006-parse_nested_parens.dfy

method parse_paren_group(s : string) returns (max_depth : int)
    // pre-conditions-start
    requires forall i :: i >= 0 && i < |s| ==> s[i] == '(' || s[i] == ')'
    // pre-conditions-end
    // post-conditions-start
    ensures max_depth >= 0
    // post-conditions-end
{
    // impl-start
    var depth: int := 0;
    max_depth := 0;
    for i := 0 to |s|
    {
        var c: char := s[i];
        if (c == '(') {
            depth := depth + 1;
            if (depth > max_depth) {
                max_depth := depth;
            }
        }
        else {
            depth := depth - 1;
        }
    }
    // impl-end
}

method split(s : string) returns (res : seq<string>)
    // pre-conditions-start
    requires forall i :: i >= 0 && i < |s| ==> s[i] == '(' || s[i] == ')' || s[i] == ' '
    // pre-conditions-end
    // post-conditions-start
    ensures forall s1 :: s1 in res ==> (forall i :: i >= 0 && i < |s1| ==> s1[i] == '(' || s1[i] == ')') && |s1| > 0
    // post-conditions-end
{
    // impl-start
    res := [];
    var current_string : string := "";
    for i := 0 to |s|
        // invariants-start
        invariant forall j :: j >= 0 && j < |current_string| ==> current_string[j] == '(' || current_string[j] == ')'
        invariant forall s1 :: s1 in res ==> (forall j :: j >= 0 && j < |s1| ==> s1[j] == '(' || s1[j] == ')') && |s1| > 0
        // invariants-end
    {
        if (s[i] == ' ')
        {
            if (current_string != "") {
                res := res + [current_string];
                current_string := "";
            }
        }
        else
        {
            current_string := current_string + [s[i]];
        }
    }
    if (current_string != "") {
        res := res + [current_string];
        current_string := "";
    }
    // impl-end
}

method parse_nested_parens(paren_string: string) returns (res : seq<int>)
    // pre-conditions-start
    requires forall i :: i >= 0 && i < |paren_string| ==> paren_string[i] == '(' || paren_string[i] == ')' || paren_string[i] == ' '
    // pre-conditions-end
    // post-conditions-start
    ensures forall x :: x in res ==> x >= 0
    // post-conditions-end
{
    // impl-start
    var strings : seq<string> := split(paren_string);
    res := [];
    for i := 0 to |strings|
        // invariants-start
        invariant forall x :: x in res ==> x >= 0
        // invariants-end
    {
        var cur : int := parse_paren_group(strings[i]);
        res := res + [cur];
    }
    // impl-end
}