Question

Using the following grammar write an attributes grammar that can calculate the decimal value of an octal number. Grammar: number = list list = list octal | octal octal = ‘0’ | ‘1’ | ‘2’ | ‘3’ | ‘4’ | ‘5’ | ‘6’ | ‘7’ Notes: An octal number consists of octal digits, i.e. 0 to 7. The following example shows how to convert the octal 67 to its equivalent decimal. The symbol star represents multiplication. 67 = 6 * 81 + 7 * 80 = 6 * 8 + 7 = 55

Questions:

1a - introduce an attribute (4 points)

1b - specify the type of your attribute, i.e. intrinsic, inherited, or synthesized. (5 points)

1c - write the attributes grammar (Syntax rule, Semantic rule, Semantic condition) for every grammar rule. (16 points)

Answer 1

Solution: In this question given grammar is  number = list list = list octal | octal octal = ‘0’ | ‘1’ | ‘2’ | ‘3’ | ‘4’ | ‘5’ | ‘6’ | ‘7’ . Means you can understand the grammar as a number can be list and list can be list and octal or simply octal and octal can be simply number from 0 to 7 which is simply total of 8 numbers . And we know that if base of the number system is 8 then total number present in the number system is 0 to seven . Hence if you get an more than 7 then get an error which means number can be a octal.

Solution 1a)  Attribute : Attribute of a grammar is nothing but attribute has well-defined domain of values, such as an integer, float, character, string, and expressions. Attribute have additional information that are appended to the given grammar or production. When parser come a cross these attribute then what ever define by these attribute it can understand and parse accordingly.

generally Attribute are Two Types :

1) Synthesized Attribute :- A attribute is said to synthesized if parent takes a value from its children then this types of attribute is called Synthesized Attribute . For example : Let's Suppose a production rule A-> B C D the { A.s= B.s or A.s=C.s} here A is taken value from its child B and C so this is Synthesized attribute.

2) Inherited Attribute: A attribute is said to inherited attribute if a parent can inherit the value from its child or child can inherit value from its parent . Then this types of attribute is called Inherited attribute . For example : Let's Suppose a same production rule which are discuss above  A-> B C D then { A.s= B.s or B.s=A.s or C.s=B.s or C.s=D.s} all are allowed in inherited attribute . Here must you careful that variable b can take value from its sibling(Sibling either right or left )and also its parent.

Solution 1b):

Another two types of attributed

i) S-Attribute:- A attribute is said to S-attribute if it can takes a value from its parents . means S-attribute are nothing but synthesized attribute . In the S-attribute you can write SDT(Syntax Direct Translation) or you can say semantic action only from right end of right side of the production.

S-attribute are evaluated during bottom up parsing .

ii) L-Attribute:- A attribute is said to L-attribute if it is synthesized as well as inherited but only restriction that it can be inherit from left side(means a variable takes value from its left of the production . It can not takes a value from its right.) So it is more power full in terms of attribute distribution because it is both synthesized as well as inherited. In L-attribute you can write the SDT you can say semantic action any where of the production of right side either right end or middle of the production or start of the production(Note-: Here write SDT only right hand side of the production ).

L-Attribute are evaluated during parsing depth first left to right.

For example: A.s= B.s or B.s=A.s or C.s=B.s or C.s=D.s, A.s= B.s or A.s=C.s or C.s = B.s (c is takes value from its left sibling B)

Solution 1c):

In this i am writing SDT for the given grammar to convert Octal Number to an equivalent Decimal number and also given along with example in which octal number 67 are converted into equivalent decimal =55 with its semantic action along with attribute.

And you can observe that here attribute are synthesized because parent taken value from its children . You can also write the same grammar using L-attribute with miner modification. In this value is an attribute which is represent the value of that variable .