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#### 2.2.5.5 Miscellaneous: length, append, concatenate, reverse, zip and count

Function: length list
Function: length+ clist

Both `length` and `length+` return the length of the argument. It is an error to pass a value to `length` which is not a proper list (finite and nil–terminated). In particular, this means an implementation may diverge or signal an error when `length` is applied to a circular list.

`length+`, on the other hand, returns `#f` when applied to a circular list.

The length of a proper list is a non–negative integer n such that `cdr` applied n times to the list produces the empty list.

Function: append list1 ...
Function: append! list1 ...

R5RS `append` returns a list consisting of the elements of list1 followed by the elements of the other list parameters.

```(append '(x) '(y))        =>  (x y)
(append '(a) '(b c d))    =>  (a b c d)
(append '(a (b)) '((c)))  =>  (a (b) (c))
```

The resulting list is always newly allocated, except that it shares structure with the final listi argument. This last argument may be any value at all; an improper list results if it is not a proper list. All other arguments must be proper lists.

```(append '(a b) '(c . d))  =>  (a b c . d)
(append '() 'a)           =>  a
(append '(x y))           =>  (x y)
(append)                  =>  ()
```

`append!` is the linear–update variant of `append`; it is allowed, but not required, to alter cons cells in the argument lists to construct the result list. The last argument is never altered; the result list shares structure with this parameter.

Function: concatenate list-of-lists
Function: concatenate! list-of-lists

These functions append the elements of their argument together. That is, `concatenate` returns:

```(apply append list-of-lists)
```

or, equivalently:

```(reduce-right append '() list-of-lists)
```

`concatenate!` is the linear–update variant, defined in terms of `append!` instead of `append`.

Note that some Scheme implementations do not support passing more than a certain number (e.g. 64) of arguments to an n–ary procedure. In these implementations, the `(apply append ...)` idiom would fail when applied to long lists, but concatenate would continue to function properly.

As with `append` and `append!`, the last element of the input list may be any value at all.

Function: reverse list
Function: reverse! list

R5RS `reverse` returns a newly allocated list consisting of the elements of list in reverse order.

```(reverse '(a b c))              =>  (c b a)
(reverse '(a (b c) d (e (f))))  =>  ((e (f)) d (b c) a)
```

`reverse!` is the linear–update variant of `reverse`. It is permitted, but not required, to alter the argument’s cons cells to produce the reversed list.

`append-reverse` returns:

```(append (reverse rev-head) tail)
```

It is provided because it is a common operation, a common list–processing style calls for this exact operation to transfer values accumulated in reverse order onto the front of another list, and because the implementation is significantly more efficient than the simple composition it replaces.

But note that this pattern of iterative computation followed by a `reverse` can frequently be rewritten as a recursion, dispensing with the `reverse` and `append-reverse` steps, and shifting temporary, intermediate storage from the heap to the stack, which is typically a win for reasons of cache locality and eager storage reclamation.

`append-reverse!` is just the linear–update variant; it is allowed, but not required, to alter rev-head’s cons cells to construct the result.

Function: zip clist1 clist2 ...

Defined as:

```(lambda lists (apply map list lists))
```

If `zip` is passed n lists, it returns a list as long as the shortest of these lists, each element of which is an n–element list comprised of the corresponding elements from the parameter lists.

```(zip '(one two three)
'(1 2 3)
'(odd even odd even odd even odd even))
=> ((one 1 odd) (two 2 even) (three 3 odd))

(zip '(1 2 3))
=> ((1) (2) (3))
```

At least one of the argument lists must be finite:

```(zip '(3 1 4 1) (circular-list #f #t))
=> ((3 #f) (1 #t) (4 #f) (1 #t))
```
Function: unzip1 list
Function: unzip2 list
Function: unzip3 list
Function: unzip4 list
Function: unzip5 list

`unzip1` takes a list of lists, where every list must contain at least one element, and returns a list containing the initial element of each such list. That is, it returns `(map car lists)`.

`unzip2` takes a list of lists, where every list must contain at least two elements, and returns two values: a list of the first elements, and a list of the second elements.

`unzip3` does the same for the first three elements of the lists, and so forth.

```(unzip2 '((1 one) (2 two) (3 three)))
=> (1 2 3)
(one two three)
```
Function: count pred clist1 ...

pred is a procedure taking as many arguments as there are lists and returning a single value. It is applied element–wise to the elements of the lists, and a count is tallied of the number of elements that produce a true value. This count is returned.

`count` is “iterative” in that it is guaranteed to apply pred to the list elements in a left–to–right order. The counting stops when the shortest list expires.

```(count even? '(3 1 4 1 5 9 2 5 6))                => 3
(count <     '(1 2 4 8) '(2 4 6 8 10 12 14 16))   => 3
```

At least one of the argument lists must be finite:

```(count < '(3 1 4 1) (circular-list 1 10)) => 2
```

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