1. Programming Language Syntax 2

2. Think-Pair-Share Activity
Assuming the following INTEGER regex:
Try to build a regex that matches arithmetic expressions, such as: 55
2 + 5
4 * 5 / -3
(9 * 4)/(2 - +4)
((4 + 7) * 10) * (69 + 7) / (44 - ( ) * +5)

3. Here’s one way Except this isn’t a regex
Regexes cannot have recursive constructs
It’s actually a context-free grammar (CFG)
Like regexes with recursion
Expressed (more or less) in Backus-Naur Form (BNF)

4. But how do you tell ANTLR what your language is like?
Recall from last time… …
ANTLR
generates
for you
But how do you tell ANTLR what your language is like?

5. … You specify token patterns using Regular Expressions
You specify patterns of tokens using a Context-Free Grammar

6. Important distinctions between regexes and CFG rules in ANTLR
Naming:
Regex names start with uppercase letter
CFG-rule names start with lowercase letter
Character versus token handling:
Regexes process stream of characters
CFG rules process stream of tokens

7. Will this regex match these strings?
“4444”?
“ ”?
Yes No

8. Will this CFG production match these strings?
“4444”?
“ ”?
Yes
Yes

9. Backus-Naur Form (BNF)
ANTLR
BNF

10. Extended BNF (EBNF)
ANTLR
BNF
Things not in BNF
EBNF

11. CFG Terminology
terminals
productions
non-terminal

12. CFG Derivation
Series of replacement operations that shows how to derive a string of terminals from the start symbol

13. Derivation Example
CFG:
String to derive:

14. CFG:
String to derive:
Derivation:

15. Parse Tree: Graphical Representation of Derivation
Can you think of another possible derivation?
Hint: This one is a “right-most” derivation

16. Here’s a “left-most” derviation
A grammar with multiple possible derivations is ambiguous
Makes generating parser more difficult

17. Two concepts important to expressions
Associativity: Group based on L-to-R order
means (10 - 4) versus (4 - 3)
Precedence: Group based on operator
3 + 4 * 5 means (4 * 5) versus (3 + 4) * 5

18. Think-Pair-Share Activity
Rewrite this CFG to be unambiguous
Left associative
Multiplication/division have higher precedence than addition/subtraction

19. Solution
Create parse tree for:
3 + 4 * 5

20. Parse Tree for * 5

21. Parse Tree for

22. What’s next?
Homework 1 assigned!