The Haskell School of Expression Learning Functional Programming through Multimedia

Recall that in Chapter 6 we used an infinite list to simulate a mathematical sequence used in the calculation or the perimeter of an ellipse. When a list is used in a context where it will always he infinite, it is commonly called a stream, Many problems can be elegantly, concisely, and efficiently expressed using streams, which we will explore in this chapter. With the power of streams there are also inherent dangers, which we will also explore. In the next chapter we will use streams in a central way in the implementation of a language for expressing reactive animations.

Lazy Evaluation

Because streams are never finite, it would seem natural to define a special polymorphic data type for them, such as:

Although we could certainly do this, it is more convenient to use Haskell lists to “simulate” streams by just never using the empty list constructor []. The main advantage of this approach is that we can then reuse many polymorphic functions already defined on lists rather than redefining them on a new data type.

In Chapter 6 we used list comprehensions to create the infinite list [2, 2.], but is there a more fundamental way to create this list? Here is one way:

Let's compute this value by calculation:

…

There is, of course, no end to this calculation, An important distinction exists, however, between this calculation and ones that we have labeled as “infinite loops” and given the value ⊥ in previous chapters: this calculation is producing useful information, namely the successive elements of a list. Its value is an infinite list, or stream, A stream contains an infinite amount of information, whereas ⊥ contains no information whatsoever.

Now consider the expression head twos.