Haskell相当于Python中的数据构造函数？

Question

在Haskell中，我可以按如下方式定义二叉树：

data Bint a = Leaf a | Branch a (Bint a) (Bint a) 

然后我可以对它进行一些操作如下：

height (Leaf a) = 1
height (Branch a l r) = 1 + (max (height l) (height r))

count (Leaf a) = 1
count (Branch a l r) = 1 + (count l) + (count r) 

我知道Python在Haskell中没有相应的data 。 如果有，请告诉我。

那么，如何在Python中定义二叉树以及如何在其中实现上述两个函数呢？

Answer 1

我将在这里与Haskell进行类似的功能编程。 从某种意义上说，这不是非常“pythonic”。 特别是，它不是面向对象的。 不过，它仍然有用且干净。

数据类型是一个类。 具有多个数据构造函数的数据类型是一个类，其中包含有关如何构造它的额外信息。 当然，它需要一些数据。 使用构造函数确保所有树都合法：

class BinTree (object):
    def __init__(self, value=None, left=None, right=None):
        if left == None and right == None and value != None:                
            self.isLeaf = True
            self.value = value
        elif left != None and right != None and value == None:
            self.isLeaf = False
            self.value = (left, right)
        else:
            raise ArgumentError("some help message")

这个构造函数调用有点不方便，所以有一些易于使用的智能构造函数：

def leaf(value):
    return BinTree(value=value)

def branch(left, right):
    return BinTree(left=left, right=right)

我们如何获得价值？ 让我们为此做一些帮助：

def left(tree):
    if tree.isLeaf:
        raise ArgumentError ("tree is leaf")
    else:
        return tree.value[0]

def right(tree):
    if tree.isLeaf:
        raise ArgumentError ("tree is leaf")
    else:
        return tree.value[1]

def value(tree):
    if not tree.isLeaf:
        raise ArgumentError ("tree is branch")
    else:
        return tree.value

而已。 你有一个纯粹的“代数”数据类型，可以通过函数访问：

def count(bin_tree):
    if bin_tree.isLeaf:
        return 1
    else:
        return count(left(bin_tree))+count(right(bin_tree))

Answer 2

最接近的可能是带方法的类：

class Leaf:
    def __init__(self, value):
        self.value = value

    def height(self):
        return 1

    def count(self):
        return 1


class Branch:
    def __init__(self, left, right):
        self.left = left
        self.right = right

    def height(self):
        return 1 + max(self.left.height(), self.right.height())

    def count(self):
        return 1 + self.left.count() + self.right.count()

虽然这有些惯用并且有其自身的优势，但它也缺乏Haskell版本的一些特性。 最重要的是，函数定义必须与类一起在同一模块中定义。 您可以使用单调度泛型函数而不是方法来获取它。 结果比方法和Haskell函数更开放世界，并且允许在有益的情况下将定义分布在多个模块上。

@singledispatch
def height(_):
    raise NotImplementedError()

@singledispatch
def count(_):
    raise NotImplementedError()

class Leaf:
    def __init__(self, value):
        self.value = value

@height.register(Leaf)
def height_leaf(leaf):
    return 1

@height.register(Leaf)
def count_leaf(leaf):
    return 1    

class Branch:
    def __init__(self, left, right):
        self.left = left
        self.right = right

@height.register(Branch)
def height_branch(b):
    return 1 + max(b.left.height(), b.right.height())

@count.register(Branch)
def count_branch(b):
    return 1 + b.left.count() + b.right.count()

Answer 3

Python没有像Haskell那样的“数据构造函数”的概念。 您可以像大多数其他OOP语言一样创建类。 或者，您始终可以使用内置函数表示数据类型，并且只定义处理它们的函数（这是用于在heapq内置模块中实现堆的方法）。

python和haskell之间的区别很大，所以最好避免在haskell和python的语法/特性之间进行严格的比较，否则你最终会编写非pythonic和低效的python代码。

即使python确实具有某些功能特性，它也不是一种功能语言，因此您必须完全改变程序的范例，以获得可读，pythonic和高效的程序。

---

使用类的可能实现可以是：

class Bint(object):
    def __init__(self, value, left=None, right=None):
        self.a = value
        self.left = left
        self.right = right

    def height(self):
        left_height = self.left.height() if self.left else 0
        right_height = self.right.height() if self.right else 0
        return 1 + max(left_height, right_height)

    def count(self):
        left_count = self.left.count() if self.left else 0
        right_height = self.right.count() if self.right else 0
        return 1 + left_count + right_count

该代码可以被简化有点提供一个“聪明”的默认值， left和right ：

class Nil(object):
    def height(self):
        return 0
    count = height

nil = Nil()

class Bint(object):
    def __init__(self, value, left=nil, right=nil):
        self.value = value
        self.left = left
        self.right = right
    def height(self):
        return 1 + max(self.left.height(), self.right.height())
    def count(self):
        return 1 + self.left.count() + self.right.count()

请注意，这些实现允许只有一个子节点的节点。

然而，你不必使用类定义的数据类型。 例如，您可以说Bint可以是单个元素的列表，根的值，也可以是包含三个元素的列表：值，左子项和右子项。

在这种情况下，您可以将函数定义为：

def height(bint):
    if len(bint) == 1:
        return 1
    return 1 + max(height(bint[1]), height(bint[2]))

def count(bint):
    if len(bint) == 1:
    return 1 + count(bint[1]) + count(bint[2])

另一种方法是使用namedtuple ：

from collections import namedtuple

Leaf = namedtuple('Leaf', 'value')
Branch = namedtuple('Branch', 'value left right')

def height(bint):
    if len(bint) == 1: # or isinstance(bint, Leaf)
        return 1
    return 1 + max(height(bint.left), height(bint.right))

def count(bint):
    if len(bint) == 1:  # or isinstance(bint, Leaf)
    return 1 + count(bint.left) + count(bint.right)

Answer 4

自上次更新以来的五年，但这是我的答案。

使data Tree a = Leaf a | Branch (Tree a) (Tree a) deriving (Show) data Tree a = Leaf a | Branch (Tree a) (Tree a) deriving (Show)到python ...

没有类型检查（更像是python）

class Tree:
    def __init__(self):
        pass

    def height(self):
        pass

    def count(self):
        pass

class Leaf(Tree):
    def __init__(self, value):
        self.value = value

    def __str__(self):
        return("Leaf " + str(self.value))

    def height(self):
        return 1

    def count(self):
        return 1

class Branch(Tree):
    def __init__(self, left, right):
        if isinstance(left, Tree) and isinstance(right, Tree):
            self.left = left
            self.right = right
        else:
            raise ValueError

    def __str__(self):
        return("Branch (" + str(self.left) + " " +
               str(self.right) + ")")

    def height(self):
        return 1 + max(self.left.height(), self.right.height())

    def count(self):
        return 1 + self.left.count() + self.right.count()


#usage : Branch(Leaf(5), Branch(Leaf(3), Leaf(2)))

带类型检查（更像是haskell）

树类的height ， count方法

class Tree:
    def __init__(self, tree, type_):
        def typecheck(subtree):
            if isinstance(subtree, Leaf):
                if not isinstance(subtree.value, type_):
                    print(subtree.value)
                    raise ValueError
            elif isinstance(subtree, Branch):
                typecheck(subtree.left)
                typecheck(subtree.right)
            else:
                raise ValueError
        typecheck(tree)
        self.tree = tree
        self.type_ = type_

    def __str__(self):
        return ("Tree " + self.type_.__name__ + "\n" + str(self.tree))

    def height(self):
        if isinstance(self, Leaf):
            return 1
        elif isinstance(self, Branch):
            return 1 + max(self.left.height(), self.right.height())
        else:
            return self.tree.height()

    def count(self):
        if isinstance(self, Leaf):
            return 1
        elif isinstance(self, Branch):
            return 1 + self.left.count() + self.right.count()
        else:
            return self.tree.count()


class Leaf(Tree):
    def __init__(self, value):
            self.value = value

    def __str__(self):
            return("Leaf " + str(self.value))


class Branch(Tree):
    def __init__(self, left, right):
        if isinstance(left, Tree) and isinstance(right, Tree):
            self.left = left
            self.right = right
        else:
            raise ValueError

    def __str__(self):
        return("Branch (" + str(self.left) + " " +
               str(self.right) + ")")


#usage tree1 = Tree(Branch(Leaf(5), Branch(Leaf(3), Leaf(2))), int)
#usage tree1.height() -> 3
#usage tree1.count() -> 5

叶子和分支类的height ， count方法

class Tree:
    def __init__(self, tree, type_):
        def typecheck(subtree):
            if isinstance(subtree, Leaf):
                if not isinstance(subtree.value, type_):
                    print(subtree.value)
                    raise ValueError
            elif isinstance(subtree, Branch):
                typecheck(subtree.left)
                typecheck(subtree.right)
            else:
                raise ValueError
        typecheck(tree)
        self.tree = tree
        self.type_ = type_

    def __str__(self):
        return ("Tree " + self.type_.__name__ + "\n" + str(self.tree))

    def height(self):
        return self.tree.height()

    def count(self):
        return self.tree.count()


class Leaf(Tree):
    def __init__(self, value):
            self.value = value

    def __str__(self):
            return("Leaf " + str(self.value))

    def height(self):
        return 1

    def count(self):
        return 1


class Branch(Tree):
    def __init__(self, left, right):
        if isinstance(left, Tree) and isinstance(right, Tree):
            self.left = left
            self.right = right
        else:
            raise ValueError

    def __str__(self):
        return("Branch (" + str(self.left) + " " +
               str(self.right) + ")")

    def height(self):
        return 1 + max(self.left.height(), self.right.height())

    def count(self):
        return 1 + self.left.count() + self.right.count()

#usage Tree(Branch(Leaf(5), Branch(Leaf(3), Leaf(2))), int)
#usage tree1.height() -> 3
#usage tree1.count() -> 5

height ， count方法以外的类（最喜欢的Haskell）

class Tree:
    def __init__(self, tree, type_):
        def typecheck(subtree):
            if isinstance(subtree, Leaf):
                if not isinstance(subtree.value, type_):
                    print(subtree.value)
                    raise ValueError
            elif isinstance(subtree, Branch):
                typecheck(subtree.left)
                typecheck(subtree.right)
            else:
                raise ValueError
        typecheck(tree)
        self.tree = tree
        self.type_ = type_

    def __str__(self):
        return ("Tree " + self.type_.__name__ + "\n" + str(self.tree))


class Leaf(Tree):
    def __init__(self, value):
            self.value = value

    def __str__(self):
            return("Leaf " + str(self.value))


class Branch(Tree):
    def __init__(self, left, right):
        if isinstance(left, Tree) and isinstance(right, Tree):
            self.left = left
            self.right = right
        else:
            raise ValueError

    def __str__(self):
        return("Branch (" + str(self.left) + " " +
               str(self.right) + ")")

def height(tree):
    if not isinstance(tree, Tree):
        raise ValueError
    if isinstance(tree, Leaf):
        return 1
    elif isinstance(tree, Branch):
        return 1 + max(height(tree.left), height(tree.right))
    else:
        return height(tree.tree)

def count(tree):
    if not isinstance(tree, Tree):
        raise ValueError
    if isinstance(tree, Leaf):
        return 1
    elif isinstance(tree, Branch):
        return 1 + count(tree.left) + count(tree.right)
    else:
        return count(tree.tree)

#usage tree1 = Tree(Branch(Leaf(5), Branch(Leaf(3), Leaf(2))), int)
#usage height(tree1) -> 3
#usage count(tree1) -> 5