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class C<U(==)> {
method M<T>(x: T, u: U) returns (y: T)
ensures x == y && u == u;
{
y := x;
}
function method F<X(==)>(x: X, u: U): bool
{
x == x && u == u
}
method Main(u: U)
{
var t := F(3,u) && F(this,u);
var kz := M(t,u);
var a := G();
assert kz && (a || !a);
}
method G<Y>() returns (a: Y)
{
}
}
class SetTest {
method Add<T>(s: set<T>, x: T) returns (t: set<T>)
ensures t == s + {x};
{
t := s + {x};
}
method Good()
{
var s := {2, 5, 3};
var t := Add(s, 7);
assert {5,7,2,3} == t;
}
method Bad()
{
var s := {2, 50, 3};
var t := Add(s, 7);
assert {5,7,2,3} == t; // error
}
}
class SequenceTest {
method Add<T>(s: seq<T>, x: T) returns (t: seq<T>)
ensures t == s + [x];
{
t := s + [x];
}
method Good()
{
var s := [2, 5, 3];
var t := Add(s, 7);
assert [2,5,3,7] == t;
}
method Bad()
{
var s := [2, 5, 3];
var t := Add(s, 7);
assert [2,5,7,3] == t || [2,5,3] == t; // error
}
}
// -------------------------
class CC<T> {
var x: T;
method M(c: CC<T>, z: T) returns (y: T)
requires c != null;
modifies this;
ensures y == c.x && x == z;
{
x := c.x;
x := z;
y := c.x;
}
}
class CClient {
method Main() {
var c := new CC<int>;
var k := c.x + 3;
if (c.x == c.x) {
k := k + 1;
}
var m := c.x;
if (m == c.x) {
k := k + 1;
}
c.x := 5;
c.x := c.x;
var z := c.M(c, 17);
assert z == c.x;
}
}
// -------------------------
static function IsCelebrity<Person>(c: Person, people: set<Person>): bool
requires c == c || c in people;
{
false
}
method FindCelebrity3(people: set<int>, ghost c: int)
requires IsCelebrity(c, people); // once upon a time, this caused the translator to produce bad Boogie
{
ghost var b: bool;
b := IsCelebrity(c, people);
b := F(c, people);
}
static function F(c: int, people: set<int>): bool
requires IsCelebrity(c, people);
{
false
}
function RogerThat<G>(g: G): G
{
g
}
function Cool(b: bool): bool
{
b
}
function Rockin'<G>(g: G): G
{
var h := g;
h
}
function Groovy<G>(g: G, x: int): G
{
var h := g;
if x == 80 then
RogerThat(h)
else
[h][0]
}
method IsRogerCool(n: int)
requires RogerThat(true); // once upon a time, this caused the translator to produce bad Boogie
{
if (*) {
assert Cool(2 < 3 && n < n && n < n+1); // the error message here will peek into the argument of Cool
} else if (*) {
assert RogerThat(2 < 3 && n < n && n < n+1); // same here; cool, huh?
} else if (*) {
assert Rockin'(false); // error
} else if (*) {
assert Groovy(n < n, 80); // error
} else if (*) {
assert Groovy(n + 1 <= n, 81); // error
}
}
method LoopyRoger(n: int)
{
var i := 0;
while (i < n)
invariant RogerThat(0 <= n ==> i <= n);
{
i := i + 1;
}
i := 0;
while (i < n)
invariant RogerThat(0 <= n ==> i <= n); // error: failure to maintain loop invariant
{
i := i + 2;
}
}
// ----------------------
class TyKn_C<T> {
var x: T;
function G(): T
reads this;
{
x
}
method M() returns (t: T)
{
}
}
class TyKn_K {
function F(): int { 176 }
}
method TyKn_Main(k0: TyKn_K) {
var c := new TyKn_C<TyKn_K>;
var k1: TyKn_K;
assert k0 != null ==> k0.F() == 176;
assert k1 != null ==> k1.F() == 176;
assert c.x != null ==> c.x.F() == 176; // the Dafny encoding needs the canCall mechanism to verify this
assert c.G() != null ==> c.G().F() == 176; // ditto
var k2 := c.M();
assert k2 != null ==> k2.F() == 176; // the canCall mechanism does the trick here, but so does the encoding
// via k2's where clause
}
// ------------------- there was once a bug in the handling of the following example
module OneLayer
{
datatype wrap<V> = Wrap(V);
}
module TwoLayers
{
import OneLayer;
datatype wrap2<T> = Wrap2(get: OneLayer.wrap<T>);
function F<U>(w: wrap2<U>) : OneLayer.wrap<U>
{
match w
case Wrap2(a) => a
}
function G<U>(w: wrap2<U>) : OneLayer.wrap<U>
{
match w
case Wrap2(a) => w.get
}
function H<U>(w: wrap2<U>) : OneLayer.wrap<U>
{
w.get
}
}
// ---------------------------------------------------------------------
datatype List<T> = Nil | Cons(T, List)
predicate InList<T>(x: T, xs: List<T>)
predicate Subset(xs: List, ys: List)
{
forall x :: InList(x, xs) ==> InList(x, ys)
}
ghost method ListLemma_T(xs: List, ys: List)
requires forall x :: InList(x, xs) ==> InList(x, ys);
{
assert Subset(xs, ys);
}
ghost method ammeLtsiL_T(xs: List, ys: List)
requires Subset(xs, ys);
{
assert forall x :: InList(x, xs) ==> InList(x, ys);
}
ghost method ListLemma_int(xs: List<int>, ys: List<int>)
requires forall x :: InList(x, xs) ==> InList(x, ys);
{
assert Subset(xs, ys);
}
ghost method ammeLtsiL_int(xs: List<int>, ys: List<int>)
requires Subset(xs, ys);
{
assert forall x :: InList(x, xs) ==> InList(x, ys);
}
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