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// RUN: %dafny /compile:0 "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
datatype Nat = Zero | Suc(Nat)
predicate Even(n: Nat)
{
match n
case Zero => true
case Suc(Zero) => false
case Suc(Suc(p)) => Even(p)
}
method checkEven(n: Nat) {
assert Even(Zero) == true;
assert Even(Suc(Zero)) == false;
assert Even(Suc(Suc(n))) == Even(n);
}
datatype List<T> = Nil | Cons(T, List<T>)
function last<T>(xs: List<T>): T
requires xs != Nil
{
match xs
case Cons(y, Nil) => y
case Cons(y, Cons(z, zs)) => last(Cons(z, zs))
}
method checkLast<T>(y: T) {
assert last(Cons(y, Nil)) == y;
assert last(Cons(y, Cons(y, Nil))) == last(Cons(y, Nil));
}
function minus(x: Nat, y: Nat): Nat
{
match (x, y)
case (Zero, _) => Zero
case (Suc(_), Zero) => x
case (Suc(a), Suc(b)) => minus(a, b)
}
method checkMinus(x:Nat, y: Nat) {
assert minus(Suc(x), Suc(y)) == minus(x,y);
}
// nested match statement
method Last<T>(xs: List<T>) returns (x: T)
requires xs != Nil
{
match xs {
case Cons(y, Nil) => x:= y;
case Cons(y, Cons(z, zs)) => x:=Last(Cons(z, zs));
}
}
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