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|
/*
method ParallelStatement_Syntax()
{
parallel (i: int | 0 <= i < a.Length && i % 2 == 0) {
a[i] := a[(i + 1) % a.Length] + 3;
}
parallel (o | o in spine) {
o.f := o.f + Repr;
}
parallel (x, y | x in S && 0 <= y+x < 100) {
Lemma(x, y);
}
parallel (p | 0 <= p)
ensures F(p) <= Sum(p) * (p-1) + 100;
{
assert G(p);
ghost var t;
if (p % 2 == 0) {
assert G(p) == F(p+2);
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);
}
}
*/
class C {
var f: set<object>;
}
method ParallelStatement_Resolve(
a: array<int>,
spine: set<C>,
Repr: set<object>,
S: set<int>
)
requires a != null;
modifies a, spine;
{
parallel (i: int | 0 <= i < a.Length && i % 2 == 0) {
a[i] := a[(i + 1) % a.Length] + 3;
}
parallel (o | o in spine) {
o.f := o.f + Repr;
}
parallel (x, y | x in S && 0 <= y+x < 100) {
Lemma(x, y);
}
parallel (p | 0 <= p)
ensures F(p) <= Sum(p) * (p-1) + 100;
{
assert 0 <= G(p);
ghost var t;
if (p % 2 == 0) {
assert G(p) == F(p+2);
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);
}
}
method Lemma(x: int, y: int)
ghost method PowerLemma(x: int, y: int)
function F(x: int): int
function G(x: int): int
function H(x: int, y: int): int
function Sum(x: int): int
|
