Fundamental Problems of Lisp, the Cons Cell (2024)
xahlee.info
xahlee.info
Lisp is not, nor has it ever been, a functional programming language. It had lambda decades before other languages figured out it was a good idea, but it had set! for just as long.
It is also not a list based language, but a tree based one. The fundamental point of lisps is that you can manipulate the abstract syntax tree directly since it's pretty much the same thing as the parse tree.
>Deep Nesting is Rare
>The lisp's cons [...] works just fine when data structure used is simple. [...] vast majority of list usage is just simple flat list, sometimes 2 level of nesting [...] 3 levels of nesting is seldom used [...] Greater than 3 level is rarely seen. Systematic manipulation and exploitation of nested list, such as mapping to leafs, to particular level, transposition by permutation on level, or list structure pattern matching in today's functional langs, etc is hardly ever to be seen.
I guess the author has never used lisp to implement a DSL in lisp. Writing a lisp interpreted in lisp is the first real program you write if you take a lisp course at university and you need to handle arbitrarily nested expressions.
Real world usage also involves writing a specialist language to solve your problem for anything more complex than a utility script, e.g. Emacs is a text editing DSL implemented in elisp.
Purity has nothing to do with functional programming.
> It is also not a list based language, but a tree based one.
It's not called Trep, it's called Lisp. Yes, you can represent trees as lists embedded in lists, and the cons cell allows that thanks to type recursion. But it's still based around lists. Trees don't allow cycles, lists formed from ordered pairs do. Every single piece of literature written by McCarthy talks about lists[1].
> The fundamental point of lisps is that you can manipulate the abstract syntax tree directly
Macros weren't introduced until 1963[2]. They might be the reason you use a Lisp, and they may have become synonymous with Lisp after 1.5, but they are not a "fundamental point" of Lisp. The fundamental point was always about lambda calculus[1].
[1] - https://history.siam.org/sup/Fox_1960_LISP.pdf
[2] - http://bitsavers.informatik.uni-stuttgart.de/pdf/mit/ai/aim/...
When Lisp was implemented for the first time, the evaluation semantics was already expressed as operations on a tree.
"Functional programming" used to just mean having first-class functions that you could pass as arguments and return from functions. Lisp has always been functional. It's never been purely functional, which is a different thing - concerning itself with referential transparency rather than first-class functions.
I was around when FP papers still discussed Miranda, and Lisp was certainly taught as FP language.
The LISP I manual describes the program feature as being "like a FORTRAN program with LISP statements", but that's not the same as saying it is there to appeal to Fortran programmers.
https://www.mirrorservice.org/sites/www.bitsavers.org/pdf/mi...
The key difference between the C primitive and the Lisp primitive is that the Lisp primitive does not require anything to be mapped onto integers whereas C does. You have to be able to increment and decrement pointers in C. You can have a fully functional Lisp with no numbers at all. In fact, this was the whole point of Lisp when it was invented: providing a model for computing on symbolic expressions rather than numbers. There is a reason that the original Lisp paper was called, "Recursive functions of symbolic expressions and their computation by machine" rather than "Cons cells: a new computational primitive".
All of the "problems" with cons cells are not problems with cons cells at all, they are problems with punning cons cells, i.e. using cons cells to implement higher-level abstractions without properly hiding the fact that the underlying implementation is a cons cell. The exact same thing happens in C when you run off the end of an array or cast a pointer to (void *). These are not problems with pointers per se, they are problems with using pointers to implement higher level abstractions (like finite arrays) without properly hiding the underlying implementation.
Punning cons cells and abusing pointers have similar consequences: segfaults in the case of C, and (typically) "NIL is not a valid argument to..." errors in Lisp. Both of these are the result of bad abstraction discipline, not a problem with the primitives.
---
[1] The author is Xah Lee, who is pretty well known in the Lisp community. He is widely considered a troll, an opinion which I personally share. I've tried to make my assessment of this post as dispassionate as I can, but I thought I should disclose the fact that I have a pretty strong bias.
The problem is everything is boxed, and the indirection mechanism is conflated with the concatenation mechanism. What you really want is the ability to compose a value (concatenate 2 things together), but store it contiguously in memory. If cons did that then you could create true products of values, without any indirection.
Then you need a different method for creating indirection. A function for each of C's malloc and '*' respectively. That would give you the control needed to create trees with arbitrary branching factors.
Aesthetically speaking, I quite like conses, in that it is powerful and flexible enough to hold both trees and lists. But performance-wise, I guess it's always the simplest things that are hard to optimize, and cons-style linked lists can't really compete with arrays [2], if you are aiming to get on par with V8.
However, I still believe that, with a JIT runtime, it is possible to have some Lisp lists backed by arrays and am working on it [3]. Currently, =setcdr= causes most trouble for me and I don't know if the additional checks are going to ruin the performance improvement brought by arrays. But if things go well, we might get to see what conses could have cost us.
[0] Emacs Lisp, in Java, with Graal Truffle
[1] https://v8.dev/blog/elements-kinds
[2] https://en.wikichip.org/wiki/pointer_chasing
[3] I am not aware of other Lisps doing this. Cdr-coding is the closest, but it is still a linked list (implicitly).
From what I see from existing ELisp code (at least in the Emacs codebase), the idiomatic representation of sequences (fixed-size or not) is using cons lists. And it is not surprising: Emacs vectors are fixed-size and that makes it very inflexible and only suitable for a few things. This matters because, for example, if you want Emacs to compete with VSCode in performance, you eventually compares how idiomatic code performs. Note that how cons lists affect performance in real-world ELisp code remains unknown because it is yet to be benchmarked, but exposing the internals of idiomatic lists as conses does pose some challenges for an implementer aiming for further optimizations.
Saying that they're a fundamental problem in Lisp is like saying that objects are a fundamental problem in Smalltalk or that arrays are a fundamental problem in APL.
If Xah doesn't like cons cells, there are other languages he can use instead. Lisp (as well as Prolog, Haskell, ML, etc.) programmers won't be persuaded to abandon cons cells or lists as they find them extremely useful.
In Haskell there's a movement to get rid of much of the special syntax for lists. And a lot of code has moved on from lists. Many people never use them, I don't.
What killed lists is the reality of their horrific performance. They were great 40 years ago. But memory and CPU speed have scaled with different factors that make lists almost always the wrong choice.
Who said anything about abandoning lists? The argument appears to be that lists don't need to be built up out of two-element cells (i.e cons cells), and that Lisp, by enforcing `cons` cells as a way to construct lists, is seeing some limitations.
TBH, I agree a little that that PoV - there is no need for exposing the implementation of the list to the programmer, much less forcing the programmer into using the implementation.
The other problem with enforcing lists to be constructed of cons cells is one of performance; the default list in Lisp is a cache-invalidating monster.
On his web page, he writes: > Lisp's cons forces programer (sic) to think of list in a low-level nested of 2-item construction, with explicit functions like “cddr”, “cadaar” etc, and even a special notation “(A . B)”.
Except, most of the time, it doesn't. For example, I think (a b c) is a list of three elements. If I want c, I call (third '(a b c)), not (caddr '(a b c)). I know it's stored as (a . (b . (c . NIL))) and that third is just an alias for caddr, but I'm not forced to think that way.
So why not just think in terms of lists, which can be nested, rather than cons-cells, which are only rarely used for anything other than to construct lists? The cons function itself would still be needed, as adding a value to a list without modifying the original list is extremely useful. Or you could think in terms of the more abstract data structures (parse trees, Lisp functions, etc.) you construct from lists.
When learning and using a language, it's important to think in that language.
Because, as he continues:
Worse, any proper list can have improper list as elements. So, you can have a list of cons, or cons of lists, cons of cons, list of lists, or any mix. The overall effect of the cons is that it prevents lisp to have a uniform high level treatment of lists, with the result that development of functions that work on tree are inconsistent and few.
In other words, the fact that the implementation details for lists are so exposed means that you have to be careful when interacting with 'lists' that turn out not to be actual lists. There is no type information, either at compile or runtime, that ensures that what you're dealing with is actually a list and not something else. So you can't _actually_ think in terms of lists; you have to think in terms of cons cells which are probably lists but might not actually be so.
Cons cells are used to construct other higher-level data structures, like trees, not just lists.
But this whole discussion seems to just be a version of the usually static vs. dynamic typing discussion, where the “you have to think in terms of cons not lists” side is the static typing side saying that without handcuffs making it statically impossible to do the wrong thing you can't ever stop thinking about the things that could be done even if you aren't doing them and the “you can think in terms of lists without a problem” is the dynamic typing side saying “no, we actually don’t need to think about other possibilities unless we actively choose to use them”.
Saying that cons is functional as long as you don't modify the result later is like saying that variable assignment in C is functional.
There are lisp dialects that have immutable cons: https://docs.racket-lang.org/reference/pairs.html
I've found the documentation for Janet to be fairly adequate. What are some parts where the documentation could be better?
If you need to explain image-based to people unfamiliar, that's not a bad analogy.
https://groups.google.com/g/comp.lang.lisp/c/T_Tozq2P53I/m/N...
Lee's post seems more of a question, but to my eye it's a "why X" question that thinly disguises an "X is bad (or ugly, redundant, useless, confusing, counterproductive, unnecessary, etc.)" argument. Essentially though it's the same topic.
The post elicited around 60 responses, among them this one from the late Erik Naggum:
https://groups.google.com/g/comp.lang.lisp/c/T_Tozq2P53I/m/g...
which includes the following gem (or turd, depending upon your point of view):
> All in all, the pairs notion is redundant.
I hope you understand and appreciate what I have written above so the
following does not apply to you anymore. you see, I wrote it all because
I _really_ wanted to say that that sentence is the single most ignorant
and shallow-minded line that I have ever seen in any programming language
newsgroup or forum and I hope _never_ to see anybody display such utter
disregard for the brilliance and genius of people who came before them
just because they grew up in an age when "simple interface" is sneered
and laughed at in favor of "simple implementation" so any dumb fsck can
implement it right out of a "for Dummies" book.
> The other fundamental problem in the language is its cons cells as its list construction primitive.
> Lisp at core is based on functional programing on lists.
I found the LISP I manual while thinking about this post and how to respond to some of the comments. An interesting paragraph from it, I think, is important to understand cons in the context of Lisp languages versus whatever Xah Lee is thinking of. From page 14:
> Compositions of car and cdr give the subexpressions of a given expression in a given position. Compositions of cons form expressions of a given structure out of parts. [emphasis in original as underscored text]
Note what is missing from this: Any mention of the word "list". cons, car, and cdr are primitives for the creation and manipulation (or navigation) of S-expressions. Some S-expressions are lists (in the "proper list" sense), but not all. This has been part of the language since the beginning and it makes sense for it to remain part of the language.
In Common Lisp, if you want list specific functions, they do exist. first and rest are synonyms to car and cdr. You can skip cons entirely and use list and append and a few other functions in its place. There are also functions which are generalized to operate on sequences (which includes strings and vectors along with lists).
https://www.mirrorservice.org/sites/www.bitsavers.org/pdf/mi...
This seems to just complain that cons is hard to understand or something, without actually saying what makes it hard or unintuitive.
--------
Cons is fundamentally a linked list. The "pair" is a (value+pointer), and sometimes "value" can itself be a pointer. So when you have (pointer, pointer), you now can create trees.
As such, "Cons" is a powerful abstraction for trees, pairs, and linked lists. That's all it is. If you need "more" than this (ie: graphs), then perhaps its insufficient.
---------
"Cons" itself is a malloc(sizeof(pair)) operation. While car/cdr depend on whatever you're doing or however you've designed the program.
If I were to criticize "Cons", its that high performance modern programming needs to use arrays because the cost of pointers has grown. Latency of memory lookups is relatively slower on modern machines (or really, latency hasn't improved in like 20 years), so you need to consolidate more members together.
But in terms of a "simple" data-structure, "cons" cells and list-programming is a thing for a reason.
This has been true of linked lists since the advent of memory caches; it’s not just the last 20 years. They’re simple to implement, but they’re usually very bad for performance; you really want better locality of reference in a primitive data structure. You almost always should be using an array of some kind instead.
There's a reason why the Linux Kernel continues to use Red-Black trees today for a huge number of its data-structures. When you need reliable performance on all operations (insert, delete, reorderings, reallocations), its hard to beat a tree (or "cons" for that matter).
If you can use an array, then use an array. But making the tree a "good default" seems like the right move. Lisp does that with cons/cdr/car and (a . b), or (a b c d e) syntax.
Turning (a b c d e) into (a b b1 c d e), especially for larger sizes, will likely be faster than arrays (which innately needs to memcpy ~half the array on the average).
In Lisp you'd pretty much have to ship your module with its own tree-construction logic, or use some common (but importantly, not technically standard) implementation, and document that's what you did, so people know how to structure the data they pass to you.
In C++, you simply take a std::map, which implements a red-black tree for you, and being part of the standard library it is accepted and commonly used nearly everywhere.
I think OP wishes Lisp had something like std::map.
> To be clear, I'm steal manning his argument as I'm not sure I agree with it. But I think the point is summarized best with an example: "Here's an API that takes a red-black tree as an argument." Okaaay, what format is the red-black tree? How do I construct one?
If the API calls for taking a red-black tree as an argument, it will also provide either the specific red-black tree implementation itself or it will refer you to an existing package to include as a dependency. This is not dissimilar from C++. In C++ if something takes a std::map, you use a std::map. If it takes another data structure that's not in the STL, then it will provide it or tell you how to obtain it as a dependency.
BTW: steel, not steal, manning.
Which like Quicksort (nearly the same analysis btw), has exceptional average case performance (even faster than RB trees on the average !!!!) but the downside of horrific O(n^2) performance on the worst case.
RBTrees or AVL trees all help at improving those worst cases (AVL strangely has its best case be the worst case of unbalanced trees lol).
In any case, there's a lot of tree flavors. Lisp is certainly sufficient and simple when it's exploring these different details.
Unbalanced trees, in any case, is actually a reasonably sane default. RB Tree or AVL is probably a better default but don't knock the unbalanced tree before you try it!!
------------
I've heard of highly optimized lisps where the typical list is turned into an array or at least a rope in the average case btw.
I've become a fan of scapegoat trees¹ lately for (immutable) balanced trees. There are certainly a ton of other options besides RB and AVL trees that are fun to explore (in any language)
>I've heard of highly optimized lisps where the typical list is turned into an array...
Back in the lisp machine days there was CDR coding² to flatten out a list into a contiguous block, but I'm not sure if any modern common lisp or scheme implementations use it.
Pointers don't always imply trees. Any Lisp object that won't directly fit in half a cons cell gets allocated separately and a pointer to it is placed in that half of the cons cell. Examples: Strings, symbols, bignums, etc.
> If you need "more" than this (ie: graphs), then perhaps its insufficient.
You can certainly represent cyclic graphs with cons cells. The *print-circle* mechanism in Common Lisp handles printing them, for example.
What is "modern"? How far back do we have to go to "pre-modern" such that dependent loads through pointers are not a performance issue?
I'm pretty sure Lisp is more the latter, about flexibility and elegance. But not the fastest.
Linux continues to use RB Trees for a huge number of its processing. Because its faster to keep a tree sorted than to sort arrays.
You talk as if linked data-structures are inferior or something. Rather than different. Now yes, linked data-structures get relatively worse when latency remains the same but CPU GHz gets faster, but then the reverse is true when cache sizes get larger. L3 caches are now 192MBs on some processors, while Intel consistently has been pushing 1MB+ L2 caches with full load/store bandwidth per core.
There is a time and place for all techniques. Including linked data-structures / cons / list-processing.
Every other tech bro blowhard likes to repeat this.
So, first of all, I want to know what they mean by "modern"---how recently was it supposedly okay to chase pointers rather than just offsets.
Oh look, it says so right near the top: 2008.
$ txr
This is the TXR Lisp interactive listener of TXR 300.
Quit with :quit or Ctrl-D on an empty line. Ctrl-X ? for cheatsheet.
TXR is written, directed and produced by, not to mention starring, Kaz.
1> [mapcar chr-toupper "abc"]
"ABC"
2> (nullify "")
nil
3> (cdr "a")
nil
4> (car "abc")
#\a
5> (car "a")
#\a
6> (cdr "a")
nil
7> (car "ab")
#\a
8> (cadr "ab")
#\b
9> (cddr "ab")
nil
10> (defstruct kons ()
bling blong
(:method car (me) me.bling)
(:method cdr (me) me.blong)
(:method rplaca (me splat) (set me.bling splat))
(:method rplacd (me plonk) (set me.blong plonk)))
#<struct-type kons>
11> (new kons bling 1 blong 2)
#S(kons bling 1 blong 2)
12> (car *11)
1
13> (cdr *11)
2
14> (rplaca *11 42)
#S(kons bling 42 blong 2)
This is not the only way to make an object which serves as a sequence; you can instead (or in addition!) implement array-like indexing via the lambda and lambda-set methods to have it vector-like rather than list-like.
The empty function and nullify are almost inverses; anyway they are implemented in the same spot of a 16000+ line file. The difference is that empty errors out on objects that are not iterable, whereas nullify takes objects of all types:
val nullify(val obj)
{
val self = lit("nullify");
seq_info_t si = seq_info(obj);
if (seq_iterable(si))
{
seq_iter_t iter;
val elem;
seq_iter_init_with_info(self, &iter, si);
return if2(seq_peek(&iter, &elem), obj);
}
return si.obj;
}
val empty(val seq)
{
val self = lit("empty");
val elem;
seq_iter_t iter;
seq_iter_init(self, &iter, seq);
return tnil(!seq_peek(&iter, &elem));
}