Functional is Beautiful
Scheme is a “mostly functional” language. Although Schemers don’t hesitate to use set! when mutation solves a problem best, Scheme programmers prefer to think functionally. Purely functional programs are easier to test, they make better and more reliable APIs, and our environments, compilers, and run-time systems take advantage of functional style.
A Schemer’s functional bias is especially strong when writing programs that process and produce lists. The map function, which does both, is a thing of beauty:
(define (map f l) (cond [(null? l) '()] [else (cons (f (car l)) (map f (cdr l)))]))
The map function is most beautiful when the given f is functional. If f has side-effects, the the above implementation over-specifies map, which is traditionally allowed to process the list in any order that it wants (though PLT Scheme guarantees left-to-right order, as above). Arguably, when some other Schemer provides a non-functional f, then it’s their problem; they have to deal with the consequences (which may well be minor compared to some benefits of using mutation).
The map function might also receive a non-list, but the map implementor can guard against such misuse of map by wrapping it with a check,
(define (checked-map f l) (if (list? l) (map f l) (error 'map "not a list")))
and then exporting checked-map instead of the raw map. This kind of checking gives nicer error messages, and it helps hide implementation details of map. We could further also imagine that the raw map is compiled without run-time checks on car and cdr.
The Problem with Mutable Pairs
What if someone calls checked-map like this?:
(define l (list 1 2 3 4 5)) (checked-map (lambda (x) (set-cdr! (cddr l) 5)) l)
The f provided to map in this case is not purely functional. Moreover, it uses mutation in a particularly unfortunate way: the list? test in checked-map succeeds, because the argument is initially a list, and the mutation is ultimately discovered by a call to cdr --- but only if checks haven't been disabled.
If you’re a Schemer, then unless you’ve seen this before, or unless you thought a bit about the title of this section, then you probably didn't think of the above test case for map. A Schemer’s view of lists is so deeply functional that it's hard to make this particular leap.
Furthermore, this example is not contrived. If you have either Chez Scheme version 6.1 or a pre-200 MzScheme sitting around, calling map as above leads to a seg fault or an invalid memory access:
Chez Scheme Version 6.1 Copyright (c) 1998 Cadence Research Systems > (define l (list 1 2 3 4 5)) > (map (lambda (x) (set-cdr! (cddr l) 5)) l) Error: invalid memory reference. Some debugging context may have been lost.
The map example illustrates how mutable pairs can break a Schemer’s natural and ingrained model of programming. Of course, if optimizing and providing friendly error messages for map were the only issues with mutable pairs, then it wouldn’t matter; Scheme implementors are smart enough to (eventually) get this right. Unfortunately, the underlying problem is more pervasive.
In the API for a typical Scheme library, lists can be used for many kinds of input and output. Flags for options might be provided in a list. A function might provide information about the current configuration (e.g., the current items in a GUI list box) in a list. Procedures or methods that deal gracefully with list mutation are few and far between. In most cases, the result of unexpected mutation is merely a bad error message; sometimes, however, unexpected mutation of a list can break the library’s internal invariants. In the worst case, the library whose internal invariants are broken plays some role in a system’s overall security.
Mutable lists also interfere with the language’s extensibility. The PLT Scheme contract system, for example, offers a way to wrap an exported function with a contract that constrains its input and outputs, which are optionally (in principle) enforced by run-time checks. Higher-order contracts, such as “a list of functions that consume and produce numbers”, require wrappers on sub-pieces, and these wrappers can be installed only by copying the enclosing list. Copying a mutable list changes the semantics of a program, however, whereas contracts are supposed to enforce invariants without otherwise changing the program. Copying an immutable list creates no such problem.
Finally, mutable lists make the language’s specification messy. The R6RS editors spent considerable energy trying to pin down the exception-raising guarantees of map; the possibility of mutable pairs made it difficult to provide much of a guarantee. The standard says that implementations should check that the lists provided to map are the same length, but it’s not worth much to require that check, since an argument’s length as a list can change via mutation to the list’s pairs.
Switching to Immutable Pairs
The designers of PLT Scheme long ago recognized the problems of mutable pairs, and we introduced functions like cons-immutable and list-immutable to support programming with immutable lists. These additions solved some problems --- but only in the cases where we were careful to use immutable lists. The R6RS editors also recognized the problems of mutable pairs, so that set-car! and set-cdr! were banished to their own library --- but programmers are still free to use that library.
While these are worthwhile steps for many reasons, they do not solve the underlying problem. Library implementors who deal in lists must still either set up elaborate guards against mutation, pretend that the problem doesn't matter, or require the use of a special immutable-list datatype that is incompatible with libraries whose authors set up elaborate guards or ignore the problem.
Why all this hassle? If most Scheme code really does use and expect pairs in a functional way, can't we just switch to immutable pair? Most Scheme code will still work, untold security holes will have been closed, specifications will become instantly tighter, and language extensions like contracts will work better.
Schemers have been reluctant to make this leap, because it has never been clear just how much code relies on mutable pairs. We don’t know how much the switch will cost in porting time and long-term incompatibility, and we don’t really know how much we will gain. We won't know until we try it.
For PLT Scheme v4.0, we’re going to try it. In our main dialects of Scheme (such as the mzscheme language), cons will create immutable pairs, and pair? and list? will recognize only immutable pairs and lists. The set-car! and set-cdr procedures will not exist. A new set of procedure mcons, mcar, mcdr, set-mcar!, and set-mcdr! will support mutable pairs. (A related v4.0 change is that define-struct by default creates immutable structure types.)
Of course, PLT Scheme v4.0 will support an R5RS language where cons is mcons, and so on, so many old programs can still run easily in the new version. The difference is that interoperability between R5RS libraries and PLT Scheme libraries will be less direct than before.
Experience So Far
PLT Scheme v126.96.36.199 exists already in a branch of our SVN repository, and it will soon move to the SVN trunk. That is, we have already ported at least a half million lines of Scheme code to a dialect without set-car! and set-cdr!.
The conversion took about eight hours. Obviously, relatively little code had to change. The following are the typical porting scenarios:
The reverse! and append! functions were frequently used for “linear updates” by performance-conscious implementors. As our underlying Scheme implementation has improved, however, the performance benefits of these functions has become less. All uses could be replaced with reverse and append.
The set-cdr! operation was often used to implement an internal queue. Such internal queues were easily changed to use mcons, mcar, mcdr, and set-mcdr!.
An association-list mapping was sometimes updated with set-cdr! when a mapping was present, otherwise the list was extended. Since the extension case was supported, it was easy to just update the list functionally. (The relevant lists were short; if the lists were long, the right change would be to use a hash table instead of a list.)
A pair was sometime used for an updatable mapping where a distinct structure type is better. The quick solution was to throw in a mutable box in place of the value.
The PLT Scheme code might be better positioned for the switch than arbitrary Scheme code. Most of it was written by a handful of people who understood the problems of mutable pairs, and who might therefore shy away from them. However, the PLT Scheme code base includes a lot of code that was not written specifically for PLT Scheme, including Slatex, Tex2page, and many SRFI reference implementations. With the exception of SRFI-9, which generalizes set! to work with pairs, the SRFI implementations were remarkably trouble free. (Thanks to Olin Shivers for making mutation optional in the “linear update” functions like reverse! from SRFIs 1 and 32.)
In addition, we looked at a number of standard Scheme benchmarks, which can be found here:
Of the 28 benchmarks, eight of them mutate pairs. Four of those are trivially converted to functional programs, along the lines of the scenarios above. One, destruct, is designed specifically to test mutation performance, so it makes no sense to port. Another, sort1, is a sorting algorithm that inherently relies on mutation; a functional sort is obviously possible, but that would be a different benchmark. The conform benchmark uses mutable pairs for tables in a relatively non-local way; as a modern Scheme program, it would probably be written with structures, but it’s not trivial to port. The peval benchmark uses pairs to represent Scheme programs, and it partially evaluates the program by mutating it, so it is not trivial to port. To summarize, out of 28 old, traditional benchmark programs, only two represent interesting programs that are not easily adapted to immutable pairs. (They run in PLT Scheme’s R5RS language, of course.)
Finally, we selected a useful third-party library that is not included with PLT Scheme. We checked the generic SSAX implementation (not the PLT Scheme version), and we found a couple of uses of set-car! and set-cdr!. Again, they fall into the above queue and association-list categories that are easily and locally converted.
Meanwhile, as we start to use v3.99 to run scripts in our day-to-day work, immutable pairs have so far created no difficulty at all. So far, then, our optimism in trying immutable pairs seems to be justified; it just might work.
But It’s Lisp Tradition!
A typical response to news of the demise of mutable pairs is that it will create lot of trouble, because mutable pairs are Scheme tradition, and surely lots of useful old code exploits them in lots of places.
We’re eager to hear whether anyone has such code. Our initial hypothesis is that practically all old code falls into one of two categories:
The code is easily ported to immutable pairs, along the same lines as above (i.e., local queues and small association lists).
The code so old and generic that it can be run as an R5RS program. It won’t call into the large PLT Scheme set of libraries that will expect immutable pairs, and it can easily be used as a library with wrappers that convert mutable pairs back and forth with immutable pairs.
Frankly, we’re not so eager to hear opinions based on guesswork about existing code and how it might get used. Download v3.99 from SVN or as a nightly build when it becomes available; let us know your guesses about how running your old code would go, but then let us know what actually happens.
The immutable-pairs plan for v4.0 is not set in stone, but we won’t make the decision based on guesswork. More libraries (other than R5RS) to aid compatibility may be useful, but so far we don’t have a tangible need for them. In any case, we’ll revert to mutable pairs only if significant experience with the pre-release version demonstrates that it really won’t work.