A Scheme Idiom
June 16, 2017
We begin with a simple setter:
(define (make-setter x)
(case-lambda
(() x)
((y) (set! x y) x)))
> (define x (make-setter #f))
> x
#<procedure>
> (x)
#f
> (x "hello")
"hello"
> (x)
"hello"
Next we write an accumulator, as in the code I was reading:
(define (make-accumulator n)
(case-lambda
(() n)
((m) (set! n (+ n m)) n)))
> (define n (make-accumulator 10))
> (n)
10
> (n 20)
30
> (n)
30
Finally we have a setter for vectors:
(define (make-vector-setter vec)
(case-lambda
((idx) (vector-ref vec idx))
((idx val) (vector-set! vec idx val) vec)))
> (define v (make-vector-setter (make-vector 3 #f)))
> (v 0 "hello")
#("hello" #f #f)
> (v 1 "goodbye")
#("hello" "goodbye" #f)
> (v 2 "Scheme is fun!")
#("hello" "goodbye" "Scheme is fun!")
> (v 2)
"Scheme is fun!"
> (v 0)
"hello"
> (v 1)
"goodbye"
This is useful because it simplifies the syntax for dealing with vectors. The standard method of incrementing a vector element looks like this:
(vector-set! vec idx (+ (vector-ref vec idx) 1))
But with the idiom, we can write it like this:
(vec idx (+ (vec idx) 1))
That’s simpler and easier to read. But it does come at a cost in execution time:
> (time (let ((vec (make-vector 100 0)))
(do ((i 0 (+ i 1))) ((= i 1000000))
(do ((j 0 (+ j 1))) ((= j 100))
(vector-set! vec j
(+ (vector-ref vec j) 1))))
(vector-ref vec 50)))
(time (let ((...)) ...))
17 collections
9189 ms elapsed cpu time, including 0 ms collecting
9214 ms elapsed real time, including 1 ms collecting
72002728 bytes allocated, including 71454184 bytes reclaimed
1000000
> (time (let ((vec (make-vector-setter (make-vector 1000000 0))))
(do ((i 0 (+ i 1))) ((= i 1000000))
(do ((j 0 (+ j 1))) ((= j 100))
(vec j (+ (vec j) 1))))
(vec 50)))
(time (let ((...)) ...))
208 collections
15007 ms elapsed cpu time, including 30 ms collecting
15018 ms elapsed real time, including 23 ms collecting
876027512 bytes allocated, including 873920680 bytes reclaimed
1000000
Fifteen seconds versus nine seconds is a lot to pay for the readability and safety of the idiom, and probably explains why I’ve never seen it before. Regardless, it is a delightful way to show off the power of closures, and a good lesson in the power of Scheme; you can’t do that in most other languages.
You can run the program at http://ideone.com/7maOBT.
Programming Praxis 
Perl has a cool idiom that was borrowed from LISP called the Schwartzian transform, named after Randal Schwartz, the first person to document its use in Perl. The basic idea is that you have a potentially expensive computation that you need to run on N elements and then you need to sort them. The Schwartzian Transform avoids recomputing the expensive computation for last passes of the sort.
This lets you do interesting things like:
1. Sort strings by their length
#!perl use strict; use warnings; use feature qw/say/; my @strings = qw/ eren mikasa armin levi erwin reiner ymir historia bertholdt pixis /; say join "\n", map { $_->[0] } sort { $a->[1] cmp $b->[1] } map { [$_, length($_)] } @strings; # eren # levi # ymir # armin # erwin # pixis # mikasa # reiner # historia # bertholdt2. Sort IPv4 addresses numerically
#!/usr/bin/perl use strict; use warnings; use feature qw/say/; my @ips = qw/ 213.61.108.26 235.94.112.131 162.219.166.100 26.190.195.43 96.113.27.227 96.112.27.227 96.112.29.227 96.112.29.255 164.124.74.26 58.5.201.175 228.131.119.187 191.226.212.172 65.70.48.227 35.214.73.61 149.14.104.245 /; say join "\n", map { join '.', @$_ } sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] || $a->[2] <=> $b->[2] || $a->[3] <=> $b->[3] } map { [split /\./] } @ips; # 26.190.195.43 # 35.214.73.61 # 58.5.201.175 # 65.70.48.227 # 96.112.27.227 # 96.112.29.227 # 96.112.29.255 # 96.113.27.227 # 149.14.104.245 # 162.219.166.100 # 164.124.74.26 # 191.226.212.172 # 213.61.108.26 # 228.131.119.187 # 235.94.112.131@programmingpraxis: Is this a closure? Seems I’ve seen something similar before and it was termed a closure.
@bookofstevegraham: Yes, this is a closure. The value of the variable n is enclosed within the function, and not available to the rest of the program except through the interface defined by the function.