Implementing Call by Need

As we have seen, there are a number of advantages for lazy evaluation, but its main disadvantage is the fact that it is extremely inefficient, to the point of rendering lots of programs impractical, for example, in:

we end up adding 4 and 5 twice. In other words, we don’t suffer from textual redundancy (each expression is written once), but we don’t avoid dynamic redundancy. We can get it back by simply caching evaluation results, using a box that will be used to remember the results. The box will initially hold #f, and it will change to hold the VAL that results from evaluation:

We need a utility function to create an evaluation promise, because when an ExprV is created, its initial cache box needs to be initialized.

(And note that Typed Racket needs to figure out that the #f in this definition has a type of (U #f VAL) and not just #f.)

This eval-promise is used instead of ExprV in eval. Finally, whenever we force such an ExprV promise, we need to check if it was already evaluated, otherwise force it and cache the result. This is simple to do since there is a single field that is used both as a flag and a cached value:

But note that this makes using side-effects in our interpreter even more confusing. (It was true with call-by-name too.)

The resulting code follows.

Side Effects in a Lazy Language

We’ve seen that a lazy language without the call-by-need optimization is too slow to be practical, but the optimization makes using side-effects extremely confusing. Specifically, when we deal with side-effects (I/O, mutation, errors, etc) the order of evaluation matters, but in our interpreter expressions are getting evaluated as needed. (Remember tracing the prime-numbers code in Lazy Racket — numbers are tested as needed, not in order.) If we can’t do these things, the question is whether there is any point in using a purely functional lazy language at all — since computer programs often interact with an imperative world.

There is a solution for this: the lazy language does not have any (sane) facilities for doing things (like printf that prints something in plain Racket), but it can use a data structure that describes such operations. For example, in Lazy Racket we cannot print stuff sanely using printf, but we can construct a string using format (which is just like printf, except that it returns the formatted string instead of printing it). So (assuming Racket syntax for simplicity), instead of:

we will write:

and get back a string. We can now change the way that our interpreter deals with the output value that it receives after evaluating a lazy expression: if it receives a string, then it can take that string as denoting a request for printout, and simply print it. Such an evaluator will do the printout when the lazy evaluation is done, and everything works fine because we don’t try to use any side-effects in the lazy language — we just describe the desired side-effects, and constructing such a description does not require performing side-effects.

But this only solves printing a single string, and nothing else. If we want to print two strings, then the only thing we can do is concatenate the two strings — but that is not only inefficient, it cannot describe infinite output (since we will not be able to construct the infinite string in memory). So we need a better way to chain several printout representations. One way to do so is to use a list of strings, but to make things a little easier to manage, we will create a type for I/O descriptions — and populate it with one variant holding a string (for plain printout) and one for holding a chain of two descriptions (which can be used to construct an arbitrarily long sequence of descriptions):

Now we can use this to chain any number of printout representations by turning them into a single Begin2 request, which is very similar to simply using a loop to print the list. For example, the eager printout code:

turns to the following code:

This will basically scan an input list like the eager version, but instead of printing the list, it will convert it into a single output request that forms a recipe for this printout. Note that within the lazy world, the result of print-list is just a value, there are no side effects involved. Turning this value into the actual printout is something that needs to be done on the eager side, which must be part of the implementation. In the case of Lazy Racket, we have no access to the implementation, but we can do so in our Sloth implementation: again, run will inspect the result and either print a given string (if it gets a Print value), or print two things recursively (if it gets a Begin2 value). (To implement this, we will add an IOV variant to the VAL type definition, and have it contain an IO description of the above type.)

Because the sequence is constructed in the lazy world, it will not require allocating the whole sequence in memory — it can be forced bits by bits (using strict) as the imperative back-end (the run part of the implementation) follows the instructions in the resulting IO description. More concretely, it will also work on an infinite list: the translation of an infinite-loop printout function will be one that returns an infinite IO description tree of Begin2 values. This loop will also force only what it needs to print and will go on recursively printing the whole sequence (possibly not terminating). For example (again, using Racket syntax), the infinite printout loop

is translated into a function that returns an infinite tree of print operations:

When this tree is converted to actions, it will result in an infinite loop that produces the same output — it is essentially the same infinite loop, only now it’s derived by an infinite description rather than an infinite process.

Finally, how should we deal with inputs? We can add another variant to our type definition that represents a read-line operation, assuming that like read-line it does not require any arguments:

Now the eager implementation can invoke read-line when it encounters a ReadLine value — but what should it do with the resulting string? Even worse, naively binding a value to ReadLine

doesn’t get us the string that is read — instead, the value is a description of a read operation, which is very different from the actual string value that we want in the binding.

The solution is to take the “code that acts on the string value” and make it be the argument to ReadLine. In the above example, that could would be the let expression without the (ReadLine) part — and as you rememebr from the time we introduced fun into WAE, taking away a named expression from a binding expression leads to a function. With this in mind, it makes sense to make ReadLine take a function value that represents what to do in the future, once the reading is actually done.

This receiver value is a kind of a continuation of the computation, provided as a callback value — it will get the string that was read on the terminal, and will return a new description of side-effects that represents the rest of the process:

Now, when the eager side sees a ReadLine value, it will read a line, and invoke the callback function with the string that it has read. By doing this, the control goes back to the lazy world to process the value and get back another IO value to continue the processing. This results in a process where the lazy code generates some IO descriptions, then the imperative side will execute it and control goes back to the lazy code, then back to the imperative side, etc.

As a more verbose example of all of the above, this silly loop:

is now translated to:

Using this strategy to implement side-effects is possible, and you will do that in the homework — some technical details are going to be different but the principle is the same as discussed above. The last problem is that the above code is difficult to work with — in the homework you will see how to use syntactic abstractions to make things much simpler.