### 1.1.4 Scheme compound data types

There are also compound data types in Scheme. The types commonly used in LilyPond programming include pairs, lists, alists, and hash tables.

#### Pairs

The foundational compound data type of Scheme is the `pair`. As might be expected from its name, a pair is two values glued together. The operator used to form a pair is called `cons`.

 ```guile> (cons 4 5) (4 . 5) guile> ```

Note that the pair is displayed as two items surrounded by parentheses and separated by whitespace, a period (`.`), and more whitespace. The period is not a decimal point, but rather an indicator of the pair.

Pairs can also be entered as literal values by preceding them with a single quote character.

 ```guile> '(4 . 5) (4 . 5) guile> ```

The two elements of a pair may be any valid Scheme value:

 ```guile> (cons #t #f) (#t . #f) guile> '("blah-blah" . 3.1415926535) ("blah-blah" . 3.1415926535) guile> ```

The first and second elements of the pair can be accessed by the Scheme procedures `car` and `cdr`, respectively.

 ```guile> (define mypair (cons 123 "hello there") … ) guile> (car mypair) 123 guile> (cdr mypair) "hello there" guile> ```

Note: `cdr` is pronounced "could-er", according Sussman and Abelson, see http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-14.html#footnote_Temp_133

#### Lists

A very common Scheme data structure is the list. Formally, a ‘proper’ list is defined to be either the empty list with its input form `'()` and length 0, or a pair whose `cdr` in turn is a shorter list.

There are many ways of creating lists. Perhaps the most common is with the `list` procedure:

 ```guile> (list 1 2 3 "abc" 17.5) (1 2 3 "abc" 17.5) ```

Representing a list as individual elements separated by whitespace and enclosed in parentheses is actually a compacted rendition of the actual dotted pairs constituting the list, where the dot and an immediately following starting paren are removed along with the matching closing paren. Without this compaction, the output would have been

 ```(1 . (2 . (3 . ("abc" . (17.5 . ()))))) ```

As with the output, a list can also be entered (after adding a quote to avoid interpretation as a function call) as a literal list by enclosing its elements in parentheses:

 ```guile> '(17 23 "foo" "bar" "bazzle") (17 23 "foo" "bar" "bazzle") ```

Lists are a central part of Scheme. In, fact, Scheme is considered a dialect of lisp, where ‘lisp’ is an abbreviation for ‘List Processing’. Scheme expressions are all lists.

#### Association lists (alists)

A special type of list is an association list or alist. An alist is used to store data for easy retrieval.

Alists are lists whose elements are pairs. The `car` of each element is called the key, and the `cdr` of each element is called the value. The Scheme procedure `assoc` is used to retrieve an entry from the alist, and `cdr` is used to retrieve the value:

 ```guile> (define my-alist '((1 . "A") (2 . "B") (3 . "C"))) guile> my-alist ((1 . "A") (2 . "B") (3 . "C")) guile> (assoc 2 my-alist) (2 . "B") guile> (cdr (assoc 2 my-alist)) "B" guile> ```

Alists are widely used in LilyPond to store properties and other data.

#### Hash tables

A data structure that is used occasionally in LilyPond. A hash table is similar to an array, but the indexes to the array can be any type of Scheme value, not just integers.

Hash tables are more efficient than alists if there is a lot of data to store and the data changes very infrequently.

The syntax to create hash tables is a bit complex, but you can see examples of it in the LilyPond source.

 ```guile> (define h (make-hash-table 10)) guile> h # guile> (hashq-set! h 'key1 "val1") "val1" guile> (hashq-set! h 'key2 "val2") "val2" guile> (hashq-set! h 3 "val3") "val3" ```

Values are retrieved from hash tables with `hashq-ref`.

 ```guile> (hashq-ref h 3) "val3" guile> (hashq-ref h 'key2) "val2" guile> ```

Keys and values are retrieved as a pair with `hashq-get-handle`. This is a preferred way, because it will return `#f` if a key is not found.

 ```guile> (hashq-get-handle h 'key1) (key1 . "val1") guile> (hashq-get-handle h 'frob) #f guile> ```

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