CH4.1 CSE244 More on LR Parsing Aggelos Kiayias Computer Science & Engineering Department The University of Connecticut 371 Fairfield Road, Unit 1155 Storrs, CT

CH4.2 CSE244 LR(1) Items  DEF. A LR(1) item is a production with a marker together with a terminal: E.g. []  DEF. A LR(1) item is a production with a marker together with a terminal: E.g. [ S  aA.Be, c ] intuition: it indicates how much of a certain production we have seen already (aA) + what we could expect next (Be) + a lookahead that agrees with what should follow in the input if we ever do Reduce by the production S  aABe By incorporating such lookahead information into the item concept we will make more wise reduce decisions.  Direct use of lookahead in an LR(1) item is only performed in considering reduce actions. (I.e. when marker is in the rightmost).  Core of an LR(1) item [] is the LR(0) item  Core of an LR(1) item [ S  aA.Be, c ] is the LR(0) item S  aA.Be   Different LR(1) items may share the same core.

CH4.3 CSE244 Usefulness of LR(1) items  E.g. if we have two LR(1) items of the form   [ A  ., a ] [ B  ., b ] we will take advantage of the lookahead to decide which reduction to use (the same setting would perhaps produce a reduce/reduce conflict in the SLR approach).   How the Notion of Validity changes:   An item [ A   1.  2, a ] is valid for a viable prefix  1 if we have a rightmost derivation that yields  Aaw which in one step yields  1  2 aw

CH4.4 CSE244 Constructing the Canonical Collection of LR(1) items   Initial item: [ S’ .S, $]   Closure. if [A .B , a] belongs to the set of items, and B   is a production of the grammar, then: we add the item [B . , b] for all b  FIRST(  a)  Goto.  Goto. A state containing [A .X , a] will move to a state containing [A  X. , a] with label X   Every state is closed according to Closure.   Every state has transitions according to Goto.

CH4.5 CSE244 Constructing the LR(1) Parsing Table  Shift actions: If is in state I k and I k moves to state I m with label then we add the action action[k, ] = “shift m”  Shift actions: If [A .b , a] is in state I k and I k moves to state I m with label b then we add the action action[k, b] = “shift m”  Reduce actions: If is in state I k then we add the action: “Reduce ” into action[A, ] Observe that we don’t use information from FOLLOW(A) anymore.  Reduce actions: If [A ., a] is in state I k then we add the action: “Reduce A  ” into action[A, a] Observe that we don’t use information from FOLLOW(A) anymore.  Goto part of the table is as before.

CH4.6 CSE244Example S’  S S  L = R | R L  * R | id R  L FIRST S * id L * id R * id

CH4.7 CSE244 Compare to S’  S S  L = R | R L  * R | id R  L I 0 = { S’ .S, S .L = R, S .R, L .* R, L . id, R .L } I 1 = { S’  S. } I 2 = { S  L. = R, R  L. } I 3 = { S  R. } I 4 = { L  *.R, R .L, L .* R, L . id } I 5 = { L  id. } I 6 = { S  L =. R, R .L, L .* R, L . id } I 7 = { L  *R. } I 8 = { R  L. } I 9 = { S  L = R. } action[2, = ] ?s 6 (because of S  L. = R ) r R  L (because of R  L. and = follows R )

CH4.8 CSE244 LALR Parsing  Canonical sets of LR(1) items  Number of states much larger than in the SLR construction  LR(1) = Order of thousands for a standard prog. Lang.  SLR = order of hundreds for a standard prog. Lang.  LALR (lookahead-LR)  A tradeoff:  Collapse states of the LR(1) table that have the same core.  LALR never introduces a Shift/Reduce Conflict.  It might introduce a Reduce/Reduce Conflict (that did not exist in the LR(1))…  Still much better than SLR (larger set of languages)  … but smaller than LR(1)