Question

Algorithm查找第一集：

Given a grammar with the rules A1 → w1, ..., An → wn, we can compute the Fi(wi) and Fi(Ai) for every rule as follows:

    initialize every Fi(Ai) with the empty set
    set Fi(wi) to Fi(wi) for every rule Ai → wi, where Fi is defined as follows:
        Fi(a w' ) = { a } for every terminal a
        Fi(A w' ) = Fi(A) for every nonterminal A with ε not in Fi(A)
        Fi(A w' ) = Fi(A) \ { ε } ∪ Fi(w' ) for every nonterminal A with ε in Fi(A)
        Fi(ε) = { ε }
    add Fi(wi) to Fi(Ai) for every rule Ai → wi
    do steps 2 and 3 until all Fi sets stay the same.

语法：

A -> B C c
A -> g D B
B -> EPSILON | b C D E
C -> D a B | c a
D -> EPSILON | d D
E -> g A f | c

此website生成第一个集合，如下所示：

Non-Terminal Symbol     First Set

A                        g, ε, b, a, c, d
B                        ε, b
C                        a, c, ε, d
D                        ε, d
E                        g, c

但算法显示Fi(A w' ) = Fi(A) for every nonterminal A with ε not in Fi(A)，因此根据此算法的First（A）不应包含ε。 First(A) = {g, b, a, c, d}。

问：上述语法的第一个（A）是= First(B) - ε U First(C) U {g}？

此video也遵循上述算法，不选择ε。

Answer 1

First(B) = {ε, b}
First(D) = {ε, d}
First(E) = {g, c}
First(C) = {c, d, a}
First(A) = {b, g, c, d, a}

示例：

X -> Y a | b
Y -> c | ε

First(X) = {c, a, b}
First(Y) = {c, ε}

第一个（X）没有ε因为如果用ε代替Y，那么First（Y a）等于First（εa）= {a}

首先在我的github上设置实现。

修改：更新了链接
https://github.com/amirbawab/EasyCC-CPP/blob/master/src/syntax/grammar/Grammar.cpp#L229
计算第一组和后续组都可以在上面的新链接中找到。

从语法生成第一组

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