Question

我正在尝试在Idris中实现McCarthy91功能并证明它的一些属性（完整代码为here）。但我在这里遇到了一个问题。

该功能通过分为两种情况来定义：＆gt; 100和＆lt; = 100.为了达到这个目的，我定义了一个类型级函数isLte（几乎和标准库中的函数一样）：

data (<=): (x, y: Peano) -> Type where
  OLte: (x: Peano) -> O <= x
  SLte: x <= y -> ((++)x) <= ((++)y)

total
isLte: (x, y: Peano) -> Result (x <= y) ((++)y <= x)
isLte O x = Yes (OLte x)
isLte ((++)x) O = No (SLte (OLte x))
isLte ((++)x) ((++)y) = case isLte x y of
  No revLteProof => No (SLte revLteProof)
  Yes lteProof => Yes (SLte lteProof)

mcCarthy: Peano -> Peano
mcCarthy n = case n `isLte` Main.hundred of
  No hundredOneLteN => totalMinus (trans tenLteHundredOne hundredOneLteN)
  Yes lteProof => mcCarthy (mcCarthy (n + Main.eleven))

我想要证明的内容可以写成：

mcCarthyIdentity2: (hundredOneLteX: Main.hundredOne <= x) -> mcCarthy x = totalMinus (trans Main.tenLteHundredOne hundredOneLteX)

mcCarthyIdentity: n <= Main.hundred -> mcCarthy x = Main.ninetyOne

问题是，我如何告诉Idris n <= Main.hundred，例如，mcCarthy n会让rewrite落入案件的第二个分支？简单地Refl或total f: Nat -> Nat f x = if x > 10 then 1 else 2 total proofOfF: x < 4 -> f x = 2 -- What to write?似乎无效。

一个更简单的问题（可能或可能不直接相关）可以证明：

class MenuViewController1: UIViewController,UITableViewDataSource, UITableViewDelegate{

    /**
     *  Array to display menu options
     */
    @IBOutlet var tblMenuOptions : UITableView!

    /**
     *  Transparent button to hide menu
     */
    @IBOutlet var btnCloseMenuOverlay : UIButton!

    /**
     *  Array containing menu options
     */
    var arrayMenuOptions = [Dictionary<String,String>]()

    /**
     *  Menu button which was tapped to display the menu
     */
    var btnMenu : UIButton!

    /**
     *  Delegate of the MenuVC
     */
    var delegate : SlideMenuDelegate?

  //  var delegateP: Profile?

    @IBOutlet weak var userProfilePhoto: UIImageView!

    @IBOutlet weak var userName: UILabel!

    override func viewDidLoad() {
        super.viewDidLoad()
        tblMenuOptions.tableFooterView = UIView()
        // Do any additional setup after loading the view.


        //let name = userName.text
        self.delegateP?.name_changed(name: userName.text!)

         }

    override func didReceiveMemoryWarning() {
        super.didReceiveMemoryWarning()
        // Dispose of any resources that can be recreated.
    }

    override func viewWillAppear(_ animated: Bool) {
        super.viewWillAppear(animated)
        updateArrayMenuOptions()
    }

    func updateArrayMenuOptions(){
        arrayMenuOptions.append(["title":"Home", "icon":"HomeIcon"])
        arrayMenuOptions.append(["title":"LogIn", "icon":"LogIn"])
        arrayMenuOptions.append(["title":"House Owner","icon":"House Owner"])
        arrayMenuOptions.append(["title":"ShortTerm", "icon":"ShortTerm"])
        arrayMenuOptions.append(["title":"LongTerm","icon":"LongTerm"])

        tblMenuOptions.reloadData()
    }

    @IBAction func onCloseMenuClick(_ button:UIButton!){
        btnMenu.tag = 0

        if (self.delegate != nil) {
            var index = Int32(button.tag)
            if(button == self.btnCloseMenuOverlay){
                index = -1
            }
            delegate?.slideMenuItemSelectedAtIndex(index)
        }

        UIView.animate(withDuration: 0.3, animations: { () -> Void in
            self.view.frame = CGRect(x: -UIScreen.main.bounds.size.width, y: 0, width: UIScreen.main.bounds.size.width,height: UIScreen.main.bounds.size.height)
            self.view.layoutIfNeeded()
            self.view.backgroundColor = UIColor.clear
        }, completion: { (finished) -> Void in
            self.view.removeFromSuperview()
            self.removeFromParentViewController()
        })
    }

    func tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {
        let cell : UITableViewCell = tableView.dequeueReusableCell(withIdentifier: "cellMenu")!
        cell.selectionStyle = UITableViewCellSelectionStyle.none
        cell.layoutMargins = UIEdgeInsets.zero
        cell.preservesSuperviewLayoutMargins = false

        cell.backgroundColor = UIColor.clear


        let lblTitle : UILabel = cell.contentView.viewWithTag(101) as! UILabel
        let imgIcon : UIImageView = cell.contentView.viewWithTag(100) as! UIImageView

        imgIcon.image = UIImage(named: arrayMenuOptions[indexPath.row]["icon"]!)
        lblTitle.text = arrayMenuOptions[indexPath.row]["title"]!

        return cell
    }

    func tableView(_ tableView: UITableView, didSelectRowAt indexPath: IndexPath) {
        let btn = UIButton(type: UIButtonType.custom)
        btn.tag = indexPath.row
        self.onCloseMenuClick(btn)
    }

    func tableView(_ tableView: UITableView, numberOfRowsInSection section: Int) -> Int {
        return arrayMenuOptions.count
    }

    func numberOfSections(in tableView: UITableView) -> Int {
        return 1;
    }
}

我怎样才能真正告诉Idris条件与分支有关？

如何用Idris中的条件分支证明？

0 个答案: