用 nltk 编写上下文无关语法 - 一个以两个单词或更多为结尾的规则

问题描述

这是我的任务：

这是我的实现：

#Todo - construct a CFG for simple arithmetic expressions 
all_numbers = "'zero' | 'one' | 'two' | 'three' | 'four' | 'five' " \
            + "| 'six' | 'seven' | 'eight' | 'nine' | 'ten' | 'eleven' " \
            + "| 'twelve' | 'thirteen' | 'fourteen' | 'fifteen' " \
            + "| 'sixteen' | 'seventeen' | 'eighteen' | 'nineteen' | 'twenty'"
arithmetic_grammar = nltk.CFG.fromstring(""" 
    S -> operand operator operand | S operator operand | S operator S 
    operand -> """+all_numbers+"""
    operator -> 'plus' | 'minus' | 'times' | 'divided by'
""")
print(arithmetic_grammar)

这是打印 CFG 的结果：

现在我这样做：

 #Todo
# "fifteen minus five"
tree2 = nltk.Tree.fromstring("(S (operand fifteen) (operator minus) (operand fifteen))")
# "four divided by two plus one"
tree3 = nltk.Tree.fromstring("(S (S (operand four) (operator divided by) (operand two)) (operator plus) (operand one))")

这是绘制树木的结果：

def validate(tree,grammar):
    return functools.reduce(lambda accum,production: 
                               accum and production in grammar.productions(),tree.productions())

使用它来指示我的 CFG 是否正确编写，我得到：

print(validate(tree2,arithmetic_grammar))
print(validate(tree3,arithmetic_grammar))

如何通过保留最初的“除以”表达式来表示除法来解决这个问题？ 我可以将其更改为“divided_by”，但我希望它保持原样。 提前致谢。

解决方法

我发现一个有效的解决方案是：

#TODO - construct a CFG for simple arithmetic expressions 
all_numbers = "'zero' | 'one' | 'two' | 'three' | 'four' | 'five' " \
            + "| 'six' | 'seven' | 'eight' | 'nine' | 'ten' | 'eleven' " \
            + "| 'twelve' | 'thirteen' | 'fourteen' | 'fifteen' " \
            + "| 'sixteen' | 'seventeen' | 'eighteen' | 'nineteen' | 'twenty'"
arithmetic_grammar = nltk.CFG.fromstring(""" 
    S -> operand operator operand | S operator operand | S operator S 
    operand -> """+all_numbers+"""
    operator -> 'plus' | 'minus' | 'times' | 'divided' b
    b -> 'by'
""")
print(arithmetic_grammar)

给出了这些推导规则：

和那些派生树：