This ppt gives all details about the parsing phase of compiler design.

1. Akhil Kaushik
Asstt. Prof., CE Deptt.,
TIT Bhiwani
Parsing Introduction

2. What is Parsing?
• In the syntax analysis phase, a compiler verifies
whether or not the tokens generated by the lexical
analyzer are grouped according to the syntactic
rules of the language.
• This is done by a parser.
• It detects and reports any syntax errors and
produces a parse tree from which intermediate code
can be generated.

3. What is Parsing?

4. Context-Free Grammars
• Terminals - Basic symbols from which strings are
formed.
• Non-terminals - Syntactic variables that denote sets
of strings.
• Start Symbol - Denotes the nonterminal that
generates strings of the languages
• Productions - A = X … X
- Head/left side (A) is a nonterminal
- Body/right side (X … X) zero or more terminals and non-
terminals

5. Context-Free Grammars
• Non-terminals, terminals
can be derived from
productions.
• First production defines
start symbol.

6. CFG Notation
• A, B, C: non-terminals
• l: terminals
• a, b, c: strings of non-terminals and terminals
• (alpha, beta, gamma in math)
• w, v: strings of terminal symbols

7. Derivations
• Derivation - derives in zero or
more steps
• E =>* "-" "(" ID "+" ID ")"
• Derivation step: replace symbol
by RHS of production.
• Repeatedly apply derivations

8. Derivations
• Left-most derivation:
Expand left-most non-
terminal at each step.
• Right-most derivation:
Expand right-most
non-terminal at each
step

9. Types of Parser
• The process of deriving the string from the given
grammar is known as derivation (parsing).
• Depending upon how derivation is done we have
two kinds of parsers :-
• Top Down Parser
• Bottom Up Parser

10. Top Down Parser
• Top down parsing
attempts to build the
parse tree from root to
leave.
• Top down parser will start
from start symbol and
proceeds to string.
• It follows leftmost
derivation.

11. Bottom Up Parser
• Bottom-up parsing starts from
the leaf nodes of a tree and
works in upward direction till it
reaches the root node.
• Here, we start from a
sentence and then apply
production rules in reverse
manner in order to reach the
start symbol.

12. Left Factoring

13. Left Factoring - Examples
Consider the following grammar:-
• S → iEtS / iEtSeS / a
• E → b
Solution:-
• S → iEtSS’ / a
• S’ → eS / ∈
• E → b

14. Left Factoring - Examples
Consider the following grammar:-
• A → aAB / aBc / aAc
Solution:-
• A → aA’
• A’ → AB / Bc / Ac // This has to done again
• A → aA’
• A’ → AD / Bc
• D → B / c

15. Left Factoring - Examples
Consider the following grammar:-
• S → aAd / aB
• A → a / ab
• B → ccd / ddc
Solution:-
• S → aS’
• S’ → Ad / B
• A → aA’
• A’ → b / ∈

16. Eliminating Left Recursion

17. Left Recursion - Examples
Consider the following grammar -
• A → ABd / Aa / a
• B → Be / b
The grammar after eliminating left recursion is-
• A → aA’
• A’ → BdA’ / aA’ / ∈
• B → bB’
• B’ → eB’ / ∈

18. Left Recursion - Examples
Consider the following grammar and eliminate left
recursion-
• E → E + E / E x E / a
The grammar after eliminating left recursion is-
• E → aA
• A → +EA / xEA / ∈

19. Left Recursion - Examples
• Consider the following grammar and eliminate left
recursion-
• E → E + T / T
• T → T x F / F
• F → id
• E → E + T
• E → T
• T → T x F
• T → F
• F → id
OR

20. Left Recursion - Examples
The grammar after eliminating left recursion is-
• E → TE’
• E’ → +TE’ / ∈
• T → FT’
• T’ → xFT’ / ∈
• F → id

21. First & Follow
• FIRST(X) for a grammar symbol X is the set of
terminals that begin the strings derivable from X.
• Follow(X) to be the set of terminals that can appear
immediately to the right of Non-Terminal X in some
sentential form.
• Why calculate FIRST?
– It is useful to calculate FOLLOW.
– Both are useful in parsing (both Top-Down and Bottom-
Up)

22. First & Follow Rules
Rules to compute FIRST set:-
• If x is a terminal, then FIRST(x) = { ‘x’ }
• If x-> Є, is a production rule, then add Є to
FIRST(x).
• If X->Y1 Y2 Y3….Yn is a production, then FIRST(X) =
FIRST(Y1)
• If FIRST(Y1) contains Є then FIRST(X) = {
FIRST(Y1) – Є } U { FIRST(Y2) }
• If FIRST (Yi) contains Є for all i = 1 to n, then add Є
to FIRST(X).

23. First - Examples
Calculate the first functions for the given grammar-
• S → aBDh
• B → cC
• C → bC / ∈
• D → EF
• E → g / ∈
• F → f / ∈

24. First - Examples
• First(S) = { a }
• First(B) = { c }
• First(C) = { b , ∈ }
• First(D) = { First(E) – ∈ } ∪ First(F) = { g , f , ∈}
• First(E) = { g , ∈ }
• First(F) = { f , ∈ }

25. First - Examples
Calculate the first functions for the given grammar-
• S → A
• A → aB / Ad
• B → b
• C → g

26. First - Examples
• First(S) = First(A) = { a }
• First(A) = { a }
• First(A’) = { d , ∈ }
• First(B) = { b }
• First(C) = { g }

27. First & Follow Rules
Rules to compute FOLLOW set:-
• Follow(S) = {$} where S is the start symbol.
• If A->pBq is a production where p, B, q any
grammar symbols then everything in FIRST(q)
except Є is in FOLLOW(B).
• If A->pB is a production or a production A->pBq
where FIRST(q) contains Є then everything in
FOLLOW(A) is in FOLLOW(B).

28. Follow - Examples
Calculate the follow functions for the given grammar-
• S → aBDh
• B → cC
• C → bC / ∈
• D → EF
• E → g / ∈
• F → f / ∈

29. Follow - Examples
• Follow(S) = { $ }
• Follow(B) = { First(D) – ∈ } ∪ First(h) = { g , f , h }
• Follow(C) = Follow(B) = { g , f , h }
• Follow(D) = First(h) = { h }
• Follow(E) = { First(F) – ∈ } ∪ Follow(D) = { f , h }
• Follow(F) = Follow(D) = { h }

30. Follow - Examples
Calculate the follow functions for the given grammar-
• S → A
• A → aB / Ad
• B → b
• C → g

31. Follow - Examples
• Follow(S) = { $ }
• Follow(A) = Follow(S) = { $ }
• Follow(A’) = Follow(A) = { $ }
• Follow(B) = { First(A’) – ∈ } ∪ Follow(A) = { d , $ }
• Follow(C) = NA

32. First & Follow - Examples
• Calculate the first and follow functions for the
given grammar-
• S → AaAb / BbBa
• A → ∈
• B → ∈

33. First & Follow - Examples
• First(S) = { First(A) – ∈ } ∪ First(a) ∪ { First(B) – ∈
} ∪ First(b) = { a , b }
• First(A) = { ∈ }
• First(B) = { ∈ }
• Follow(S) = { $ }
• Follow(A) = First(a) ∪ First(b) = { a , b }
• Follow(B) = First(b) ∪ First(a) = { a , b }

34. First & Follow - Examples
Calculate the first and follow functions for the given
grammar-
• E → E + T / T
• T → T x F / F
• F → (E) / id

35. First & Follow - Examples
• The given grammar is left recursive.
After eliminating left recursion, we get -
• E → TE’
• E’ → + TE’ / ∈
• T → FT’
• T’ → x FT’ / ∈
• F → (E) / id

36. First & Follow - Examples
• First(E) = First(T) = First(F) = { ( , id }
• First(E’) = { + , ∈ }
• First(T) = First(F) = { ( , id }
• First(T’) = { x , ∈ }
• First(F) = { ( , id }

37. First & Follow - Examples
• Follow(E) = { $ , ) }
• Follow(E’) = Follow(E) = { $ , ) }
• Follow(T) = { First(E’) – ∈ } ∪ Follow(E) ∪
Follow(E’) = { + , $ , ) }
• Follow(T’) = Follow(T) = { + , $ , ) }
• Follow(F) = { First(T’) – ∈ } ∪ Follow(T) ∪
Follow(T’) = { x , + , $ , ) }

38. Akhil Kaushik
akhilkaushik05@gmail.com
9416910303
CONTACT ME AT:
Akhil Kaushik
akhilkaushik05@gmail.com
9416910303
THANK YOU !!!