编译原理(八) wu-kan

考虑以下语法制导定义(Syntax Directed Definition),对于输入串 gbbabbccd 构造带注释的分析树(annotated parse tree)

语法规则语义规则
$S\to ABCD$S.val = A.val + B.val + C.val + D.val
$A\to gBa$A.val = B.val * 5
$B\to B1b$B.val = B1.val * 2
$B\to b$B.val = 2
$C\to C1c$C.val = C1.val * 3
$C\to c$C.val = 3
$D\to d$D.val = 1
flowchart TB
I0-->I1
I0-->I2
I0-->I3
I0-->I4
I1-->I5
I1-->I6
I1-->I7
I2-->I9
I2-->I10
I3-->I11
I3-->I12
I4-->I13
I6-->I14
I6-->I15
I9-->I16
I11-->I17
I14-->I18
I0["
    S
    S.val #equals; A.val + B.val + C.val + D.val #equals; 34
"]
I1["
    A
    A.val #equals; B.val * 5 #equals; 20
"]
I2["
    B
    B.val #equals; B1.val * 2 #equals; 4
"]
I3["
    C
    C #equals; C1.val * 3 #equals; 9
"]
I4["
    D
    D.val #equals; 1
"]
I5[g]
I6["
    B
    B.val #equals; B1.val * 2 #equals; 4
"]
I7[a]
I9["
    B1
    B1.val #equals; 2
"]
I10[b]
I11["
    C1
    C1.val #equals; 3
"]
I12[c]
I13[d]
I14["
    B1
    B1.val #equals; 2
"]
I15[b]
I16[b]
I17[c]
I18[b]

以下文法定义了二进制浮点数常量的语法规则。试给出一个 S 属性的语法制导定义,其作用是求出该二进制浮点数的十进制值,并存放在开始符号 S 相关联的一个综合属性 value 中。例如,对于输入串 101.101,S 的 value 属性值结果应该是 5.625。要求在编写语法制导定义时,不得改写文法

\[S\to L.L\vert L\\ L\to LB\vert B\\ B\to 0\vert 1\]
语法规则语义规则
$S\to L$S.val = L.val
$S\to L_1.L_2$S.val = L1.val + L2.val * pow(0.5, L2.len)
$L\to L_1B$L.val = L1.val *2 + B.val, L.len = L1.len + 1
$L\to B$L.val = B.val, L.len = 1
$B\to 0$B.val = 0
$B\to 1$B.val = 1