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schemelispracketthe-little-schemer
Tumok A. Byrd
Tumok A. Byrd

Reputation: 53

Does a non-null Scheme list contain at least one atom?

In The Little Schemer (4th Ed.) it is claimed that a list for which null? is false contains at least one atom, or so I understand from my reading of the text.

This doesn't make sense to me, since (atom '()) is false, and we can stick those into a list to make it non-null:

> (null? '(()))
#f

So my question is, is this a mistake in my reading, or a matter of definitions? Since it's not in the errata I assume such a well-studied book wouldn't have a mistake like this.

If we considered (()) to be the same as (() . ()) or even (cons '() '()) and then considered cons an atom then I could see how you can get there, but I don't think that's what's going on.

(this was tested in Racket 7.0, with the definition of atom? given in the book, i.e.

(define atom?
  (lambda (x)
  (and (not (pair? x)) (not (null? x)))))

I know this doesn't cover funny Racket features, but should be sufficient here.)

Upvotes: 1

Views: 293

Answers (3)

soegaard
soegaard

Reputation: 31147

As a concept an “atom” is something that can not be broken into smaller parts. A number 42 is an atom, a list (42 43) is not an atom since it contains two smaller parts (namely the numbers 42 and 43). Since an empty list does not contain any smaller parts, it is by this logic an atom.

Now let’s attempt to implement an atom? predicate, that determines whether it’s input is an atom. 

(define (atom? x)
  (cond
     [(number? x) #t]
     [(symbol? x) #t]
     [(char? x)   #t]
     ...
     [else #f]))

Here the ... needs to be replaced with a test for every atomic data type supported by the implementation. This can potentially be a long list. In order to avoid this, we can try to be clever:

(define (atom? x)
  (not (list? x)))

This will correctly return false for non-empty lists, and true for numbers, characters etc. However it will return false for the empty list.

Since it is up to the authors of the book to define the term “atom” (the word does not appear in the language standard) they might have opted for the above simple definition.

Note that the definition as non-list is misleading when the language contains other compound data structures such as vectors and structures. If I recall correctly the only compound data structure discussed in the book is lists.

Upvotes: 1

Sylwester
Sylwester

Reputation: 48745

I think lat indicates list of atoms. Thus if lat is not null?, then it needs to contain at least one atom.

There is a procedure called lat? defined as such:

(define lat?
  (lambda (l)
    (cond
      ((null? l) #t)
      ((atom? (car l)) 
       (lat? (cdr l)))
      (else #f))))

(lat? '(()) ; ==> #f so by definition '(()) is not a lat and thus the statement does not apply to that list.

A list can contain any type of elements, including empty and other lists, both which are not atoms. lat is a restricted to a flat list with only atomic elements.

Upvotes: 1

Will Ness
Will Ness

Reputation: 71074

lat is assumed to be a list of atoms at that point in the book.

If it's not empty, by definition it contains some atoms in it.

It's not about Lisp, it's about the book's presentation.

Upvotes: 2

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