1. Bottom-up parsing Goal of parser : build a derivation
Top-down parser : build a derivation by working from the start symbol towards the input.
Builds parse tree from root to leaves
Builds leftmost derivation
Bottom-up parser : build a derivation by working from the input back toward the start symbol
Builds parse tree from leaves to root
Builds reverse rightmost derivation

2. Bottom-up parsing
The parser looks for a substring of the parse tree's frontier...
...that matches the rhs of a production and
...whose reduction to the non-terminal on the lhs represents on step along the reverse of a rightmost derivation
Such a substring is called a handle.
Important:
Not all substrings that match a rhs are handles.

3. Bottom-up parsing techniques
LR Parsing
Also called “Shift-Reduce Parsing”
Shift input symbols until a handle is found. Then, reduce the substring to the non-terminal on the lhs of the corresponding production.
Operator-precedence parsing
Based on shift-reduce parsing.
Identifies handles based on precedence rules.

4. Example: Shift-reduce parsing
STACK
ACTION $
Shift
Grammar:
$ id1
Reduce (rule 5)
1. S  E
2. E  E + E
3. E  E * E
4. E  num
5. E  id
$ E
Shift
$ E +
Shift
$ E + num
Reduce (rule 4)
$ E + E
Shift
$ E + E *
Shift
$ E + E * id2
Reduce (rule 5)
Input to parse:
id1 + num * id2
$ E + E * E
Reduce (rule 3)
$ E + E
Reduce (rule 2)
$ E
Reduce (rule 1)
Handles:
underlined
$ S
Accept

5. Shift-Reduce parsing A shift-reduce parser has 4 actions:
Shift -- next input symbol is shifted onto the stack
Reduce -- handle is at top of stack
pop handle
push appropriate lhs
Accept -- stop parsing & report success
Error -- call error reporting/recovery routine