Can this Swift code be simplified?

Optional chaining can be used to condense the check into a single line.

Example:

let name_cache = NSCache<NSString, NSString>()
if let name = name_cache.object(forKey: "name") ?? (dictionary["name"] as? String) {
    name_cache.setObject(name, forKey: "name")
    self.name_text_field.text = name as String
}

This first tries to unwrap the value from name_cache. If the result is nil then it tries to unwrap the value from dictionary. If one of these has a value then name will be defined. The inner block will execute and set the cache value and the text field.

Advice: Encapsulating the cache and dictionary into a helper class would lead to cleaner separation of responsibilities. E.g.

Model

struct Model {
    var cache = NSCache<NSString, NSString>()
    var dictionary = Dictionary<String, String>()
    mutating func value(forKey key: String) -> String? {
        guard let value = cache.object(forKey: key) ?? dictionary[key] else {
            return nil
        }
        cache.setObject(value, forKey: key)
        return value
    }
}

Usage

var model = Model()
self.name_text_field.text = model.value(forKey: "name")