1. Compiler Construction
Sohail Aslam
Lecture 25
compiler: Bottom-up Parsing

2. Sets of LR(1) Items
I0 ={ [S → E, $], [E → E+(E), $/+], [E → int, $/+] }

3. The Closure Procedure Rationale:
if [A → bCd,a]  s, then one potential completion for the left context is to find a string that reduces to C, followed by da

4. The Closure Procedure
This completion should cause a reduction to A, since it fills out the production’s right-hand side (Cd), and follows it with a valid lookahead symbol

5. The Closure Procedure
For a production C → g, closure must insert '' before g and add appropriate lookahead symbols – all terminals that can appear as the initial symbol in da

6. The Closure Procedure
This includes every terminal in FIRST(d). If e  FIRST(d), it also includes a, thus FIRST(da) in the algorithm

7. The goto Procedure
The second critical step in the construction is to derive other parser states from I0

8. The goto Procedure
To accomplish this, we compute, for each state Ii and each grammar symbol y, the state that would arise if the parser recognized an y while in state Ii

9. The goto Procedure
A state s that contains [X → ayb, b] has a transition (goto) labeled y to the state that contains the items goto(s, y)
y can be terminal or a non-terminal

10. goto(s, y)
m  { }
for each item [X → ayb, b]  s
m ← m  {[X → ayb, b]}
return closure(m)

11. Finite Automaton of Items
The LR(1) items are used as the states of a finite automaton that maintains information about the parsing stack and progress of a shift-reduce parser

12. Finite Automaton of Items
This will start out as a nondeterministic finite automaton (NFA)
The DFA can be constructed from this NFA using the subset construction, similar to one we used for lexical analysis

13. Finite Automaton of Items
This will start out as a nondeterministic finite automaton (NFA)
The DFA can be constructed from this NFA using the subset construction, similar to one we used for lexical analysis

14. Finite Automaton of Items
What are the transitions of the NFA of LR(0) items?
Consider the item A→ ag
Suppose g begins with symbol X which may be a terminal (token) or non-terminal

15. Finite Automaton of Items
What are the transitions of the NFA of LR(0) items?
Consider the item A→ ag
Suppose g begins with symbol X which may be a terminal (token) or non-terminal

16. Finite Automaton of Items
What are the transitions of the NFA of LR(0) items?
Consider the item A→ ag
Suppose g begins with symbol X which may be a terminal (token) or non-terminal

17. Finite Automaton of Items
The item can be written as A→ aXh
Then there is a transition on symbol X for state represented by item A→ aXh to state represented by item A→ aXh

18. Finite Automaton of Items
The item can be written as A→ aXh
Then there is a transition on symbol X for state represented by item A→ aXh to state represented by item A→ aXh
compiler: Bottom-up Parsing

19. Finite Automaton of ItemsX
A → aXh
A → aX h

20. Finite Automaton of ItemsX
A → aXh
A → aX h
If X is a terminal, then this transition corresponds to a shift of X from input to top of parse stack

21. Finite Automaton of ItemsX
A → aXh
A → aX h
If X is a non-terminal, then the interpretation of this transition is more complex because non-terminals donot appear in input

22. Finite Automaton of ItemsX
A → aXh
A → aX h
In fact, such a transition will correspond to pushing of X onto the stack during the parse

23. Finite Automaton of ItemsX
A → aXh
A → aX h
But this can only occur during a reduction by the production X → b

24. Finite Automaton of ItemsX
A → aXh
A → aX h
Such a reduction must be preceded by recognition of a b

25. Finite Automaton of ItemsX
A → aXh
A → aX h
The state given by X → b represents the beginning of this process (dot indicates we are about to recognize b)