Python 内建常量 Ellipsis

version Python3.5.3

查阅 Python 文档时发现了这么一个常量 Ellipsis

文档中表述如下

Ellipsis
The same as .... Special value used mostly in conjunction with extended slicing syntax for user-defined container data types.

In [25]: ... is Ellipsis
Out[25]: True

有了这个常量，我们便可以定义一些有趣的东西，比如一个和 Haskell 中类似的 list

λ [1, 2]
[1,2]
:: Num t => [t]
λ [1..10]
[1,2,3,4,5,6,7,8,9,10]
:: (Enum t, Num t) => [t]
λ [1, 4 .. 10]
[1,4,7,10]
:: (Enum t, Num t) => [t]

为此我们先来看看 Python 中的序列协议 __getitem__

In [1]: class Seq(object):
   ...:     def __getitem__(self, key):
   ...:         return key
   ...:     

In [2]: seq = Seq()

In [3]: seq[1, 2, 3, 4, 5]
Out[3]: (1, 2, 3, 4, 5)

In [4]: seq[1:2]
Out[4]: slice(1, 2, None)

In [5]: seq[1:10:2]
Out[5]: slice(1, 10, 2)

In [6]: seq[3, 1:10:2]
Out[6]: (3, slice(1, 10, 2))

我们可以看出，传入的是一个 tuple 类型，如果有切片操作的话，则对应一个 slice 对象

知道这点便好办了，至于无穷 list 我们可以使用 generator 来解决

class InfiniteSeq(object):
    def __getitem__(self, items):
        if isinstance(items, tuple):
            index = 0
            while index < len(items):
                if items[index] is Ellipsis:
                    end = items[index+1] if index+1 < len(items) else float('INF')
                    if index > 1:
                        step = items[index-1] - items[index-2]
                    else:
                        step = 1 if end > items[index-1] else -1
                    value = items[index-1] + step
                    while (step > 0 and value <= end) or (step < 0 and value >= end):
                        yield value
                        value = value + step
                    index = index + 1
                else:
                    yield items[index]
                index = index + 1
        else:
            raise SyntaxError

测试结果

In [109]: seq = InfiniteSeq()

In [110]: list(seq[1, 2, 3, 4, 5])
Out[110]: [1, 2, 3, 4, 5]

In [111]: list(seq[1, ..., 5])
Out[111]: [1, 2, 3, 4, 5]

In [112]: list(seq[1, 3, ..., 7])
Out[112]: [1, 3, 5, 7]

In [113]: list(seq[1, 3, ..., 8])
Out[113]: [1, 3, 5, 7]

In [114]: list(seq[1, 3, ..., 9])
Out[114]: [1, 3, 5, 7, 9]

In [115]: list(seq[10, 1, 3, ..., 9, 12])
Out[115]: [10, 1, 3, 5, 7, 9, 12]

In [116]: list(seq[10, ..., 1])
Out[116]: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]

In [117]: list(seq[10, 8, ..., 0])
Out[117]: [10, 8, 6, 4, 2, 0]

In [118]: for i in seq[1, ...]:
     ...:     print(i)
     ...:     if i > 5:
     ...:         break
     ...:     
1
2
3
4
5
6

Update 2017.05.06: 注 Numpy 在多维数组切片时有用到这个常量。比如 x 是一个四维数组，则 x[i, ...] 等价于 x[i, :, :, :]