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domain Option__Node {
unique function Option__Node__Some(): Option__Node
unique function Option__Node__None(): Option__Node
function variantOfOptionNode(self: Ref): Option__Node
function isOptionNode(self: Ref): Bool
axiom ax_variantOfOptionNodeChoices {
forall x: Ref :: { variantOfOptionNode(x) }
(variantOfOptionNode(x) == Option__Node__Some() || variantOfOptionNode(x) == Option__Node__None())
}
axiom ax_isCounterState {
forall x: Ref :: { variantOfOptionNode(x) }
isOptionNode(x) == (variantOfOptionNode(x) == Option__Node__Some() ||
variantOfOptionNode(x) == Option__Node__None())
}
}
predicate validOption(this: Ref) {
isOptionNode(this) &&
variantOfOptionNode(this) == Option__Node__Some() ==> (
acc(this.Option__Node__Some__1, write) &&
acc(validNode(this.Option__Node__Some__1))
)
}
field Option__Node__Some__1: Ref
field Node__v: Int
field Node__next: Ref
predicate validNode(this: Ref) {
acc(this.Node__v) &&
acc(this.Node__next) &&
acc(validOption(this.Node__next))
}
function length(this: Ref): Int
requires acc(validNode(this), write)
ensures result >= 1
{
(unfolding acc(validNode(this), write) in
unfolding acc(validOption(this.Node__next)) in
(variantOfOptionNode(this.Node__next) == Option__Node__None()) ?
1 : 1 + length(this.Node__next.Option__Node__Some__1)
)
}
function itemAt(this: Ref, i: Int): Int
requires acc(validNode(this), write)
requires 0 <= i && i < length(this)
{
unfolding acc(validNode(this), write) in unfolding acc(validOption(this.Node__next)) in (
(i == 0) ?
this.Node__v:
(variantOfOptionNode(this.Node__next) == Option__Node__Some()) ?
itemAt(this.Node__next.Option__Node__Some__1, i-1) : this.Node__v
)
}
function sum(this$1: Ref): Int
requires acc(validNode(this$1), write)
{
(unfolding acc(validNode(this$1), write) in unfolding acc(validOption(this$1.Node__next)) in
(variantOfOptionNode(this$1.Node__next) == Option__Node__None()) ? this$1.Node__v : this$1.Node__v + sum(this$1.Node__next.Option__Node__Some__1))
}
method append(this: Ref, val: Int)
requires acc(validNode(this), write)
ensures acc(validNode(this), write) /* POST1 */
ensures length(this) == (old(length(this)) + 1) /* POST2 */
ensures (forall i: Int :: (0 <= i && i < old(length(this))) ==> (itemAt(this, i) == old(itemAt(this, i)))) /* POST3 */
ensures itemAt(this, length(this) - 1) == val /* POST4 */
ensures true ==> true
{
var tmp_node: Ref
var tmp_option: Ref
unfold acc(validNode(this), write)
unfold acc(validOption(this.Node__next), write)
if (variantOfOptionNode(this.Node__next) == Option__Node__None()) {
tmp_node := new(Node__next, Node__v)
tmp_node.Node__next := null
tmp_node.Node__v := val
assume variantOfOptionNode(tmp_node.Node__next) == Option__Node__None()
fold acc(validOption(tmp_node.Node__next))
fold acc(validNode(tmp_node), write)
tmp_option := new(Option__Node__Some__1)
tmp_option.Option__Node__Some__1 := tmp_node
assume variantOfOptionNode(tmp_option) == Option__Node__Some()
fold acc(validOption(tmp_option))
this.Node__next := tmp_option
unfold validOption(tmp_option)
assert length(tmp_node) == 1 /* TODO: Required by Silicon, POST2 fails otherwise */
assert itemAt(tmp_node, 0) == val /* TODO: Required by Silicon, POST4 fails otherwise */
fold validOption(tmp_option)
} else {
append(this.Node__next.Option__Node__Some__1, val)
fold acc(validOption(this.Node__next), write)
}
fold acc(validNode(this), write)
}
method prepend(tail: Ref, val: Int) returns (res: Ref)
requires acc(validNode(tail))
ensures acc(validNode(res))
//ensures acc(validNode(tail))
ensures length(res) == old(length(tail)) + 1
ensures (forall i: Int :: (1 <= i && i < length(res)) ==> (itemAt(res, i) == old(itemAt(tail, i-1)))) /* POST3 */
ensures itemAt(res, 0) == val
{
var tmp_option: Ref
res := new(Node__v, Node__next)
res.Node__v := val
tmp_option := new(Option__Node__Some__1)
tmp_option.Option__Node__Some__1 := tail
assume variantOfOptionNode(tmp_option) == Option__Node__Some()
res.Node__next := tmp_option
assert acc(validNode(tail))
fold acc(validOption(res.Node__next))
fold acc(validNode(res))
}
method length_iter(list: Ref) returns (len: Int)
requires acc(validNode(list), write)
ensures old(length(list)) == len
// TODO we have to preserve this property
// ensures acc(validNode(list))
{
var curr: Ref := list
var tmp: Ref := list
len := 1
unfold acc(validNode(curr))
unfold acc(validOption(curr.Node__next))
while(variantOfOptionNode(curr.Node__next) == Option__Node__Some())
invariant acc(curr.Node__v)
invariant acc(curr.Node__next)
invariant (variantOfOptionNode(curr.Node__next) == Option__Node__Some() ==> (
acc(curr.Node__next.Option__Node__Some__1, write) &&
acc(validNode(curr.Node__next.Option__Node__Some__1))
))
invariant (variantOfOptionNode(curr.Node__next) == Option__Node__Some() ==> len + length(curr.Node__next.Option__Node__Some__1) == old(length(list)))
invariant (variantOfOptionNode(curr.Node__next) == Option__Node__None() ==> len == old(length(list)))
{
assert acc(validNode(curr.Node__next.Option__Node__Some__1))
len := len + 1
tmp := curr
curr := curr.Node__next.Option__Node__Some__1
unfold acc(validNode(curr))
unfold acc(validOption(curr.Node__next))
}
}
method t1()
{
var l: Ref
l := new(Node__v, Node__next)
l.Node__next := null
l.Node__v := 1
assume variantOfOptionNode(l.Node__next) == Option__Node__None()
fold validOption(l.Node__next)
fold validNode(l)
assert length(l) == 1
assert itemAt(l, 0) == 1
append(l, 7)
assert itemAt(l, 1) == 7
assert itemAt(l, 0) == 1
assert length(l) == 2
l := prepend(l, 10)
assert itemAt(l, 2) == 7
assert itemAt(l, 1) == 1
assert itemAt(l, 0) == 10
assert length(l) == 3
//assert sum(l) == 18
}
method t2(l: Ref) returns (res: Ref)
requires acc(validNode(l), write)
ensures acc(validNode(res), write)
ensures length(res) > old(length(l))
{
res := prepend(l, 10)
}
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