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
|
//
// IntervalEnvironmentBase.cs
//
// Authors:
// Alexander Chebaturkin (chebaturkin@gmail.com)
//
// Copyright (C) 2012 Alexander Chebaturkin
//
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the
// "Software"), to deal in the Software without restriction, including
// without limitation the rights to use, copy, modify, merge, publish,
// distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to
// the following conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//
using System;
using System.Collections.Generic;
using System.IO;
using Mono.CodeContracts.Static.DataStructures;
using Mono.CodeContracts.Static.Lattices;
namespace Mono.CodeContracts.Static.Analysis.Numerical {
abstract class IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> : IIntervalEnvironment<TVar, TExpr, TInterval, TNumeric>,
IEnvironmentDomain<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>, TVar, TExpr>
where TInterval : IntervalBase<TInterval, TNumeric>
where TVar : IEquatable<TVar> {
public abstract IntervalAssumerBase<TVar, TExpr, TInterval, TNumeric> Assumer { get; }
public abstract IntervalContextBase<TInterval, TNumeric> Context { get; }
public readonly IExpressionDecoder<TVar, TExpr> Decoder;
readonly EnvironmentDomain<TVar, TInterval> vars_to_intervals;
public IEnumerable<TVar> Variables { get { return vars_to_intervals.Keys; } }
protected IntervalEnvironmentBase
(IExpressionDecoder<TVar, TExpr> decoder,
EnvironmentDomain<TVar, TInterval> varsToInterval)
{
Decoder = decoder;
vars_to_intervals = varsToInterval;
}
protected IntervalEnvironmentBase (IExpressionDecoder<TVar, TExpr> decoder)
: this (decoder, EnvironmentDomain<TVar, TInterval>.TopValue (null))
{
}
public TInterval Eval (TExpr expr)
{
int intValue;
if (Decoder.IsConstantInt (expr, out intValue))
return Context.For (intValue);
var evaluator = new EvaluateExpressionVisitor<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>, TVar, TExpr, TInterval, TNumeric> (Decoder);
var interval = evaluator.Visit (expr, new Counter<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>> (this));
if (evaluator.DuplicatedOccurences.Length () >= 1) {
var noDuplicates = true;
TInterval result = null;
foreach (var var in evaluator.DuplicatedOccurences.AsEnumerable ()) {
TInterval intv;
if (TryGetValue (var, out intv) && intv.IsFinite &&
Context.IsGreaterEqualThanZero (intv.LowerBound)) {
var extreme = EvalWithExtremes (expr, var, intv);
if (noDuplicates) {
noDuplicates = false;
result = extreme;
}
else
result = result.Join (extreme);
}
}
if (!noDuplicates)
interval = result;
}
return interval;
}
public TInterval Eval (TVar var)
{
TInterval intv;
if (TryGetValue (var, out intv))
return intv;
return Context.TopValue;
}
/// <summary>
/// Evaluates expression with variable equal to var's lowerbound or upperbound.
/// </summary>
/// <param name="expr"></param>
/// <param name="var"></param>
/// <param name="intv"></param>
/// <returns></returns>
TInterval EvalWithExtremes (TExpr expr, TVar var, TInterval intv)
{
var evaluator = new EvaluateExpressionVisitor<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>, TVar, TExpr, TInterval, TNumeric> (Decoder);
var envLowerBound = With (var, Context.For (intv.LowerBound));
// replace current intv with it's only lowerbound
var withLowerBound = evaluator.Visit (expr, new Counter<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>> (envLowerBound));
var envUpperBound = With (var, Context.For (intv.UpperBound));
// replace current intv with it's only upperBound
var withUpperBound = evaluator.Visit (expr, new Counter<IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>> (envUpperBound));
return withLowerBound.Join (withUpperBound);
}
public string ToString (TExpr expr)
{
if (IsBottom)
return "_|_";
if (IsTop)
return "Top";
var list = new List<string> ();
foreach (var variable in Variables) {
var intv = vars_to_intervals[variable];
if (!intv.IsTop) {
var name = Decoder != null
? Decoder.NameOf (variable)
: variable.ToString ();
list.Add (name + ": " + intv);
}
}
list.Sort ();
return string.Join (", ", list);
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> AssumeTrue (TExpr guard)
{
Assumer.AssumeNotEqualToZero (Decoder.UnderlyingVariable (guard), this);
return new IntervalTestVisitor (Decoder).VisitTrue (guard, this);
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> AssumeFalse (TExpr guard)
{
return Assumer.AssumeEqualToZero (Decoder.UnderlyingVariable (guard), this);
}
public FlatDomain<bool> CheckIfHolds (TExpr expr)
{
return FlatDomain<bool>.TopValue;
}
public bool Contains (TVar v)
{
return vars_to_intervals.Contains (v);
}
public bool TryGetValue (TVar v, out TInterval interval)
{
return vars_to_intervals.TryGetValue (v, out interval);
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> With (TVar var, TInterval interval)
{
return NewInstance (vars_to_intervals.With (var, interval));
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> RefineVariable (TVar var, TInterval interval)
{
TInterval current;
if (TryGetValue (var, out current))
interval = interval.Meet (current);
if (interval.IsBottom)
return Bottom;
return With (var, interval);
}
#region Implementation of IAbstractDomain<T>
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Top { get { return NewInstance (EnvironmentDomain<TVar, TInterval>.TopValue (null)); } }
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Bottom { get { return NewInstance (EnvironmentDomain<TVar, TInterval>.BottomValue ()); } }
public bool IsTop { get { return vars_to_intervals.IsTop; } }
public bool IsBottom { get { return vars_to_intervals.IsBottom; } }
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Join (IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> that)
{
return NewInstance (vars_to_intervals.Join (that.vars_to_intervals));
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Join (IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> that, bool widen, out bool weaker)
{
return NewInstance (vars_to_intervals.Join (that.vars_to_intervals, widen, out weaker));
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Widen (IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> that)
{
return NewInstance (vars_to_intervals.Widen (that.vars_to_intervals));
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Meet (IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> that)
{
return NewInstance (vars_to_intervals.Meet (that.vars_to_intervals));
}
public bool LessEqual (IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> that)
{
return vars_to_intervals.LessEqual (that.vars_to_intervals);
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> ImmutableVersion ()
{
return this;
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> Clone ()
{
return this;
}
public void Dump (TextWriter tw)
{
vars_to_intervals.Dump (tw);
}
#endregion
protected abstract IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> NewInstance (EnvironmentDomain<TVar, TInterval> varsToIntervals);
class IntervalTestVisitor {
readonly IntervalAssumeTrueVisitor<TVar, TExpr, TInterval, TNumeric> true_visitor;
readonly IntervalAssumeFalseVisitor<TVar, TExpr, TInterval, TNumeric> false_visitor;
public IntervalTestVisitor (IExpressionDecoder<TVar, TExpr> decoder)
{
true_visitor =
new IntervalAssumeTrueVisitor<TVar, TExpr, TInterval, TNumeric> (decoder);
false_visitor =
new IntervalAssumeFalseVisitor<TVar, TExpr, TInterval, TNumeric> (decoder);
true_visitor.FalseVisitor = false_visitor;
false_visitor.TrueVisitor = true_visitor;
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> VisitTrue (TExpr guard, IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> data)
{
return true_visitor.Visit (guard, data);
}
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> VisitFalse (TExpr guard, IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> data)
{
return false_visitor.Visit (guard, data);
}
}
public abstract IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> AssumeVariableIn (TVar var, Interval interval);
public IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric> AssumeLessEqualThan (TExpr left, TExpr right)
{
return Assumer.AssumeLessEqualThan (left, right, this);
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Top { get { return Top; } }
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Bottom { get { return Bottom; } }
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Join (INumericalEnvironmentDomain<TVar, TExpr> that)
{
return Join (that as IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>);
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Join
(INumericalEnvironmentDomain<TVar, TExpr> that, bool widen, out bool weaker)
{
return Join (that as IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>, widen,
out weaker);
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Widen (INumericalEnvironmentDomain<TVar, TExpr> that)
{
return Widen (that as IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>);
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Meet (INumericalEnvironmentDomain<TVar, TExpr> that)
{
return Meet (that as IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>);
}
bool IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.LessEqual (INumericalEnvironmentDomain<TVar, TExpr> that)
{
return LessEqual (that as IntervalEnvironmentBase<TVar, TExpr, TInterval, TNumeric>);
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.ImmutableVersion ()
{
return ImmutableVersion ();
}
INumericalEnvironmentDomain<TVar, TExpr> IAbstractDomain<INumericalEnvironmentDomain<TVar, TExpr>>.Clone ()
{
return Clone ();
}
INumericalEnvironmentDomain<TVar, TExpr> IEnvironmentDomain<INumericalEnvironmentDomain<TVar, TExpr>, TVar, TExpr>.AssumeTrue (TExpr guard)
{
return AssumeTrue (guard);
}
INumericalEnvironmentDomain<TVar, TExpr> IEnvironmentDomain<INumericalEnvironmentDomain<TVar, TExpr>, TVar, TExpr>.AssumeFalse (TExpr guard)
{
return AssumeFalse (guard);
}
INumericalEnvironmentDomain<TVar, TExpr> INumericalEnvironmentDomain<TVar, TExpr>.AssumeVariableIn (TVar var, Interval interval)
{
return AssumeVariableIn (var, interval);
}
INumericalEnvironmentDomain<TVar, TExpr> INumericalEnvironmentDomain<TVar, TExpr>.AssumeLessEqualThan (TExpr left, TExpr right)
{
return AssumeLessEqualThan (left, right);
}
}
}
|
