Swift: Lazy take and takeWhile sequence functions

struct TakeSequenceView<Base : SequenceType> : SequenceType {
    let base: Base
    let n: Int
    
    init(_ base: Base, n: Int) {
        self.base = base
        self.n = n
    }
    
    func generate() -> GeneratorOf<Base.Generator.Element> {
        var i = 0
        var g = base.generate()
        
        return GeneratorOf {
            i++ < self.n ? g.next() : nil
        }
    }
}

struct TakeWhileSequenceView<Base : SequenceType> : SequenceType {
    let base: Base
    let predicate: Base.Generator.Element -> Bool
    
    init(_ base: Base, predicate: Base.Generator.Element -> Bool) {
        self.base = base
        self.predicate = predicate
    }
    
    func generate() -> GeneratorOf<Base.Generator.Element> {
        var g = base.generate()
        
        return GeneratorOf {
            if let x = g.next() {
                if self.predicate(x) {
                    return x
                }
            }
            
            return nil
        }
    }
}

extension LazySequence {
    func take(n: Int) -> LazySequence<TakeSequenceView<LazySequence>> {
        return lazy(TakeSequenceView(self, n: n))
    }
    
    func takeWhile(predicate: S.Generator.Element -> Bool) -> LazySequence<TakeWhileSequenceView<LazySequence>> {
        return lazy(TakeWhileSequenceView(self, predicate))
    }
}

extension LazyForwardCollection {
    func take(n: Int) -> LazySequence<TakeSequenceView<LazyForwardCollection>> {
        return lazy(TakeSequenceView(self, n: n))
    }
    
    func takeWhile(predicate: S.Generator.Element -> Bool) -> LazySequence<TakeWhileSequenceView<LazyForwardCollection>> {
        return lazy(TakeWhileSequenceView(self, predicate))
    }
}

extension LazyBidirectionalCollection {
    func take(n: Int) -> LazySequence<TakeSequenceView<LazyBidirectionalCollection>> {
        return lazy(TakeSequenceView(self, n: n))
    }
    
    func takeWhile(predicate: S.Generator.Element -> Bool) -> LazySequence<TakeWhileSequenceView<LazyBidirectionalCollection>> {
        return lazy(TakeWhileSequenceView(self, predicate))
    }
}

extension LazyRandomAccessCollection {
    func take(n: Int) -> LazySequence<TakeSequenceView<LazyRandomAccessCollection>> {
        return lazy(TakeSequenceView(self, n: n))
    }
    
    func takeWhile(predicate: S.Generator.Element -> Bool) -> LazySequence<TakeWhileSequenceView<LazyRandomAccessCollection>> {
        return lazy(TakeWhileSequenceView(self, predicate))
    }
}


lazy(1...10).take(3).array // [1, 2, 3]

var prev = 0
var lstw = lazy([1, 2, 3, 2, 1]).takeWhile { (x: Int) in
    if (x < prev) {
        return false
    }
    prev = x
    return true
}.array // => [1, 2, 3]

Just to help the next person who looks at this, unfortunately prefix isn't lazy.