in-nest-sequence is a sequence generator that takes a function and an initial value, and the return value of invoking the function on the current value is used as the subsequent value. For example, (in-nest-sequence add1 0) returns the sequence (0 1 2 3 4 ...).

Recently, soegaard challenged me to write a define-sequence-syntax version of in-nest-sequence, that is, a macro-based version. I decided to give it a try:

#lang racket
(require (for-syntax unstable/syntax))
(provide (rename-out [*in-nest-sequence in-nest-sequence]))

(define in-nest-sequence
    [(func init)
      (thunk (values identity func init #f #f #f)))]
    [(func . inits)
      (thunk (values (curry apply values)
                     (lambda (args)
                       (call-with-values (thunk (apply func args)) list))
                     inits #f #f #f)))]))

(define-sequence-syntax *in-nest-sequence
  (lambda () #'in-nest-sequence)
  (lambda (stx)
    (syntax-case stx ()
      [[(x ...) (_ func init ...)]
       (unless (= (syntax-length #'(x ...)) (syntax-length #'(init ...)))
         (raise-syntax-error 'in-nest-sequence
                             (format "~a values required" (syntax-length #'(x ...)))
                             stx #'(init ...)))
       (with-syntax ([for-arity (syntax-length #'(init ...))]
                     [(value ...) (generate-temporaries #'(init ...))]
                     [(y ...) (generate-temporaries #'(init ...))])
         #'[(x ...) (:do-in ([(f) func])
                            (unless (procedure-arity-includes? f for-arity)
                              (raise-arity-error f (procedure-arity f) init ...))
                            ([value init] ...)
                            ([(x ...) (values value ...)]
                             [(y ...) (f value ...)])
                            (y ...))])])))

I'm a complete noob at using define-sequence-syntax, so I appreciate any and all style, performance, and/or general feedback about my code. (See the original post for some usage examples.)

  • \$\begingroup\$ The error (for/list ([x (in-nest-sequence 42 0)]) x) can be improved if a (procedure? func) test is inserted before make-do-sequence is called. Also: I am a bit torn about removing the one-value case. I am not 100% sure the optimizer can produce code that works equally well from the multiple values case. \$\endgroup\$
    – soegaard
    Oct 16, 2015 at 15:08

1 Answer 1


For cases where the the user follows the syntax and the function returns and receives the correct number of values, this works fine.

It is a good principle to catch errors as early as possible.

Consider this example:

(in-iterate add1)

Here the user supplies a function add1 that has arity 1, but supplies no arguments. This will eventually lead to an "result arity mismatch;" error, when add1. This error can be caught earlier in using procedure-arity to check that enough init values are supplied. The error message presented to the user can be "expected 1 initial value, but received 0".

In the *in-iterate consider: [(x ...) (_ func init ...)] . Here the number of bound identifiers (the xs) must be the same as the number of init expressions. If they are not, a raise-syntax-error with stx as the source of the error can be used.

An example that should be a syntax-error (and not a runtime error):

(define (add1/2 x y) (values (+ x 1) (+ y 2)))
(for/list ([n     10]
           [(x y) (in-iterate add1/2 0)])
  (list x y))

The name of the construct is a bit off. In in-list and in-sequence we have the pattern in-noun, so that suggest in-iteration might be better. However iteration is a bit vague. Maybe one in-nested-sequence or in-nest-sequence based on the name used in Mathematica? http://reference.wolfram.com/language/ref/NestList.html

  • \$\begingroup\$ Wow, that's awesome feedback. Thanks! For checking that (x ...) and (init ...) are the same length, I guess one possible solution is to use a syntax-case fender/guard. Am I just checking whether (= (length (syntax->list #'(x ...))) (length (syntax->list #'(init ...)))) or is there a better way? \$\endgroup\$ Oct 7, 2015 at 12:27
  • \$\begingroup\$ I would use the same expression to the lengths. You could add a fender - and then add a new case to handle the error. When reading code I have a tendency to overlook fenders (and thus make mistakes). So I might be tempted to add the error checking directly to the existing clause - but that's just a matter of personal preference. \$\endgroup\$
    – soegaard
    Oct 7, 2015 at 12:36
  • \$\begingroup\$ Turns out that (syntax-length stx) is in unstable/syntax. Hopefully it will be moved to racket/syntax at some point. \$\endgroup\$
    – soegaard
    Oct 7, 2015 at 12:46
  • \$\begingroup\$ I don't know how to parse "I would use the same expression to the lengths", sorry. :-( BTW, I feel horrible about using unstable/syntax (which you just mentioned, lol), but apparently it provides syntax-length which simplifies the length-checking code a little. ;-) \$\endgroup\$ Oct 7, 2015 at 12:47
  • \$\begingroup\$ to compare the lengths :-) \$\endgroup\$
    – soegaard
    Oct 7, 2015 at 12:47

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