy
blob: 93a16475c32c2be871cbcecab141642580365c9c (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
// RUN: %dafny /compile:0 /print:"%t.print" /dprint:"%t.dprint" "%s" > "%t"
// RUN: %diff "%s.expect" "%t"

class C {
  var data: int
  var n: nat
  var st: set<object>

  ghost method CLemma(k: int)
    requires k != -23
    ensures data < k  // magic, isn't it (or bogus, some would say)
}

// This method more or less just tests the syntax, resolution, and basic verification
method ParallelStatement_Resolve(
    a: array<int>,
    spine: set<C>,
    Repr: set<object>,
    S: set<int>,
    clx: C, cly: C, clk: int
  )
  requires a != null && null !in spine
  modifies a, spine
{
  forall i | 0 <= i < a.Length && i % 2 == 0 {
    a[i] := a[(i + 1) % a.Length] + 3;
  }

  forall o | o in spine {
    o.st := o.st + Repr;
  }

  forall x, y | x in S && 0 <= y+x < 100 {
    Lemma(clx, x, y);  // error: precondition does not hold (clx may be null)
  }

  forall x, y | x in S && 0 <= y+x < 100 {
    cly.CLemma(x + y);  // error: receiver might be null
  }

  forall p | 0 <= p
    ensures F(p) <= Sum(p) + p - 1  // error (no connection is known between F and Sum)
  {
    assert 0 <= G(p);
    ghost var t;
    if p % 2 == 0 {
      assert G(p) == F(p+2);  // error (there's nothing that gives any relation between F and G)
      t := p+p;
    } else {
      assume H(p, 20) < 100;  // don't know how to justify this
      t := p;
    }
    PowerLemma(p, t);
    t := t + 1;
    PowerLemma(p, t);
  }
}

lemma Lemma(c: C, x: int, y: int)
  requires c != null
  ensures c.data <= x+y
lemma PowerLemma(x: int, y: int)
  ensures Pred(x, y)

function F(x: int): int
function G(x: int): nat
function H(x: int, y: int): int
function Sum(x: int): int
function Pred(x: int, y: int): bool

// ---------------------------------------------------------------------

method M0(S: set<C>)
  requires null !in S
  modifies S
  ensures forall o :: o in S ==> o.data == 85
  ensures forall o :: o != null && o !in S ==> o.data == old(o.data)
{
  forall s | s in S {
    s.data := 85;
  }
}

method M1(S: set<C>, x: C)
  requires null !in S && x in S
{
  forall s | s in S
    ensures s.data < 100
  {
    assume s.data == 85;
  }
  if * {
    assert x.data == 85;  // error (cannot be inferred from forall ensures clause)
  } else {
    assert x.data < 120;
  }

  forall s | s in S
    ensures s.data < 70  // error
  {
    assume s.data == 85;
  }
}

method M2() returns (a: array<int>)
  ensures a != null
  ensures forall i,j :: 0 <= i < a.Length/2 <= j < a.Length ==> a[i] < a[j]
{
  a := new int[250];
  forall i: nat | i < 125 {
    a[i] := 423;
  }
  forall i | 125 <= i < 250 {
    a[i] := 300 + i;
  }
}

method M4(S: set<C>, k: int)
  modifies S
{
  forall s | s in S && s != null {
    s.n := k;  // error: k might be negative
  }
}

method M5()
{
  if {
  case true =>
    forall x | 0 <= x < 100 {
      PowerLemma(x, x);
    }
    assert Pred(34, 34);

  case true =>
    forall x,y | 0 <= x < 100 && y == x+1 {
      PowerLemma(x, y);
    }
    assert Pred(34, 35);

  case true =>
    forall x,y | 0 <= x < y < 100 {
      PowerLemma(x, y);
    }
    assert Pred(34, 35);

  case true =>
    forall x | x in set k | 0 <= k < 100 {
      PowerLemma(x, x);
    }
    assert Pred(34, 34);
  }
}

method Main()
{
  var a := new int[180];
  forall i | 0 <= i < 180 {
    a[i] := 2*i + 100;
  }
  var sq := [0, 0, 0, 2, 2, 2, 5, 5, 5];
  forall i | 0 <= i < |sq| {
    a[20+i] := sq[i];
  }
  forall t | t in sq {
    a[t] := 1000;
  }
  forall t,u | t in sq && t < 4 && 10 <= u < 10+t {
    a[u] := 6000 + t;
  }
  var k := 0;
  while k < 180 {
    if k != 0 { print ", "; }
    print a[k];
    k := k + 1;
  }
  print "\n";
}

method DuplicateUpdate() {
  var a := new int[180];
  var sq := [0, 0, 0, 2, 2, 2, 5, 5, 5];
  if * {
    forall t,u | t in sq && 10 <= u < 10+t {
      a[u] := 6000 + t;  // error: a[10] (and a[11]) are assigned more than once
    }
  } else {
    forall t,u | t in sq && t < 4 && 10 <= u < 10+t {
      a[u] := 6000 + t;  // with the 't < 4' conjunct in the line above, this is fine
    }
  }
}

lemma DontDoMuch(x: int)
{
}

method OmittedRange() {
  forall x: int { }  // a type is still needed for the bound variable
  forall x {
    DontDoMuch(x);
  }
}

// ----------------------- two-state postconditions ---------------------------------

class TwoState_C { ghost var data: int }

// It is not possible to achieve this postcondition in a ghost method, because ghost
// contexts are not allowed to allocate state.  Callers of this ghost method will know
// that the postcondition is tantamount to 'false'.
ghost method TwoState0(y: int)
  ensures exists o: TwoState_C {:nowarn} :: o != null && fresh(o)

method TwoState_Main0() {
  forall x { TwoState0(x); }
  assert false;  // no prob, because the postcondition of TwoState0 implies false
}

method X_Legit(c: TwoState_C)
  requires c != null
  modifies c
{
  c.data := c.data + 1;
  forall x | c.data <= x
    ensures old(c.data) < x  // note that the 'old' refers to the method's initial state
  {
  }
}

// At first glance, this looks like a version of TwoState_Main0 above, but with an
// ensures clause.
// However, there's an important difference in the translation, which is that the
// occurrence of 'fresh' here refers to the initial state of the TwoStateMain2
// method, not the beginning of the 'forall' statement.
method TwoState_Main2()
{
  forall x: int
    ensures exists o: TwoState_C {:nowarn} :: o != null && fresh(o)
  {
    TwoState0(x);
  }
  assert false;  // fine, for the postcondition of the forall statement implies false
}

// At first glance, this looks like an inlined version of TwoState_Main0 above.
// However, there's an important difference in the translation, which is that the
// occurrence of 'fresh' here refers to the initial state of the TwoState_Main3
// method, not the beginning of the 'forall' statement.
// Still, care needs to be taken in the translation to make sure that the forall
// statement's effect on the heap is not optimized away.
method TwoState_Main3()
{
  forall x: int
    ensures exists o: TwoState_C {:nowarn} :: o != null && fresh(o)
  {
    assume false;  // (there's no other way to achieve this forall-statement postcondition)
  }
  assert false;  // it is known that the forall's postcondition is contradictory, so this assert is fine
}

// ------- empty forall statement -----------------------------------------

class EmptyForallStatement {
  var emptyPar: int

  method Empty_Parallel0()
    modifies this
    ensures emptyPar == 8
  {
    forall () {
      this.emptyPar := 8;
    }
  }

  function EmptyPar_P(x: int): bool
  lemma EmptyPar_Lemma(x: int)
    ensures EmptyPar_P(x)

  method Empty_Parallel1()
    ensures EmptyPar_P(8)
  {
    forall {
      EmptyPar_Lemma(8);
    }
  }

  method Empty_Parallel2()
  {
    forall
      ensures exists k :: EmptyPar_P(k)
    {
      var y := 8;
      assume EmptyPar_P(y);
    }
    assert exists k :: EmptyPar_P(k);  // yes
    assert EmptyPar_P(8);  // error: the forall statement's ensures clause does not promise this
  }
}

// ---------------------------------------------------------------------
// The following is an example that once didn't verify (because the forall statement that
// induction inserts had caused the $Heap to be advanced, despite the fact that Th is a
// ghost method).

datatype Nat = Zero | Succ(tail: Nat)

predicate ThProperty(step: nat, t: Nat, r: nat)
{
  match t
  case Zero => true
  case Succ(o) => step>0 && exists ro:nat, ss | ss == step-1 :: ThProperty(ss, o, ro) //WISH: ss should be autogrnerated. Note that step is not a bound variable.
}

lemma Th(step: nat, t: Nat, r: nat)
  requires t.Succ? && ThProperty(step, t, r)
  // the next line follows from the precondition and the definition of ThProperty
  ensures exists ro:nat, ss | ss == step-1 :: ThProperty(ss, t.tail, ro) //WISH same as above
{
}