Does match against list traverse the whole list?

[Christopher Lemmer Webber]

Imagine the following code:

(let lp ([items '(1 2 3 4 5)])
(match items
[(list head rest ...)
(cons (* head 2)
(lp rest))]))

My gut feeling is "oh, this is just O(n) because it's pulling the top
off the list.... quite efficient."

But then I realized that:

(match '(1 2 3 4 . 5)
[(list head rest ...)
(* head 2)])

throws an exception because it's a dotted list.

But the documentation says that the `list?` predicate is O(n). I'm
suddenly fearing, have I been writing O(n^2) code this whole time? Does
match against list actually check the whole list every time?

[Shu-Hung You]

From the expansion result, match does check whether the inspected
value is a list using list?. But at least for the current version of
Racket (and the C VM), list? is handled specially and ``effectively
takes constant time due to internal caching.'' (quoted from:
https://docs.racket-lang.org/reference/pairs.html?q#(def._((quote._~23~25kernel)._list~3f))
)

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[Alexis King]

> On Oct 29, 2019, at 12:41, Christopher Lemmer Webber <cwe...@dustycloud.org> wrote:
>
> But the documentation says that the `list?` predicate is O(n).

I’m not sure where you’re seeing that, but the documentation actually says just the opposite. Specifically, it says this:

> This procedure effectively takes constant time due to internal caching (so that any necessary traversals of pairs can in principle count as an extra cost of allocating the pairs).

In other words, `list?` is amortized constant time.

[Sam Tobin-Hochstadt]

Here are some quick numbers on the traditional Racket VM:

```
> (define v (build-list 10000000 values))
> (time (list? v))
cpu time: 47 real time: 47 gc time: 0
#t
> (time (list? v))
cpu time: 31 real time: 31 gc time: 0
#t
> (time (list? v))
cpu time: 13 real time: 13 gc time: 0
#t
> (time (list? v))
cpu time: 15 real time: 16 gc time: 0
#t
> (time (list? v))
cpu time: 4 real time: 4 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 1 gc time: 0
#t
> (time (list? v))
cpu time: 2 real time: 2 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 1 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 0 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 0 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 0 gc time: 0
#t
> (define v2 (drop v (/ 10000000 2) ))
> (time (list? v2))
cpu time: 0 real time: 0 gc time: 0
#t
```
Here's some RacketCS numbers, which are a little different:

```
[samth@huor:~/.../extra-pkgs/typed-racket/typed-racket-test (master)
plt] racketcs
Welcome to Racket v7.5.0.4 [cs].
> (define v (build-list 10000000 values))
> (time (list? v))
cpu time: 77 real time: 77 gc time: 0
#t
> (time (list? v))
cpu time: 73 real time: 73 gc time: 0
#t
> (time (list? v))
cpu time: 53 real time: 53 gc time: 0
#t
> (time (list? v))
cpu time: 37 real time: 37 gc time: 0
#t
> (time (list? v))
cpu time: 25 real time: 25 gc time: 0
#t
> (time (list? v))
cpu time: 12 real time: 13 gc time: 0
#t
> (time (list? v))
cpu time: 2 real time: 2 gc time: 0
#t
> (time (list? v))
cpu time: 3 real time: 3 gc time: 0
#t
> (time (list? v))
cpu time: 1 real time: 1 gc time: 0
#t
> (time (list? v))
cpu time: 0 real time: 0 gc time: 0
#t
> (define v2 (drop v (/ 10000000 2) ))
> (time (list? v2))
cpu time: 61 real time: 61 gc time: 0
#t
> (time (list? v2))
cpu time: 50 real time: 50 gc time: 0
#t
> (time (list? v2))
cpu time: 15 real time: 15 gc time: 0
#t
> (time (list? v2))
cpu time: 25 real time: 25 gc time: 0
#t
> (time (list? v2))
cpu time: 22 real time: 22 gc time: 0
#t
> (time (list? v2))
cpu time: 3 real time: 3 gc time: 0
#t
> (time (list? v2))
cpu time: 0 real time: 0 gc time: 0
#t
```

If you want to make that match pattern faster, use `cons` or `list-rest`.

Sam

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[Christopher Lemmer Webber]

Thanks everyone. I guess I misread the docs. Great to hear re:
caching. Guess I wasn't screwing things up as I momentarily feared. :)