8.9 KiB
Pairs, Lists, and Racket Syntax
The cons
function actually accepts any two values, not just a list for
the second argument. When the second argument is not empty
and not
itself produced by cons
, the result prints in a special way. The two
values joined with cons
are printed between parentheses, but with a
dot i.e., a period surrounded by whitespace
in between:
> (cons 1 2)
'(1 . 2)
> (cons "banana" "split")
'("banana" . "split")
Thus, a value produced by cons
is not always a list. In general, the
result of cons
is a pair. The more traditional name for the cons?
function is pair?
, and we’ll use the traditional name from now on.
The name rest
also makes less sense for non-list pairs; the more
traditional names for first
and rest
are car
and cdr
,
respectively. (Granted, the traditional names are also nonsense. Just
remember that “a” comes before “d,” and cdr
is pronounced
“could-er.”)
Examples:
> (car (cons 1 2))
1
> (cdr (cons 1 2))
2
> (pair? empty)
#f
> (pair? (cons 1 2))
#t
> (pair? (list 1 2 3))
#t
Racket’s pair datatype and its relation to lists is essentially a
historical curiosity, along with the dot notation for printing and the
funny names car
and cdr
. Pairs are deeply wired into to the culture,
specification, and implementation of Racket, however, so they survive in
the language.
You are perhaps most likely to encounter a non-list pair when making a
mistake, such as accidentally reversing the arguments to cons
:
> (cons (list 2 3) 1)
'((2 3) . 1)
> (cons 1 (list 2 3))
'(1 2 3)
Non-list pairs are used intentionally, sometimes. For example, the
make-hash
function takes a list of pairs, where the car
of each pair
is a key and the cdr
is an arbitrary value.
The only thing more confusing to new Racketeers than non-list pairs is the printing convention for pairs where the second element is a pair, but is not a list:
> (cons 0 (cons 1 2))
'(0 1 . 2)
In general, the rule for printing a pair is as follows: use the dot
notation unless the dot is immediately followed by an open parenthesis.
In that case, remove the dot, the open parenthesis, and the matching
close parenthesis. Thus, '(0 . (1 . 2))
becomes '(0 1 . 2)
, and '(1 . (2 . (3 . ())))
becomes '(1 2 3)
.
1. Quoting Pairs and Symbols with quote
A list prints with a quote mark before it, but if an element of a list is itself a list, then no quote mark is printed for the inner list:
> (list (list 1) (list 2 3) (list 4))
'((1) (2 3) (4))
For nested lists, especially, the quote
form lets you write a list as
an expression in essentially the same way that the list prints:
> (quote ("red" "green" "blue"))
'("red" "green" "blue")
> (quote ((1) (2 3) (4)))
'((1) (2 3) (4))
> (quote ())
'()
The quote
form works with the dot notation, too, whether the quoted
form is normalized by the dot-parenthesis elimination rule or not:
> (quote (1 . 2))
'(1 . 2)
> (quote (0 . (1 . 2)))
'(0 1 . 2)
Naturally, lists of any kind can be nested:
> (list (list 1 2 3) 5 (list "a" "b" "c"))
'((1 2 3) 5 ("a" "b" "c"))
> (quote ((1 2 3) 5 ("a" "b" "c")))
'((1 2 3) 5 ("a" "b" "c"))
If you wrap an identifier with quote
, then you get output that looks
like an identifier, but with a '
prefix:
> (quote jane-doe)
'jane-doe
A value that prints like a quoted identifier is a symbol. In the same
way that parenthesized output should not be confused with expressions, a
printed symbol should not be confused with an identifier. In particular,
the symbol (quote map)
has nothing to do with the map
identifier or
the predefined function that is bound to map
, except that the symbol
and the identifier happen to be made up of the same letters.
Indeed, the intrinsic value of a symbol is nothing more than its
character content. In this sense, symbols and strings are almost the
same thing, and the main difference is how they print. The functions
symbol->string
and string->symbol
convert between them.
Examples:
> map
#<procedure:map>
> (quote map)
'map
> (symbol? (quote map))
#t
> (symbol? map)
#f
> (procedure? map)
#t
> (string->symbol "map")
'map
> (symbol->string (quote map))
"map"
In the same way that quote
for a list automatically applies itself to
nested lists, quote
on a parenthesized sequence of identifiers
automatically applies itself to the identifiers to create a list of
symbols:
> (car (quote (road map)))
'road
> (symbol? (car (quote (road map))))
#t
When a symbol is inside a list that is printed with '
, the '
on the
symbol is omitted, since '
is doing the job already:
> (quote (road map))
'(road map)
The quote
form has no effect on a literal expression such as a number
or string:
> (quote 42)
42
> (quote "on the record")
"on the record"
2. Abbreviating quote
with '
As you may have guessed, you can abbreviate a use of quote
by just
putting '
in front of a form to quote:
> '(1 2 3)
'(1 2 3)
> 'road
'road
> '((1 2 3) road ("a" "b" "c"))
'((1 2 3) road ("a" "b" "c"))
In the documentation, '
within an expression is printed in green along
with the form after it, since the combination is an expression that is a
constant. In DrRacket, only the '
is colored green. DrRacket is more
precisely correct, because the meaning of quote
can vary depending on
the context of an expression. In the documentation, however, we
routinely assume that standard bindings are in scope, and so we paint
quoted forms in green for extra clarity.
A '
expands to a quote
form in quite a literal way. You can see this
if you put a '
in front of a form that has a '
:
> (car ''road)
'quote
> (car '(quote road))
'quote
The '
abbreviation works in output as well as input. The REPL’s
printer recognizes the symbol 'quote
as the first element of a
two-element list when printing output, in which case it uses ’
to
print the output:
> (quote (quote road))
”road
> '(quote road)
”road
> ''road
”road
3. Lists and Racket Syntax
Now that you know the truth about pairs and lists, and now that you’ve
seen quote
, you’re ready to understand the main way in which we have
been simplifying Racket’s true syntax.
The syntax of Racket is not defined directly in terms of character streams. Instead, the syntax is determined by two layers:
-
a reader layer, which turns a sequence of characters into lists, symbols, and other constants; and
-
an expander layer, which processes the lists, symbols, and other constants to parse them as an expression.
The rules for printing and reading go together. For example, a list is printed with parentheses, and reading a pair of parentheses produces a list. Similarly, a non-list pair is printed with the dot notation, and a dot on input effectively runs the dot-notation rules in reverse to obtain a pair.
One consequence of the read layer for expressions is that you can use the dot notation in expressions that are not quoted forms:
> (+ 1 . (2))
3
This works because (+ 1 . (2))
is just another way of writing (+ 1 2)
. It is practically never a good idea to write application
expressions using this dot notation; it’s just a consequence of the way
Racket’s syntax is defined.
Normally, .
is allowed by the reader only with a parenthesized
sequence, and only before the last element of the sequence. However, a
pair of .
s can also appear around a single element in a parenthesized
sequence, as long as the element is not first or last. Such a pair
triggers a reader conversion that moves the element between .
s to the
front of the list. The conversion enables a kind of general infix
notation:
> (1 . < . 2)
#t
> '(1 . < . 2)
'(< 1 2)
This two-dot convention is non-traditional, and it has essentially
nothing to do with the dot notation for non-list pairs. Racket
programmers use the infix convention sparingly—mostly for asymmetric
binary operators such as <
and is-a?
.