In a language with lazy evaluation, a value is computed only when it is needed, and then the computed value is stored. This is in contrast with strict evaluation (which is by far the most common), where values are computed as soon as they are defined.
Haskell uses lazy evaluation, and I think it’s one of the great strengths of the language. But the prevalent opinion in the programming world is that it’s maybe a nice idea, but bad in practice. After all, you can always explicitly introduce laziness in the form of function calls when you need it. Well, I think it’s a better default. So let’s start out with some pros of laziness:
- The language becomes more uniform.
I dislike special cases in languages, I like things to be nice and simple and uniform. I expect most programmers would agree with me. And yet there are many instances of non-uniformity which everyone seems happy with!
Consider the simple boolean and operator with short-circuiting,
&&. Could you define this in a strict language? No. Boolean operators tend to have special evaluation rules associated with them (called a special form in the Lisp world), because the right argument is typically not evaluated if the result can be determined purely from the left argument.
In Haskell, here is how you can define the short-circuiting boolean and:
(&&) :: Bool -> Bool -> Bool True && b = b False && _ = False
Another common special form is the if/then/else statement. This cannot be defined in a strict language for much the same reason: only one branch is evaluated depending on the value of the conditional. It’s just a normal function given laziness:
ifThenElse :: Bool -> a -> a -> a ifThenElse True t _ = t ifThenElse False _ f = f
Laziness lets you define new control structures which the designers of the language had not foreseen, this makes the language much more flexible.
- It does at most as much computation as would be done under strict evaluation.
The “worst case” for lazy evaluation is when all values are needed. Everything is evaluated, so there is no saving over strict evaluation. On the other hand, if even one value is not needed, less work has been done than would have been under strict evaluation.
This observation comes from an early paper on lazy evaluation, called CONS Should Not Evaluate Its Arguments, done in the context of Lisp.
- Code can be more modular.
Here’s an example of the Newton-Raphson method of finding square roots, taken from Why Functional Programming Matters. Firstly, we define a function to repeatedly apply a function to a value and gather the results into a list:
repeat :: (a -> a) -> a -> [a] repeat f a = a : repeat f (f a)
Oops, we’ve already moved out of the realm of what strictness can deal with. There’s no base case for the recursion in
repeat, so a strict language would just enter an infinite loop.
Anyway, now we need a function which, given some tolerance and a list of approximations, finds the first value where two successive approximations don’t differ by more than that tolerance:
within :: Double -> [Double] -> Double within epsilon (a:b:rest) = if abs (a - b) <= epsilon then b else within epsilon (b:rest)
And now the square root function is almost trivial:
sqrt a0 epsilon n = within epsilon (repeat next a0) where next x = (x + n/x) / 2
It may not look like we’ve gained much, but actually we have: both
within can be re-used in other contexts. In order to make the program modular like this in a strict language, we would need to explicitly introduce laziness in the form of a generator. That’s more work.
The paper then goes on to re-use these functions to calculate the square root a slightly different way; to implement numerical differentiation; and to implement numerical integration. It turns out that
repeat are just the things you need to implement numerical algorithms.
- Memoisation (can be) free!
A common optimisation technique is to store the result of a function in some sort of lookup table, so if the function is given the same arguments, the result can be returned without needing to recalculate it. Well, if you can represent your function as a data structure, laziness does that for you for free! Caching results is what it is good for, after all.
We can use this to implement a simple function to get the nth prime in linear time after it is first calculated:
primes :: [Int] primes = ... prime :: Int -> Int prime n = primes !! n
The first time
prime n is computed for some
primes list will be evaluated up to that point and the value returned. If we ever call
primes m, where
m <= n, then all the function does is traverse the list to find the value which has already been computed! This is a classic example of trading space for time, the lookup table uses memory, but we don’t need to do a potentially expensive calculation every time. The nice thing here is that this doesn’t require any special support for explicit memoisation; it’s just a consequence of lazy evaluation.
Naturally, there are disadvantages to lazy evaluation as well:
- If potentially uses more memory.
Laziness is implemented by introducing thunks. A thunk is a pointer to some code and an environment. When the value represented by a thunk is demanded, the code is evaluated and the thunk replaced with its result. This gives us the evaluation only when we need it and the caching. When a value is needed immediately, the thunk is just a waste of space.
Laziness is a bit of a gamble; you’re making the judgement that the space saved by not needing to compute things will offset the space wasted by allocating these thunks.
- It’s difficult to predict when memory is freed.
It’s just really hard to build up an intuition for this. Profilers are all but essential if you get a nontrivial space leak. Fortunately, Haskell has pretty good support for heap profiling, but it is certainly much easier to debug space leaks in a strict language.
- Refactoring can have non-local effects.
A friend was refactoring some nontrivial code he had part-inherited part-written, and in doing so he changed the strictness of a function slightly. This immediately caused the program to crash with a pattern match failure in a completely separate module.
Cue a long and frustrating debugging session, trying to figure out why this was happening and how to fix it.
It turns out that the change in strictness was rippling backwards through the rest of the program, and forced something to be computed which wasn’t being before. Some function that had been written years ago by someone who had since left had a missing case in a pattern match. This had been fine, but now the result of applying this function to a value which matched that case was needed: hence the error.
That is awful. In a strict language, the missing case would have been found when that code was first written, and would have been corrected. In a lazy language, you get to discover it months (or even years) after it was introduced and the original author is gone.
The Killer Feature of Laziness
You can make a lazy function strict, but you can’t make a strict function lazy without rewriting it.
And this, to me, is the reason why laziness is the better default.
Let’s say we have a lazy function we want to make strict. Haskell provides a function called
seq, which evaluates its first argument and returns its second. Given this, we can construct a function to fully evaluate a data structure. Let’s keep it simple and operate on lists for now:
seqList :: [a] -> b -> b seqList (a:as) b = a `seq` seqList as b seqList  b = b
Demanding the result of
seqList as b recurses along the entire list (because that is the termination condition of the recursion), using
seq to evaluate each element1.
Give this, we can make an arbitrary function operating on lists completely strict:
lazyFunction :: [a] -> [b] -> [c] -> [d] lazyFunction foo bar baz = ... strictFunction :: [a] -> [b] -> [c] -> [d] strictFunction foo bar baz = let foo' = seqList foo foo bar' = seqList bar bar baz' = seqList baz baz result = lazyFunction foo' bar' baz' in foo' `seq` bar' `seq` baz' `seq` seqList result result
When the result of
strictFunction is demanded, both the arguments and it will be fully evaluated before being returned. This is because
seqList fully evaluates its first argument before returning the second, and we’re giving it the same list for both arguments. A neat trick! In fact, this pattern is so useful that the deepseq package, which provides utilities for fully evaluating data structures, provides a function to this effect called
force, which evaluates its argument and returns it.
Caveat: The evaluation of
lazyFunction will still allocate thunks, which will then be immediately forced by
seqList. This results in churn in the heap and extra work for the garbage collector, which is bad. A better function can be achieved if the lazy one is rewritten with strictness in mind, as then these excess thunks can be avoided. This is typically only an issue in performance-critical code: for example the implementations of data structures. Most of the time you don’t need to worry about that extra bit of allocation.
We can even go for a middle-ground, where the function is strict in its result but potentially lazy (depends on how the function is defined) in its arguments:
strictishFunction :: [a] -> [b] -> [c] -> [d] strictishFunction foo bar baz = let result = lazyFunction foo bar baz in seqList result result
This is more useful. Wanting to be strict in the arguments like that is quite an uncommon use-case in practice.
Now let’s think about how to make a strict function lazy without poking around in its implementation. So we want something of this form again:
strictFunction :: [a] -> [b] -> [c] -> [d] strictFunction foo bar baz = ... lazyFunction :: [a] -> [b] -> [c] -> [d] lazyFunction foo bar baz = let result = strictFunction foo bar baz in ??? result
Wait, that’s not right. Anything we pass in to
strictFunction will be fully evaluated, because it’s strict! So the function can’t be that shape. We can’t alter the arguments to
strictFunction to make the laziness explicit either, as that would change its type! We can wrap up the result of
strictFunction in a thunk, but as soon as we try to do anything with it, any arguments passed in will be fully evaluated.
We just can’t make it lazy.
Addendum: Strict and Lazy Data Structures
“If laziness is so great, then why does pretty much every Haskell data structure library provide both strict and lazy versions of everything?”
A good question, but not as related as it appears at first glance. Lazy evaluation is about functions, lazy data is about the representation of data structures in memory. Using strict data structures does not necessarily make your program strict.
Suppose I have a strict string type:
silly :: [a] -> StrictString silly _ = "hello world"
Unless the list type is also strict, this function will work just fine on infinite lists, even though the result is a totally strict value which is always fully evaluated.
The reason we have both strict and lazy versions of data structures is because quite often you know that you will be using something in a strict context, in which case you can write things in a way which will avoid allocating the useless thunks. But not every use is completely strict, in which case the lazy version is preferable.
This is actually a slight lie,
seqonly evaluates to “weak-head normal form”, which corresponds to the outermost constructor of a datatype. We actually need to appropriately define a
seqList-like function for every type we want to be able to fully evaluate. The deepseq package provides a typeclass to handle this.↩︎