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// RUN: %dafny /compile:0 /print:"%t.print" /dprint:"%t.dprint" "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
function Fib(n: int): int
requires 0 <= n;
ensures 0 <= Fib(n);
{
if n < 2 then n else
Fib(n-2) + Fib(n-1)
}
datatype List = Nil | Cons(int, List)
function Sum(a: List): int
ensures 0 <= Sum(a);
{
match a
case Nil => 0
case Cons(x, tail) => if x < 0 then 0 else Fib(x)
}
function FibWithoutPost(n: int): int
requires 0 <= n;
{
if n < 2 then n else
FibWithoutPost(n-2) + FibWithoutPost(n-1)
}
function SumBad(a: List): int
ensures 0 <= Sum(a); // this is still okay, because this is calling the good Sum
ensures 0 <= SumBad(a); // error: cannot prove postcondition
{
match a
case Nil => 0
case Cons(x, tail) => if x < 0 then 0 else FibWithoutPost(x)
}
function FibWithExtraPost(n: int): int
ensures 2 <= n ==> 0 <= FibWithExtraPost(n-1); // This is fine, because the definition of the function is discovered via canCall
ensures 1 <= n ==> 0 <= FibWithExtraPost(n-1); // Error: In the current implementation of Dafny, one needs to actually call the
// function in order to benefit from canCall. This may be improved in the future.
ensures 0 <= FibWithExtraPost(n);
{
if n < 0 then 0 else
if n < 2 then n else
FibWithExtraPost(n-2) + FibWithExtraPost(n-1)
}
function DivergentPost(n: int): int
requires 0 <= n;
ensures 1 <= n ==> DivergentPost(n-1) == DivergentPost(n-1);
ensures DivergentPost(2*n - n) == DivergentPost(2*(n+5) - 10 - n); // these are legal ways to denote the result value of the function
ensures DivergentPost(n+1) == DivergentPost(n+1); // error: call may not terminate
{
if n < 2 then n else
DivergentPost(n-2) + DivergentPost(n-1)
}
function HoldsAtLeastForZero(x: int): bool
ensures x == 0 ==> HoldsAtLeastForZero(x);
{
x < -2 // error: this does not hold for 0
}
// ----- Some functions that deal with let-such-that and if-then-else expressions and having them pass
// ----- the subrange test (which they didn't always do).
function IncA(x: nat): nat
ensures x < IncA(x);
{
if x == 17 then
18
else
var y :| x < y;
y
}
ghost method M() {
var z := IncA(10);
assert z != 0;
}
function IncB(i: nat): nat
{
var n :| n>i; n
}
function IncC(i: nat): int
ensures IncC(i)>=0;
{
var n :| n>i; n
}
/////////////////////////////////////////////////////////////
// Test :opaque functions
/////////////////////////////////////////////////////////////
// Test basic function hiding
function {:opaque} secret(x:int, y:int) : int
requires 0 <= x < 5;
requires 0 <= y < 5;
ensures secret(x, y) < 10;
{ x + y }
method test_secret()
{
assert secret(2, 3) >= 5; // Should fail because secret's body is hidden
reveal_secret();
assert secret(2, 3) == 5; // Should pass now that the body is "visible"
assert secret(4, 1) == 7; // Make sure it catches incorrect applications as well
}
// Check that opaque doesn't break recursion unrolling
// Also checks that opaque functions that do terminate are verified as such
function {:opaque} recursive_f(x:int) : int
requires x >= 0;
{
if x == 0 then 0
else 1 + recursive_f(x - 1)
}
method test_recursive_f()
{
if * {
assert recursive_f(4) == 4; // Should fail because body is hidden
} else {
reveal_recursive_f();
assert recursive_f(4) == 4; // Should pass now body is visible and can be unrolled
assert recursive_f(3) == 5; // Make sure it catches incorrect applications as well
}
}
// Check that opaque doesn't interfere with ensures checking
function {:opaque} bad_ensures(x:int, y:int):int
requires x >= 0 && y >= 0;
ensures bad_ensures(x, y) > 0;
{
x + y
}
// Check that opaque doesn't interfere with termination checking
function {:opaque} f(i:int):int
decreases i;
{
f(i) + 1
}
// Try a sneakier (nested) version of the test above
function {:opaque} g(i:int):int
decreases i;
{
h(i) + 1
}
function h(i:int):int
{
g(i)
}
// Check that using the reveal_ lemma to prove the well-definedness of a function
// in a lower SCC does not cause a soundness problem
function A(): int
ensures A() == 5;
{
reveal_B(); // error: should not be allowed to invoke reveal_B() here
6 // this result value is not what the postcondition specification says
}
function {:opaque} B(): int
ensures B() == 5;
{
A()
}
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