CS 461

1
CS 461 Oct. 7

• Applications of CFLs Compiling
• Scanning vs. parsing
• Expression grammars
• Associativity
• Precedence
• Programming language (handout)

2
Compiling

• Grammars are used to define programming language
  and check syntax.
• Phases of a compiler

source code
scanner
stream of tokens
parser
parse tree
3
Scanning

• Scanner needs to know what to expect when eating
  your program.
• identifiers
• numbers
• strings
• comments
• Specifications for tokens can be expressed by
  regular expression (or regular grammar).
• While scanning, we can be in different states,
  such as inside a comment.

4
Parser

• Purpose is to understand structure of program.
• All programming structures can be expressed as
  CFG.
• Simple example for and
• expr ? expr digit expr digit digit
• digit ? 0 1 2 3 4 5 6 7 8 9
• How would we derive the string 9 5 2 ?

5
9 5 2

• expr ? expr digit expr digit digit
• digit ? 0 1 2 3 4 5 6 7 8 9
• expr
• expr digit
• expr - digit 2
• digit 5
• 9
• Leftmost derivation expr ? expr digit
• ? expr digit digit
• ? digit digit digit
• ? 9 digit digit
• ? 9 5 digit
• ? 9 5 2

parse tree
6
Left right recursion

• What is the difference between these 2 grammars?
  Which one is better?
• expr ? expr digit expr digit digit
• digit ? 0 1 2 3 4 5 6 7 8 9
• expr ? digit expr digit expr digit
• digit ? 0 1 2 3 4 5 6 7 8 9
• Lets try 9 5 2 on both of these. The
  grammar must convey the order of operations!
• Operators may be left associative or right
  associative.

7
- /

• Question
• How do we write grammar for all 4 operators? Can
  we do it this way
• expr ? expr digit expr digit
• expr digit expr / digit
• digit
• digit ? 0 1 2 3 4 5 6 7 8 9
• BTW, we can ignore digits and from now on just
  replace them with num, and understand its any
  single number.

8
Precedence

• ( /) bind stronger than ( -)
• ( -) separate better than ( /)
• Need to break up expression into terms
• Ex. 9 8 2 4 / 5
• We want to say that an expression consists of
  terms separated by and
• And each term consists of numbers separated by
  and /
• But which should we define first, expr or term?

9
Precedence (2)

• Which grammar is right?
• expr ? expr term expr term term
• term ? term num term / num num
• Or this one
• expr ? expr term expr / term term
• term ? term num term num num
• Lets try examples 1 2 3 and 1 2
  3

10
Moral

• If a grammar is defining something hierarchical,
  like an expression, define large groupings first.
• Lower precedence operators appear first in
  grammar. (They separate better)
• Ex. appears lower in parse tree than because
  it gets evaluated first.
• In a real programming language, there can be more
  than 10 levels of precedence. C has 15!

11
C language ?

• Handout
• How does the grammar begin?
• Where are the mathematical expressions?
• Do you agree with the precedence?
• Do you see associativity?
• What else is defined in grammar?
• Where are the terminals?