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RubyKaigi 2025
Ehime Prefectural Convention Hall
2025/04/17(Thu.)
The Implementations of
Advanced LR Parser Algorithm
Junichi Kobayashi (@junk0612)
ESM, Inc.
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自己紹介 Junichi
Kobayashi
● X / GitHub: @junk0612
● Working at ESM, Inc.
○ Work as a Rails engineer
○ A Member of Parser Club
● Committer of Lrama
● Hobbies
○ Parsers
○ Rhythm games
○ Board games
○ Haiku
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No content
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No content
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Drinkup Sponsor
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Ruby on Timeline
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Attendee
@nsgc
Attendee
@colorbox
Attendees from ESM
Attendee
@S.H.
Karaoke
@fugakkbn
Speaker
@koic
Attendee
@wai-doi
Speaker
@junk0612
Attendee
@kasumi8pon
Attendee
@mhirata
Attendee
@haruguchi
Attendee
@maimux2x
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✦ An LR parser generator built with Ruby
Lrama
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✦ An algorithm of LR parser generation
✦ https://www.sciencedirect.com/science/article/pii/S0167
642309001191
IELR
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✦ https://github.com/ruby/lrama/pull/398
✦ Support since Lrama 0.7 for CRuby 3.5
IELR in Lrama
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Usage
$ gem install lrama
# from CLI
$ lrama -D lr.type=ielr grammar.y
# in grammar file
%define lr.type ielr
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✦ Theoretical side
✦ Utilize the tokens read so far to narrow down the set of
possible next tokens more accurately than LALR
✦ Practical side
✦ Propagating conflict info backward and lookahead forward
✦ Identify the conflict's cause and split states if necessary
"After All, What is IELR?"
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Theoretical Side
Estimated: 5/30 min
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✦ Shift-Reduce Parsing
✦ One of Bottom-up Parsing
✦ Use 2 types of actions
✦ Shift: Get a next symbol from Lexer
✦ Reduce: Collapse recognized symbols into a parent node
✦ Use one of the actions depending on the situation
✦ Match one of grammar rules: Reduce
✦ Don't match any grammar rules: Shift
Basis of LR Parser
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
num
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
num
exp
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Behavior Example of LR Parser
exp: exp + num
| exp * num
| num
num: 0
| 1
1 + 0 * 1
num
exp
num
exp
num
exp
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Issue #1:
Identifying Rule Matches
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Motivating Examples
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
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Issue #2:
Collecting Next Tokens
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✦ Modifier conditional statements
Motivating Examples
statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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statement: method_call 'if' exp
| method_call 'unless' exp
method_call: method_name
| method_name '(' args ')'
save!(name: 'Junichi')
save! if valid?
save! end valid?
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✦ The next token is...
✦ included in same (or child) rule → Shift
✦ included in parent (or ancestors / sibling) rule → Reduce
✦ not included in both of the above → Error
Select Actions
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✦ A set of tokens used to determine whether to Reduce
✦ LALR and IELR differ in how they compute their
lookahead sets
✦ LALR: The set of all tokens that can appear immediately after
a given nonterminal, based on the entire language
✦ IELR: The set of all tokens that can appear immediately after a
given nonterminal, but only within the subset of language
elements matching the tokens read so far
Lookahead Set
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✦ conditional statements
Motivating Examples
cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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cond_stmt: 'if' method_call 'then' body 'end'
| 'while' method_call 'do' body 'end'
method_call: method_name
| method_name '(' args ')'
if valid? then save! end
while valid? do save! end
if valid? do save! end
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✦ original example in the paper
Motivating Examples
S: 'a' A 'a'
| 'b' A 'b'
A: 'a'
| 'a' 'a'
aaa / aaaa / bab / baab
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✦ original example
Motivating Examples
S: 'a' A 'a'
| 'b' A 'b'
A: 'a'
| 'a' 'a'
baab
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✦ original example
Motivating Examples
S: 'a' A 'a'
| 'b' A 'b'
A: 'a'
| 'a' 'a'
baab
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✦ A Conflict occurs when the parser can't uniquely decide
the next action
✦ There are 2 types of Conflict
✦ Shift/Reduce Conflict
✦ Reduce/Reduce Conflict
Conflicts
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Practical Side
Estimated: 15/30 min
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LR Parser Model
Parser
State 0
State 1 State 2 State 3
NUM
+
exp
State 4 State 5 State 6
*
(
exp
NUM
-
…
Token Stream
Source Code
Lexer
Grammar File
Parser
Generator
8
4
1
0
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Shift Action
8
6
4
0
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Shift Action
13
8
6
4
0
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Reduce Action
13
8
6
4
0
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Reduce Action
8
6
4
0
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Reduce Action
6
4
0
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Reduce Action
1
6
4
0
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✦ Can be parsed IELR but not LALR
✦ Caused by the difference of lookahead set
✦ May resolve by splitting states
✦ There are 3 types of Mysterious Conflicts
✦ Mysterious New Conflicts
✦ Mysterious Invasive Conflicts
✦ Mysterious Mutated Conflicts
Mysterious Conflicts
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Mysterious New Conflicts
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Mysterious Invasive Conflicts
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Mysterious Mutated Conflicts
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Lrama's Implementation
States
State
@states
Transition
Shift
Goto
Reduce
@transitions
@reduces
@items
@conflicts
@id
@next_sym
@from_state
@to_state
@next_sym
@from_state
@to_state
@look_ahead
@item
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✦ Annotate conflicting states and their predecessors
✦ Recompute lookahead set from scratch
✦ Propagate it to next state
✦ Split the next state if the propagating lookahead set has
no "compatibilities" with already propagated ones
IELR Basic Idea
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✦ Indicates potential contribution to conflicts
✦ Has the following conflict information inside
✦ State
✦ Token
✦ Actions
✦ Items
Inadequacy Annotations
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Inadequacy Annotation
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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Inadequacy Annotation
State: 22
Token: 'end'
Actions: [S, R1, R2]
Items: {R1 => [...], R2 => [...]}
State: 27
Token: 'do'
Actions: [R5, R6]
Items: {R5 => [...], R6 => [...]}
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1. Lookahead sets: from its associated item's lookahead
2. Kernel lookahead: from the same item's lookahead in
predecessor states (dot is one symbol to the left)
3. Non-kernel lookahead: from the follow set of the state's
goto on the LHS (i.e., tokens that can appear next)
4. Goto follow set:
a. the remainder of the RHS after the goto’s nonterminal
b. The lookahead sets of items where the remainder is nullable
Recompute Lookahead Set
original: https://www.sciencedirect.com/science/article/pii/S0167642309001191
summarized by: @junk0612
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Check Compatibilities
S: 'a' A 'a'
| 'b' A 'b'
A: 'a'
| 'a' 'a'
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Check Compatibilities
● A: 'a'・, ['a', 'b']
● A: 'a'・'a', ['a', 'b']
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Check Compatibilities
● A: 'a'・, ['a', 'b']
● A: 'a'・'a', ['a', 'b']
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Check Compatibilities
● A: 'a'・, ['a', 'b']
● A: 'a'・'a', ['a', 'b']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
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Check Compatibilities
● A: 'a'・, ['a', 'b']
● A: 'a'・'a', ['a', 'b']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
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Check Compatibilities
● A: 'a'・, ['a', 'b']
● A: 'a'・'a', ['a', 'b']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
Token: 'a'
Actions: [S, R]
Items: {R => [A: 'a'・]}
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Check Compatibilities
● A: 'a'・, ['a']
● A: 'a'・'a', ['a']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
Token: 'a'
Actions: [S, R]
Items: {R => [A: 'a'・]}
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Check Compatibilities
● A: 'a'・, ['a']
● A: 'a'・'a', ['a']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
Token: 'a'
Actions: [S, R]
Items: {R => [A: 'a'・]}
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Check Compatibilities
● A: 'a'・, ['b']
● A: 'a'・'a', ['b']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
Token: 'a'
Actions: [S, R]
Items: {R => [A: 'a'・]}
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Check Compatibilities
● A: 'a'・, ['b']
● A: 'a'・'a', ['b']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
Token: 'a'
Actions: [S, R]
Items: {R => [A: 'a'・]}
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Check Compatibilities
● A: 'a'・, ['a']
● A: 'a'・'a', ['a']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
● A: 'a'・, ['b']
● A: 'a'・'a', ['b']
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Check Compatibilities
● A: 'a'・, ['a']
● A: 'a'・'a', ['a']
● S: 'b'・A 'b', ['#']
● A:・'a', ['b']
● A:・'a' 'a', ['b']
● S: 'a'・A 'a', ['#']
● A:・'a', ['a']
● A:・'a' 'a', ['a']
a
a
● A: 'a'・, ['b']
● A: 'a'・'a', ['b']
No Conflicts!
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$ bundle exec lrama -D lr.type=ielr parse.y
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$ bundle exec lrama -D lr.type=ielr parse.y
def compute_ielr
(...snip...)
rescue Interrupt
end
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✦ Automaton has loops
✦ Compute lookahead sets slowly
✦ Create many "useless" annotations
Why got stack
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Looped Automatons
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Looped Automatons
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✦ Introduce some caches
✦ Use strongly connected components algorithm
✦ Following the LALR Lookahead set computation
Fasten Computation
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Useless Annotations
Actions: [R1, R2]
Items: {R1 => [...], R2 => [...]}
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Useless Annotations
Actions: [R1, R2]
Items: {R1 => [...], R2 => [...]}
R1
R2
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Useless Annotations
Actions: [R1, R2]
Items: {R1 => [...], R2 => [...]}
R1
R2
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$ time bundle exec lrama -D lr.type=ielr parse.y
69.02s user 0.29s system 99% cpu 1:09.38 total
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Use IELR Parser in Ruby
Estimated: 25/30 min
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Generate IELR parser simply
$ lrama --report=states parse.y
$ mv parse.output lalr.output
$ lrama --report=states -D lr.type=ielr parse.y
$ mv parse.output ielr.output
$ diff ielr.output lalr.output
#=> no diffs!
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✦ There are 4 'do's in Ruby
✦ keyword_do
✦ keyword_do_cond
✦ keyword_do_block
✦ keyword_do_LAMBDA
✦ The tokens read so far provide sufficient information to
decide
Identify 4 'do's Smart
obj.m(arg) do ... end
while(true) do ... end
obj.m arg do ... end
-> (arg) do ... end
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while obj.m do #=> keyword_do_cond
while(obj.m do #=> keyword_do
while(obj.m arg do #=> keyword_do_block
while -> do #=> keyword_do_LAMBDA
while obj.m -> do #=> keyword_do_LAMBDA
while(obj.m -> do end do #=> keyword_do_block
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✦ Optimize IELR calculation
✦ Introduce IELR to CRuby and make parse.y better
Future Work
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✦ @yui-knk, @ydah
✦ #LR_parser_gangs
✦ @koic, @S.H.
✦ #esm_parser_club
✦ My Wife
✦ #a_beautiful_life
Acknowledgements
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✦ Theoretical side
✦ Utilize the tokens read so far to narrow down the set of
possible next tokens more accurately than LALR
✦ Practical side
✦ Propagating conflict info backward and lookahead forward
✦ Identify the conflict's cause and split states if necessary
"After All, What is IELR?"