LR parser

LR PARSER

LR parsers are a type of bottom-up parsers that efficiently handle deterministic context - LR free languages in guaranteed linear time.

LR parsers are often mechanically generated from a formal grammar for the language by a parser generator tool. 

LR parser are very widely used for the processing of computer languages, more than other kinds of generated parsers. 

In LR parse, the L means that the parser reads input text in one direction without backing up; that direction is typically Left to right within each line, and top to bottom across the lines of the full input file. 

In LR parser, the R means that the parser produces a reversed Rightmost derivation; it does a bottom-up parse. 

The name LR is often followed by a numeric qualifier, as in LR(1) or sometimes LR(k). 

What is 'k' in LR(k) ?
To avoid backtracking or guessing, the LR parser is allowed to peek ahead at k look ahead input symbols before deciding how to parse earlier symbols. Typically k is 1 and is not mentioned.

Common variant of LR parser:
  1. LALR
  2. SLR

SLR Parser: 

SLR grammars are the class of formal grammars accepted by a Simple LR parser. 

SLR grammars are a superset of all LR(0) grammars and a subset of all LALR(1) and LR(1) grammars.

What if grammar is SLR and not SLR ?

When processed by an SLR parser, an SLR grammar is converted into parse tables with no shift/reduce or reduce/reduce conflicts for any combination of LR(0) parser state and expected look ahead symbol. 

If the grammar is not SLR, the parse tables will have shift/reduce conflicts or reduce/reduce conflicts for some state and some lookahead symbols, and the resulting rejected parser is no longer deterministic.

LALR:

The LALR parser was invented by Frank DeRemer in his 1969 PhD dissertation, Practical Translators for LR(k) languages, in his treatment of the practical difficulties at that time of implementing LR(1) parsers. 

He showed that the LALR parser has more language recognition power than the LR(0) parser, while requiring the same number of states as the LR(0) parser for a language that can be recognized by both parsers.

This makes the LALR parser a memory-efficient alternative to the LR(1) parser for languages that are not LR(0).

It was also proved that there exist LR(1) languages that are not LALR.

Despite this weakness, the power of the LALR parser is enough for many mainstream computer languages, including Java though the reference grammars for many languages fail to be LALR due to being ambiguous.

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