1. Readahead FSMs, Readback FSMs, and Reduce States
Readahead FSMs, Readback FSMs, and Reduce States

2. How does a Parser Work Again!
Find the right end of a handle (while munching inputs, stacking stuff (3 stacks that grow on the right), and moving R (indicator for the right end of a handle))
Find the left end of a handle (while traversing the stack from right to left and moving L)
Reduce to a nonterminal A (using the stack contents between L and R, build a new tree and replace everything by an A-token)
and repeat until no more input (EndOfFile encountered); equivalent to reaching an accept table.

3. The Process ReadaheadFSM ReadbackFSM Reduce to A
{lookahead}
Computed from Follow (A);
i.e., what comes after
ReadaheadFSM
Build and stacks input from left to right
Stops when it reaches the right end of a unique handle with R pointing at the rightmost stack entry
{lookback}
ReadbackFSM
Computed from ReadaheadFSM;
i.e., what comes before
Scans stack from right to left
Stops when it reaches the left end of a unique handle with L pointing at the leftmost stack entry
Reduce to A
Build a tree from information between L and R, pops it off, and replaces it by A and the new tree
The lookahead and lookback is used as a bridge to interconnect different parts
The process keeps repeating

4. Example -1 -1 G {EndOfFile}-> a b c d Acc grammar 12 G Ra Ra Ra Ra
Readahead FSM 1 2 3 4 5 Rb Rb Rb Rb Rb
{-1} a2 b3 c4 d5
Readback FSM 10 9 8 7 6
Red G 11
bridging lookahead
bridging lookback
Some initial entry -1
How the stack grows during readahead a2 c4
Left initially past right b3 d5 R L
How left moves during readback L -1
How stack (generally) shrinks by the reduce
G12

5. Parsing Versus Derivations
grammar
G {EndOfFile}-> a b c d
Input
a b c d EndOfFile
As we saw on the previous slide, the stack changes as follows
This corresponds to the derivation -1 G
=> abcd a2 b3 c4 d5 -1 G2
So the parser works in the reverse order of a derivation. More specifically, from left-to-right and bottom-up, simulating a specific type of derivation (but we can’t show that here since the example is too simple)

6. What Precisely Is The Stack Information-1
Stack as shown on previous slide a2 b3 c4 d5
In reality, these are 2 parallel stacks.
Token stack - a b c d
Table number stack 1 2 3 4 5
They grow on the right
Also, there exists a 3rd parallel stack.
Tree stack
Each entry is an entire tree (not a node in the tree), This is easy to do with object-oriented programming

7. Bridging G {EndOfFile}-> a b c d Acc grammar 12 G Ra Ra Ra Ra Ra a
Readahead FSM 1 2 3 4 5 Rb Rb Rb Rb Rb
{-1} a2 b3 c4 d5
Readback FSM 10 9 8 7 6
Red A 11
bridging lookahead
bridging lookback
Computing lookahead:
For each nonterminal A, we need to compute Follow (A); i.e., what can come after “according to the grammar”.
Computing lookback:
Computed from the information in the readahead FSM.

8. What Order Do We Implement Things
Standard order
Compute Follow Sets
1 week to do
Build readahead and readback FSMs
2 week sto do
What we might want to do instead
Switch the order
So we have to pretend we have the follows sets
What if we don’t
Takes a long time to explain latter, could waste a week of assignment time.