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
|
//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation. All Rights Reserved.
//
//-----------------------------------------------------------------------------
package chalice;
import scala.util.parsing.input.Position
import scala.util.parsing.input.NoPosition
object Boogie {
sealed abstract class Decl
case class Const(id: String, unique: Boolean, t: BType) extends Decl
case class Proc(id: String, ins: List[BVar], outs: List[BVar],
mod: List[String], PrePost: List[String],
body: List[Stmt]) extends Decl
case class Function(id: String, ins: List[BVar], out: BVar) extends Decl
case class Axiom(expr: Expr) extends Decl
sealed abstract class BType
case class NamedType(s: String) extends BType
case class IndexedType(id: String, t: BType) extends BType
case class Tag(s: String)
sealed abstract class Stmt {
def Locals = List[BVar]()
var tags: List[Tag] = Nil
}
case class Comment(comment: String) extends Stmt
case class Assert(e: Expr) extends Stmt {
def this(e: Expr, p: Position, txt: String) = { this(e); this.pos = p; this.message = txt; this }
def this(e: Expr, p: Position, txt: String, subsumption: Int) = { this(e, p, txt); this.subsumption = Some(subsumption); this }
var pos = NoPosition : Position
var message = "" : String
var subsumption = None: Option[Int]
}
case class Assume(e: Expr) extends Stmt
case class Assign(lhs: Expr, rhs: Expr) extends Stmt
case class AssignMap(lhs: Expr, index: Expr, rhs: Expr) extends Stmt
case class Havoc(x: Expr) extends Stmt
case class MapUpdate(map: Expr, arg0: Expr, arg1: Option[Expr], rhs: Expr) extends Stmt {
def this(map: Expr, arg0: Expr, rhs: Expr) = this(map, arg0, None, rhs)
def this(map: Expr, arg0: Expr, arg1: Expr, rhs: Expr) = this(map, arg0, Some(arg1), rhs)
}
case class If(guard: Expr, thn: List[Stmt], els: List[Stmt]) extends Stmt {
override def Locals = (thn flatMap (_.Locals)) ::: (els flatMap (_.Locals))
}
case class LocalVar(x: BVar) extends Stmt {
def this(id: String, tp: BType) = this(BVar(id, tp))
override def Locals = List(x)
}
sealed abstract class Expr {
def &&(that: Expr) = BinaryExpr("&&", this, that)
def ||(that: Expr) = BinaryExpr("||", this, that)
def ==@(that: Expr) = BinaryExpr("==", this, that)
def !=@(that: Expr) = BinaryExpr("!=", this, that)
def Equals(that: Expr) = BinaryExpr("==", this, that)
def ==>(that: Expr) = BinaryExpr("==>", this, that)
def <==>(that: Expr) = BinaryExpr("<==>", this, that)
def unary_! = UnaryExpr("!", this)
def <=(that: Expr) = BinaryExpr("<=", this, that)
def <(that: Expr) = BinaryExpr("<", this, that)
def >=(that: Expr) = BinaryExpr(">=", this, that)
def >(that: Expr) = BinaryExpr(">", this, that)
def +(that: Expr) = BinaryExpr("+", this, that)
def -(that: Expr) = BinaryExpr("-", this, that)
def *(that: Expr) = BinaryExpr("*", this, that)
def /(that: Expr) = BinaryExpr("/", this, that)
def %(that: Expr) = BinaryExpr("%", this, that)
def := (that: Expr) = Assign(this, that)
def apply(e: Expr, f: Expr) = new MapSelect(this, e, Some(f))
def apply(e: Expr) = new MapSelect(this, e, None)
def thenElse(thenE: Expr, elseE: Expr) = new Ite(this, thenE, elseE)
def select(e: Expr, s: String) = new MapSelect(this, e, s) // useful for working on heap
def forall(x: BVar) = new Forall(x, this)
def exists(x: BVar) = new Exists(x, this)
def store(e: Expr, f: Expr, rhs: Expr) = MapUpdate(this, e, Some(f), rhs)
}
case class IntLiteral(n: Int) extends Expr
case class BoolLiteral(b: Boolean) extends Expr
case class Null() extends Expr
case class VarExpr(id: String) extends Expr {
def this(v: BVar) = this(v.id)
}
case class MapSelect(map: Expr, arg0: Expr, arg1: Option[Expr]) extends Expr {
def this(map: Expr, arg0: Expr) = this(map, arg0, None) // for one-dimensional maps
def this(map: Expr, arg0: Expr, arg1: String) = this(map, arg0, Some(VarExpr(arg1)))
def this(map: Expr, arg0: Expr, arg1: String, arg2: String) = // for 3-dimensional maps
this(MapSelect(map, arg0, Some(VarExpr(arg1))), VarExpr(arg2), None)
}
case class MapStore(map: Expr, arg0: Expr, rhs: Expr) extends Expr
case class Old(e: Expr) extends Expr
case class UnaryExpr(op: String, e: Expr) extends Expr
case class BinaryExpr(op: String, e0: Expr, e1: Expr) extends Expr
case class FunctionApp(f: String, args: List[Expr]) extends Expr {
def this(f: String, a0: Expr) = this(f, List(a0))
def this(f: String, a0: Expr, a1: Expr) = this(f, List(a0, a1))
def this(f: String, a0: Expr, a1: Expr, a2: Expr) = this(f, List(a0, a1, a2))
}
case class Trigger(ts: List[Expr]) extends Expr {
def this(t: Expr) = this(List(t))
}
case class Forall(ta: List[TVar], xs: List[BVar], triggers: List[Trigger], body: Expr) extends Expr {
def this(x: BVar, body: Expr) = this(Nil, List(x), Nil, body)
def this(xs: List[BVar], trigger: Trigger, body: Expr) = this(Nil, xs, List(trigger), body)
def this(t: TVar, x: BVar, body: Expr) = this(List(t), List(x), Nil, body)
}
case class Exists(ta: List[TVar], xs: List[BVar], triggers: List[Trigger], body: Expr) extends Expr {
def this(x: BVar, body: Expr) = this(Nil, List(x), List(), body)
def this(xs: List[BVar], trigger: Trigger, body: Expr) = this(Nil, xs, List(trigger), body)
}
case class Lambda(ta: List[TVar], xs: List[BVar], body: Expr) extends Expr
case class Ite(con: Expr, then: Expr, els: Expr) extends Expr
case class BVar(id: String, t: BType) {
def this(id: String, t: BType, uniquifyName: Boolean) =
this(if (uniquifyName) {
val n = S_BVar.VariableCount
S_BVar.VariableCount = S_BVar.VariableCount + 1
id + "#_" + n
} else {
id
}, t)
val where: Expr = null
}
object S_BVar { var VariableCount = 0 }
def NewBVar(id: String, t: BType, uniquifyName: Boolean) = {
val v = new Boogie.BVar(id, t, uniquifyName)
val e = new Boogie.VarExpr(v)
(v,e)
}
case class TVar(id: String) {
def this(id: String, uniquifyName: Boolean) =
this(if (uniquifyName) {
val n = S_TVar.VariableCount
S_TVar.VariableCount = S_TVar.VariableCount + 1
id + "#_" + n
} else {
id
})
val where: Expr = null
}
object S_TVar { var VariableCount = 0 }
def NewTVar(id: String) = {
val v = new Boogie.TVar(id, true)
val e = new Boogie.NamedType(v.id)
(v,e)
}
// def out(s: String) = Console.out.print(s)
private var indentLevel = 1
def indent: String = {
def doIndent(i: Int): String = {
if(i==0) { "" } else { " " + doIndent(i-1) }
}
doIndent(indentLevel);
}
def IndentMore(what: => String) = {
val prev = indentLevel
indentLevel = indentLevel + 1
val result = what
indentLevel = prev
result
}
private val nl = System.getProperty("line.separator");
def Print[T](list: List[T], sep: String, p: T => String): String = list match {
case Nil => ""
case x :: Nil => p(x)
case x :: xs => p(x) + sep + Print(xs, sep, p)
}
def PrintType(t: BType): String = t match {
case nt@ NamedType(s) =>
s
case IndexedType(id,t) =>
id + " (" + PrintType(t) + ")"
}
def Print(d: Decl): String = d match {
case Const(id, u, t) =>
"const " + (if (u) "unique " else "" ) + id + ": " + PrintType(t) + ";" + nl
case p: Proc =>
"procedure " + p.id +
"(" + Print(p.ins, ", ", PrintVar) + ")" +
" returns (" + Print(p.outs, ", ", PrintVar) + ")" + nl +
(p.mod match {
case Nil => ""
case x :: xs =>
indent + "modifies " +
Print(p.mod, ", ", { s: String => s }) +
";" + nl
}) +
Print(p.PrePost, nl, { spec: String => indent + spec }) + nl +
"{" + nl +
Print(p.body flatMap (_.Locals), "", { v:BVar => indent + "var " + PrintVar(v) + ";" + nl}) +
Print(p.body, "", PrintStmt) +
"}" + nl
case Function(id, ins, out) =>
"function " + id + "(" + Print(ins, ", ", PrintVar) + ") returns (" + PrintVar(out) + ");" + nl
case Axiom(e) =>
"axiom " + PrintExpr(e) + ";" + nl
}
def PrintVar(v: BVar): String = {
v.id + ": " + PrintType(v.t) +
(if (v.where != null) {" where " + PrintExpr(v.where) } else { "" })
}
def PrintStmt(s: Stmt): String = s match {
case Comment(msg) => indent + "// " + msg + nl
case assert@Assert(e) =>
val pos = if (Chalice.vsMode) {
val r = assert.pos.line;
val c = assert.pos.column;
r + "," + c + "," + r + "," + (c+5) + ":"
} else if (Chalice.rise4funMode) {
val (r,c) = (assert.pos.line, assert.pos.column)
Chalice.InputFilename + "(" + r + "," + c + "): Error: "
} else {
" " + assert.pos + ": "
}
indent + "assert " + "{:msg \"" + pos + assert.message + "\"}" + (assert.subsumption match {case Some(n) => "{:subsumption " + n + "}"; case None => ""}) + " " + PrintExpr(e) + ";" + nl
case Assume(e) => indent + "assume " + PrintExpr(e) + ";" + nl
case If(guard, thn, els) =>
if (thn == Nil && els == Nil) "" else
indent + "if (" +
(if (guard == null) "*" else PrintExpr(guard)) +
") {" + nl +
IndentMore { Print(thn, "", PrintStmt) } +
indent + "}" +
(if (els == Nil) nl else
" else {" + nl +
IndentMore { Print(els, "", PrintStmt) } +
indent + "}" + nl
)
case Assign(lhs, rhs) =>
indent + PrintExpr(lhs) + " := " + PrintExpr(rhs) + ";" + nl
case AssignMap(lhs, index, rhs) =>
indent + PrintExpr(lhs) + "[" + PrintExpr(index) + "] := " + PrintExpr(rhs) + ";" + nl
case Havoc(lhs) =>
indent + "havoc " + PrintExpr(lhs) + ";" + nl
case MapUpdate(map, a0, a1, rhs) =>
indent + PrintExpr(map) + "[" +
PrintExpr(a0) +
(a1 match { case Some(e) => { ", " + PrintExpr(e) }; case None => { "" }}) +
"] := " +
PrintExpr(rhs) + ";" + nl
case _:LocalVar => "" /* print nothing */
}
def PrintExpr(e: Expr): String = {
PrintExpr(e, false)
}
def PrintExpr(e: Expr, useParens: Boolean): String = e match {
case IntLiteral(n) => n.toString
case BoolLiteral(b) => b.toString
case Null() => "null"
case VarExpr(id) => id
case MapSelect(map, arg0, arg1) =>
PrintExpr(map) + "[" + PrintExpr(arg0, false) +
(arg1 match {case Some(e) => { ", " + PrintExpr(e) }; case None => { "" }}) +
"]"
case MapStore(map, arg0, rhs) =>
PrintExpr(map) + "[" + PrintExpr(arg0) + " := " + PrintExpr(rhs, false) + "]"
case Old(e) => "old(" + PrintExpr(e, false) + ")"
case UnaryExpr(op, e) =>
(if (useParens) { "(" } else "") +
op + PrintExpr(e, true) +
(if (useParens) ")" else "" )
case BinaryExpr(op, e0, e1) =>
// reduce parentheses in a special common case:
val binIsAndImpIff = op=="&&" || op=="==>" || op=="<==>";
def IsAnd(e: Expr) = e match { case BinaryExpr(op,_,_) if op=="&&" => true case _ => false }
(if (useParens) "(" else "") + PrintExpr(e0, !(binIsAndImpIff && IsAnd(e0))) +
" " + op + " " +
PrintExpr(e1, !(binIsAndImpIff && IsAnd(e1))) +
(if (useParens) ")" else "")
case FunctionApp(f, args) =>
f + "(" +
Print(args, ", ", { e: Expr => PrintExpr(e, false) }) +
")"
case Ite(con, then, els) =>
"ite(" + PrintExpr(con) + ", " + PrintExpr(then) + ", " + PrintExpr(els) + ")"
case Trigger(ts) => Print(ts,", ", PrintExpr)
case Forall(ts, xs, triggers, body) =>
"(forall" +
(if (ts.length == 0) " " else "<" + Print(ts, ", ", { x: TVar => x.id }) + "> ") +
Print(xs, ", ", { x: BVar => x.id + ": " + PrintType(x.t) }) +
" :: " +
Print(triggers , "", { t: Trigger => "{" + PrintExpr(t) + "} " }) +
PrintExpr(body) +
")"
case Exists(ts, xs, triggers, body) =>
"(exists " +
(if (ts.length == 0) " " else "<" + Print(ts, ", ", { x: TVar => x.id }) + "> ") +
Print(xs, ", ", { x: BVar => x.id + ": " + PrintType(x.t) }) +
" :: " +
Print(triggers , "", { t: Trigger => "{" + PrintExpr(t) + "} " }) +
PrintExpr(body) +
")"
case Lambda(ts, xs, body) =>
"(lambda" +
(if (ts.length == 0) " " else "<" + Print(ts, ", ", { x: TVar => x.id }) + "> ") +
Print(xs, ", ", { x: BVar => x.id + ": " + PrintType(x.t) }) +
" :: " +
PrintExpr(body) +
")"
}
}
|
