Flashback to January 2016!
Egg

teaching machines

CS 330 Lecture 31 – Call-by-name and Call-by-need

Dear students,

Last time we introduced a different way of passing parameters. Instead of eagerly evaluating them, we delayed evaluation until they were referenced inside the function. You are probably thinking, “Call-by-name. Big deal. How many new control structures am I going to need in my life?” Probably not many, but I think the bigger deal is that just as Stroustrup made our new types indistinguishable from the builtin types, call-by-name lets our code get the same special treatment that builtin structures get. Call-by-name is just another step in the path to a language designer granting you full citizenship in the world centered on that language.

Let’s extend our table. Suppose a call-by-name function never references its lazily evaluated parameter. How many times will it have been evaluated? None. That’s a win compared to eager evaluation, especially if evaluating it was expensive. What if it’s referenced once? It will be evaluated once. What if it’s referenced many times? It will be evaluated many times.

scheme 0 references 1 reference n references
call-by-value 1 1 1
call-by-name 0 1 n

Note that we don’t explicitly pass functions as parameters to a call-by-name function. The language’s tooling wraps up our actual parameters in functions for us. Since most languages don’t support call-by-name, our only recourse to achieve something like it is to explicitly pass functions or lambdas. In Ruby we can use blocks for this. Let’s revisit repeat with blocks:

def repeat n
  i = 0
  while i < n
    yield
    i += 1
  end
end

repeat 5 do
  puts "Foobag!"
end

How about a loop-and-a-half control structure? Sadly, Ruby doesn’t let us pass more than one block to a function. We’ll use a lambda instead:

def loophalf n, outer, inner
  if n > 0
    outer.call
    n.times do
      inner.call
      outer.call
    end 
  end
end

loophalf 3, lambda { print 'x' }, lambda { print 'o' }

Even if call-by-name doesn’t exist in most of our languages, we can get close!

Okay, that’s call-by-name/pass-by-closure. There’s another scheme for passing parameters that we should look at. It too is lazy, but instead of reevaluating the parameter on every reference, we only evaluate it the first time and record the result so future references are really fast. This is termed call-by-need, and it too needs a better name. Like pass-by-jit. JIT stands for just-in-time, hinting at the lazyness of this scheme. Let’s round out our table:

scheme 0 1 n
call-by-value 1 1 1
call-by-name 0 1 n
call-by-need 0 1 1

Call-by-need semantics are all over Haskell. What are they good for, those lazy sods? Well, let’s see how they work first, and then I think we’ll be better equipped to answer that question. We will demonstrate the ideas of call-by-need in Ruby, even though it doesn’t technically support it. Let’s create a Lazy class that encapsulates the big ideas of call-by-need:

  1. The programmer expresses a computation, but it is not executed until later
  2. When the programmer does need the real value, the computation is executed and the result is stored for later quick retrieval

How do we expression a computation but not execute it? We do it all the time. Push it into a function. Or a lambda. Or a block. Someone will therefore use our class like this:

image = Lazy.new do
  open('http://www.twodee.org/tests/slowimage/slowimage.php').read
end

puts "The lazy image has been constructed, but not executed."

if some condition
  puts "Ugh! This is gonna be slow."
  puts image.eval.length
  puts "But not these!"
  puts image.eval.length
  puts image.eval.length
  puts image.eval.length
  puts image.eval.length
  puts image.eval.length
  puts image.eval.length
else
  puts "we never paid the cost of evaluating the image!"
end

Retrieving that image is a costly operation. We can avoid that cost if we don’t need it. But if we need it a lot, we’ll only take the hit once.

Alright, so how do this? Lazy‘s constructor will need to receive and hang on to a block. This is often called a thunk:

class Lazy
  def initialize &block
    @thunk = block
  end
end

We will need to evaluate that thunk when the user really needs the value:

class Lazy
  def initialize &block
    @thunk = block
  end

  def evaluate
    @thunk.call
  end
end

But there’s no performance benefit yet. We also need to hold on to (memoize) the value after the first execution. Subsequent calls will not reevaluate. They will simply return the previously cached result:

class Lazy
  def initialize &block
    @thunk = block
    @cache = nil
  end

  def evaluate
    if @cache.nil?
      @cache = @thunk.call
    end
    @cache
  end
end

So, there’s an obvious performance benefit from call-by-name semantics. In fact, this laziness can let us create infinite data structures: lists that go on forever, trees that have no leaf nodes. Let’s make an infinite list. It’s always good to start off designing a class by looking at it from the client’s perspective. We want to start it off at a particular number and have it jump by some delta between elements. We can iterate through like this for as many elements as we wish:

l = InfiniteList.new 10, 5
40.times do
  puts l.head
  l = l.tail
end

We can start to write the constructor. We know the list will have the given number as its head:

class InfiniteList
  def initialize start, delta
    @head = start
  end
end

What about its tail? That’ll be another InfiniteList whose head is start + delta. But that InfiniteList will itself have a tail that’s an InfiniteList, and things will get out of hand quickly. We need to be lazy about the tail:

def initialize start, delta
  @head = start
  @tail = Lazy.new
    InfiniteList.new start + delta, delta
  end
end

Now, we need some methods for accesing the list’s head and tail. The head is pretty easy:

def head
  @head
end

But remember that we need delayed evaluation of the tail until such a time as it was needed. That time is now. We force evaluation of the tail:

def tail
  @tail.eval 
end

Will you use call-by-name a lot in life? Well, you wouldn’t if you didn’t know it was possible. But the idea of postponing an evaluation until later and caching its result is definitely not crazy. Call-by-name semantics actually build that behavior into a data structure so that the delaying and caching is transparent to the developer. You are probably using software that uses the call-by-name idea without realizing it. I can think of a few applications:

A data structure that abstracts this laziness improves performance without burdening the clients.

Here’s your TODO list:

See you next time, when we discuss some how to tame recursion that gets out of hand.

Sincerely,

P.S. It’s Haiku Friday!

I don’t have clean bowls
It’s not because I’m lazy
I just wash by need

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