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datatype D = Green | Blue | Red | Purple;
method M0(d: D)
{
match (d) { // error: two missing cases: Blue and Purple
case Green =>
case Red =>
}
}
method M1(d: D)
requires d != D.Blue;
{
match (d) { // error: missing case: Purple
case Green =>
case Red =>
}
}
method M2(d: D)
requires d != D.Blue && d != D.Purple;
{
match (d) {
case Green =>
case Red =>
}
}
method M3(d: D)
requires d == D.Green;
{
if (d != D.Green) {
match (d) {
// nothing here
}
}
}
method M4(d: D)
requires d == D.Green || d == D.Red;
{
if (d != D.Green) {
match (d) { // error: missing case Red
// nothing here
}
}
}
function F0(d: D): int
{
match (d) // error: missing cases Red
case Purple => 80
case Green => 0
case Blue => 2
}
function F1(d: D, x: int): int
requires x < 100;
requires d == D.Red ==> x == 200; // (an impossibility, given the first precondition, so d != Red)
{
match (d)
case Purple => 80
case Green => 0
case Blue => 2
}
// --------------- alternative statements ---------------------
method A0(x: int) returns (r: int)
ensures 0 <= r;
{
if { // error: missing case (x == 0)
case x < 0 => r := 12;
case 0 < x => r := 13;
}
}
method A1(x: int) returns (r: int)
ensures 0 <= r;
{
if {
case x <= 0 => r := 12;
case 0 <= x => r := 13;
}
}
method DutchFlag(A: array<int>, N: int, l: int, r: int) returns (result: int)
requires A != null && N == A.Length;
requires 0 <= l && l+2 <= r && r <= N;
modifies A;
ensures l <= result && result < r;
ensures forall k, j :: l <= k && k < result && result <= j && j < r ==> A[k] <= A[j];
ensures forall k :: l <= k && k < result ==> A[k] <= old(A[l]);
ensures forall k :: result <= k && k < r ==> old(A[l]) <= A[k];
{
var pv := A[l];
var i := l;
var j := r-1;
A[l], A[j] := A[j], A[l];
while (i < j)
invariant l <= i && i <= j && j < r;
invariant forall k :: l <= k && k < i ==> A[k] <= pv;
invariant forall k :: j <= k && k < r ==> pv <= A[k];
{
if {
case A[i] <= pv =>
i := i + 1;
case pv <= A[j-1] =>
j := j - 1;
case A[j-1] < pv && pv < A[i] =>
A[j-1], A[i] := A[i], A[j-1];
assert A[i] < pv && pv < A[j-1];
i, j := i + 1, j - 1;
}
}
result := i;
}
// --------------- alternative loop statements ---------------
method B(x: int) returns (r: int)
ensures r == 0;
{
r := x;
while
decreases if 0 <= r then r else -r;
{
case r < 0 =>
r := r + 1;
case 0 < r =>
r := r - 1;
}
}
// --------------- breaks ---------------
method TheBreaker_AllGood(M: int, N: int, O: int)
{
var a, b, c, d, e;
var i := 0;
while (i < M)
{
var j := 0;
label InnerHasLabel:
while (j < N)
{
var u := 2000;
label MyLabelBlock:
label MyLabelBlockAgain:
if (*) {
a := 15; break;
} else if (*) {
b := 12; break break;
} else if (*) {
c := 21; break InnerHasLabel;
} else if (*) {
while (u < 10000) {
u := u + 3;
if (*) { u := 1998; break MyLabelBlock; }
if (*) { u := 1998; break MyLabelBlockAgain; }
}
assert 10000 <= u;
u := 1998;
} else {
u := u - 2;
}
assert u == 1998;
var k := 0;
while
decreases O - k;
{
case k < O && k % 2 == 0 =>
d := 187; break;
case k < O =>
if (*) { e := 4; break InnerHasLabel; }
if (*) { e := 7; break; }
if (*) { e := 37; break break break; }
k := k + 1;
}
assert O <= k || d == 187 || e == 7;
j := j + 1;
}
assert N <= j || a == 15 || c == 21 || e == 4;
i := i + 1;
}
assert M <= i || b == 12 || e == 37;
}
method TheBreaker_SomeBad(M: int, N: int, O: int)
{
var a, b, c, d, e;
var i := 0;
while (i < M)
{
var j := 0;
label InnerHasLabel:
while (j < N)
{
var u := 2000;
label MyLabelBlock:
label MyLabelBlockAgain:
if (*) {
a := 15; break;
} else if (*) {
b := 12; break break;
} else if (*) {
c := 21; break InnerHasLabel;
} else if (*) {
while (u < 10000) {
u := u + 3;
if (*) { u := 1998; break MyLabelBlock; }
if (*) { u := 1998; break MyLabelBlockAgain; }
}
assert u < 2000; // error (and no way to get past this assert statement)
} else {
u := u - 2;
}
assert u == 1998;
var k := 0;
while
decreases O - k;
{
case k < O && k % 2 == 0 =>
d := 187; break;
case k < O =>
if (*) { e := 4; break InnerHasLabel; }
if (*) { e := 7; break; }
if (*) { e := 37; break break break; }
k := k + 1;
}
assert O <= k || e == 7; // error: d == 187
j := j + 1;
}
assert N <= j || c == 21 || e == 4; // error: a == 15
i := i + 1;
}
assert M <= i || b == 12; // error: e == 37
}
|
