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// RUN: %dafny /compile:3 "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
// this is a rather verbose version of the VectorUpdate method
method VectorUpdate<A>(N: int, a : array<A>, f : (int,A) -> A)
requires a != null
requires N == a.Length
requires forall j :: 0 <= j < N ==> f.requires(j,a[j])
requires forall j :: 0 <= j < N ==> a !in f.reads(j,a[j])
modifies a
ensures forall j :: 0 <= j < N ==> a[j] == f(j,old(a[j]))
{
var i := 0;
while i < N
invariant 0 <= i <= N
invariant forall j :: i <= j < N ==> f.requires(j,a[j])
invariant forall j :: 0 <= j < N ==> f.requires(j,old(a[j]))
invariant forall j :: i <= j < N ==> a !in f.reads(j,a[j])
invariant forall j :: i <= j < N ==> a[j] == old(a[j])
invariant forall j :: 0 <= j < i ==> a[j] == f(j,old(a[j]))
{
a[i] := f(i,a[i]);
i := i + 1;
}
}
// here's a shorter version of the method above
method VectorUpdate'<A>(a : array<A>, f : (int,A) -> A)
requires a != null
requires forall j :: 0 <= j < a.Length ==> a !in f.reads(j,a[j]) && f.requires(j,a[j])
modifies a
ensures forall j :: 0 <= j < a.Length ==> a[j] == f(j,old(a[j]))
{
var i := 0;
while i < a.Length
invariant 0 <= i <= a.Length
invariant forall j :: i <= j < a.Length ==> a[j] == old(a[j])
invariant forall j :: 0 <= j < i ==> a[j] == f(j,old(a[j]))
{
a[i] := f(i,a[i]);
i := i + 1;
}
}
// here's yet another version
method VectorUpdate''<A>(a : array<A>, f : (int,A) -> A)
requires a != null
requires forall j :: 0 <= j < a.Length ==> a !in f.reads(j,a[j]) && f.requires(j,a[j])
modifies a
ensures forall j :: 0 <= j < a.Length ==> a[j] == f(j,old(a[j]))
{
forall i | 0 <= i < a.Length {
a[i] := f(i,a[i]);
}
}
method Main()
{
var v := new int[10];
// Hey, works as an initialiser:
VectorUpdate(10, v, (i,_) => i);
PrintArray(v);
VectorUpdate(10, v, (_,x) => x + 1);
PrintArray(v);
// Phew, now they are all positive, so we can do:
VectorUpdate(10, v, (_,x) requires x != 0 => 100 / x);
PrintArray(v);
var u := new int[10];
// Hey, works as a copy as well!
VectorUpdate(10, u, (i,_) requires 0 <= i < 10 reads v => v[i]);
PrintArray(u);
// Having some fun with the index:
var z := new int[9];
VectorUpdate(9, z, (i,_) requires 0 <= i < 9 reads u => u[i] + u[i+1]);
PrintArray(z);
assert z[8] == 21; // voila, the prover also knows what's going on
}
method PrintArray(a : array<int>)
requires a != null
{
var i := 0;
while i < a.Length {
if i != 0 {
print ", ";
}
print a[i];
i := i + 1;
}
print "\n";
}
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