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
|
// RUN: %dafny /compile:0 /print:"%t.print" /dprint:"%t.dprint" "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
module A {
datatype Explicit<T(==)> = Nil | Cons(set<T>, Explicit<T>);
datatype Inferred<T> = Nil | Cons(set<T>, Inferred<T>);
class C {
method M<T>(x: Explicit<T>)
method N<T>(x: Inferred<T>)
}
}
module B refines A {
class C {
method M<T>(x: Explicit<T>)
method N<T(==)>(x: Inferred<T>)
}
}
// ----------------------------
module C {
type X(==);
type Y(==);
}
module D refines C {
class X { }
datatype Y = Red | Green | Blue;
}
module E refines C {
codatatype X = Next(int, X); // error: X requires equality and codatatypes don't got it
datatype Y = Nil | Something(Z) | More(Y, Y); // error: Y does not support equality
codatatype Z = Red | Green(X) | Blue;
}
module F refines C {
datatype X<T> = Nil | Cons(T, X<T>); // error: not allowed to add a type parameter to type X
class Y<T> { } // error: not allowed to add a type parameter to type Y
}
module G refines C {
datatype X = Nil | Next(Z, X); // error: X does not support equality
datatype Y = Nil | Something(Z) | More(Y, Y); // error: Y does not support equality
codatatype Z = Red | Green | Blue;
}
// ----------------------------
module H {
datatype Dt<T> = Nil | Cons(T, Dt);
datatype BulkyList<T> = Nothing | Wrapper(T, BulkyListAux);
datatype BulkyListAux<T> = Kons(set<T>, BulkyListAuxAux);
datatype BulkyListAuxAux<T> = GoBack(BulkyList);
codatatype Stream<T> = Next(head: T, tail: Stream<T>);
method M<T(==)>(x: T)
{ }
function method F<T>(x: BulkyList<T>, y: BulkyList<T>): int
{ if x == y then 5 else 7 } // this equality is allowed
function method G<T>(x: Dt<T>, y: Dt<T>): int
{ if x == y then 5 else 7 } // error: the equality is not allowed, because Dt<T> may not support equality
function method G'<T(==)>(x: Dt<T>, y: Dt<T>): int
{ if x == y then 5 else 7 } // fine
method Caller0(b: BulkyList, y: int) {
match (b) {
case Nothing =>
case Wrapper(t, bla) =>
var u;
if (y < 100) { u := t; }
// The following call is allowed, because it will be inferred that
// 'u' is of a type that supports equality
M(u);
}
}
method Caller1(d: Dt) {
match (d) {
case Nil =>
case Cons(t, rest) =>
M(t); // error: t may be of a type that does not support equality
}
}
method Caller2(co: Stream) {
var d := Cons(co, Nil);
Caller1(d); // case in point for the error in Caller1
}
}
// ----------------------------
module Gh {
datatype D = Nil | Cons(head: int, tail: D, ghost x: int)
method M(n: nat, b: bool, d: D, e: D, ghost g: bool)
ensures b ==> d == e; // fine, this is a ghost declaration
{
ghost var g := 0;
var h := 0;
if d == e { // fine, this is a ghost statement
g := g + 1;
} else {
assert !b;
}
if d == e { // error: not allowed to compare D's in a non-ghost context
h := h + 1;
}
if n != 0 {
M(n-1, b, d, e, d==e); // fine
M(n-1, d==e, d, e, false); // error, cannot pass in d==e like we do
}
GM(d==e, d, e); // fine -- we're calling a ghost method
var y0 := F(b, d==e);
var y1 := F(d==e, false); // error
}
function method F(b: bool, ghost g: bool): int { 6 }
ghost method GM(b: bool, d: D, e: D) // all equalities are fine in a ghost method
ensures b ==> d == e;
{
ghost var g := 0;
var h := 0;
if d == e {
g := g + 1;
} else {
assert !b;
}
if d == e {
h := h + 1;
}
}
}
|
