LR(0) PARSER

LR(0) PARSER
Mr.Sameer Prembabu Mamadapure
Information Technology Department
International Institute of Information Technology, I²IT
www.isquareit.edu.in

LR(k) Parsers
• Left-to-right, rightmost derivation with k-token
lookahead.
• Most general parsing technique for deterministic
grammars.
• In general, not practical: tables too large (10^6
states for C++, Ada).
• Common subsets: SLR, LALR (1).

The states of the LR(0)
automaton
• An item is a point within a production, indicating that part
of the production has been recognized:
A a. Bb ,
seen the expansion of a, expect to see expansion of B
• A state is a set of items
• Transition within states are determined by terminals and
non-terminals
• Parsing tables are built from automaton:
action: shift / reduce depending on next symbol
goto: change state depending on synthesized non-terminal

Building LR (0) states
• If a state includes:
A a .Bb
• it also includes every state that is the start of B:
B . X Y Z
• Informally: if I expect to see B next, I expect to see
anything that B can start with, and so on:
X . G H I
• States are built by closure from individual items.

E’ E
E E + T | T; -- left-recursion ok here.
T T * F | F;
F id | (E)
S0 = { E’ .E, E .E + T, E .T,
F .id, F . ( E ) ,
T .T * F, T .F }
A grammar of expressions: initial state

Adding states
• If a state has item A a .a b,
and the next symbol in the input is a, we shift a on the
stack and enter a state that contains item
• A a a.b
(as well as all other items brought in by closure)
• if a state has as item A a. , this indicates the end of
a production: reduce action.
• If a state has an item A a .N b, then after a
reduction that find an N, go to a state with A a N. b

Construction of a predictive parsing
table
• The following rules are used to construct the
predictive parsing table:
– 1. for each terminal a in FIRST(α),
add A → α to matrix M[A,a]
– 2. if λ is in FIRST(α), then
for each terminal b in FOLLOW(A),
add A → α to matrix M[A,b]

The LR (0) states for expressions
• S1 = { E’ E., E E. + T }
• S2 = { E T., T T. * F }
• S3 = { T F. }
• S4 = { F (. E), } + S0 (by closure)
• S5 = { F id. }
• S6 = { E E +. T, T .T * F, T .F, F .id, F .(E)}
• S7 = { T T *. F, F .id, F .(E)}
• S8 = { F (E.), E E.+ T}
• S9 = { E E + T., T T.* F}
• S10 = { T T * F.}, S11 = {F (E).}

International Institute of Information Technology (I²IT)
P-14, Rajiv Gandhi Infotech Park, MIDC Phase – 1,
Hinjawadi, Pune – 411057, India
Email - info@isquareit.edu.in
Website - http://www.isquareit.edu.in/
THANK-YOU

LR(0) PARSER

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