Lazy evaluation in Haskell

This article is part of a series on Haskell about how easy it is to define infinite structures in really concise ways. Lazy evaluation is an evaluation strategy that is the foundation of many features of haskell, from performance to expressiveness. In this first article, we explore different evaluation strategies found in other languages, how they compare to Haskell's and their benefits and drawbacks.

Evaluation strategies

Call me by your value

When discussing different families of programming languages, we sometimes use the phrases call-by-value to refer to how parameters are passed to a function when it is called. Consider the following code in a generic language

def f(a, b):
  return a * 2

If we say the language is call-by-value we mean that the variables a and b are evaluated before copies of them are passed to the function f. For instance, if we called f with arguments a = 2 + 3 and b = 3 * 3 the following would happen in a call-by-value language:

  f(a, b)
= f((2 + 3), (3 * 3))
= f(5, (3 * 3))
= f(5, 9)
= 5 * 2
= 10

It takes roughly 5 steps to compute the value f(a, b). Observe that even though the value of f is only dependent on the value of a, the parameter b is still evaluated. We call this evaluation strategy strict, because it does not care about the usefulness of the values, it just computes everything as a very stubborn robot would do. This is the case with some low-level languages like C.1

Call me by your name

What if we delayed evaluation until the parameters were actually needed? We call this call-by-name and it is an example of a non-strict evaluation strategy. Let’s look at how the previous computation would look like with a call-by-name approach:

  f(a, b)
= f((2 + 3), (3 * 3))
= (2 + 3) * 2
= 5 * 2
= 10

Wow! We saved one step! This is not too much but suppose that a and b weren’t simple arithmetic expressions but complex computations instead. Then not computing b would certainly be beneficial. Is this always the case? Unfortunately, it turns out, it isn’t. Look at the following definition and compare the two evaluations:

def square(a):
  return a * a

-- Call-by-value (strict) evaluation
  square(a)
= square((2 + 3))
= square(5)
= 5 * 5
= 25

-- Call-by-name (non-strict) evaluation
  square(a)
= square((2 + 3))
= (2 + 3) * (2 + 3)
= 5 * (2 + 3)
= 5 * 5
= 10

Yikes! That’s one more step. Now a natural question is, which evaluation strategy makes more sense? Call-by-name seems better since unused values are not computed… Also, why did we calculate (2 + 3) twice? Couldn’t we have stored the value for the second calculation?

Call me lazy

Turns out if we add sharing to call-by-name, this strategy will never take more steps to evaluate an expression than call-by-value. We call this call-by-need or lazy evaluation in the context of Haskell. Call-by-need is also a form of non-strict evaluation but has this added benefit of never introducing a performance penalty (well, at least in the number of steps2).

Let’s look at how the previous examples would look like if we used call-by-need.

  f(a)
= f((2 + 3))
= (2 + 3) * 2
= 5 * 2
= 10

  square(a)
= square((2 + 3))
= (2 + 3) * (2 + 3)
= 5 * 5
= 10

We can see that in both cases the evaluation takes fewer steps than call-by-name or call-by-value.

Closing words

Call-by-need or lazy evaluation is central to both the performance and expressiveness of the Haskell language. In addition, the Haskell compiler has pureness and a strong type system at its disposal, enabling it to make much more aggressive optimisations than would be possible in other languages. More simply, expressiveness in Haskell does not come with a performance price to pay.

In the following articles we will apply lazy evaluation to create infinite structures.

Some theoretical considerations

Maybe, you just became very worried. Will the incorporation of sharing yield the same results as call-by-value or will we get different results for both strategies. Well, you have nothing (well, almost nothing) to worry about. It turns out that if functions are pure, i.e. they always return the same output given the same inputs, the Church-Rosser theorem 3 guarantees that both computations will yield the same results. It is natural that functional languages, such as Haskell, incorporate this evaluation strategy as they are mostly pure. Impure parts such as IO, networking or randomness use a different evaluation strategy so that no unexpected consequences arise.

If you want to read more about evaluation strategies, you can check out this wikipedia article

  1. Although in some languages we may substitute call-by-name with call-by-reference, the idea of strict evaluation still applies — all parameters are evaluated before the function call — only in call-by-reference the address of the value is passed instead of a copy of the value itself, allowing the function to modify it. 

  2. It may, however, introduce a memory usage penalty, but these cases are more rare and easier to detect and fix just by rewriting the order of arguments. 

  3. Wikipedia: The Church-Rosser theorem