I successfully got the Functor example to work like this:

    protocol Functor {
        typealias T
        typealias FunctorResult
        func map<P>(mappingFunction: T -> P) -> FunctorResult
    }
    
    extension Dictionary : Functor {
        func map<P>(mappingFunction: ValueType -> P) -> Dictionary<KeyType, P> {
            var newDict:Dictionary<KeyType, P> = [:]
            for (key, value) in self {
                newDict[key] = mappingFunction(value)
            }
            return newDict
        }
    }