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Which Parser Uses Leftmost Derivation?

Which Parser Uses Leftmost Derivation?

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Sep 12, 2026

In context-free grammar parsing, leftmost derivation means that at each step you replace the leftmost non-terminal in the sentential form. For deterministic top-down parsing, this naturally matches the way LL parsers expand non-terminals from left to right, producing the leftmost derivation for a successful parse. By contrast, LR parsers are bottom-up and are characterized as producing a rightmost derivation in reverse rather than a leftmost derivation. Operator-precedence parsers are also bottom-up (shift/reduce) and therefore are not associated with producing leftmost derivations in the standard theoretical description.

Key takeaway for the multiple-choice question: (i) LL parser uses leftmost derivation.
Evidence: LL parsers are described as left-to-right predictive parsers where the second “L” indicates leftmost derivation.2 LR parsers are described as left-to-right and producing rightmost derivation in reverse.2 Wikipedia’s bottom-up parsing overview lists operator-precedence parser and LR parser among bottom-up parsers, consistent with bottom-up (not leftmost-derivation) behavior.

Footnotes

  1. LL and LR Parsing Demystified - States: “LL parsers produce a leftmost derivation, while LR parsers produce a reversed rightmost derivation.” ↩

  2. Build LL(1) Parse Table (JFLAP) - Explains LL(1) and notes the second “L” means leftmost derivation. ↩

  3. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

  4. LR Parsers (CS notes) - Notes LR corresponds to a rightmost derivation in reverse (bottom-up). ↩

  5. Bottom-up parsing - Wikipedia - Lists operator-precedence parser and LR parser among bottom-up parsers. ↩

Leftmost vs Rightmost Derivation (CFG)

keywordLeftmost derivation

A derivation sequence where the parser/derivation always replaces the leftmost non-terminal at each step.

keywordLL parser

Top-down predictive parser where L L means left-to-right input and leftmost derivation.

keywordLR parser

Bottom-up parser where L means left-to-right input and R means rightmost derivation in reverse.

keywordOperator precedence parser

A bottom-up shift/reduce parsing method specialized for operator expressions using precedence relations.

Direct answer (with justification)

OptionParser typeLeftmost derivation?Why
(i)LL parserYesLL parsing expands the leftmost non-terminal; sources explicitly state “LL parsers produce a leftmost derivation.”2
(ii)Bottom-up parser (general category)Not inherentlyBottom-up parsing includes LR and operator-precedence; LR specifically yields rightmost derivation in reverse, not leftmost.2
(iii)LR parserNoLR parsers produce rightmost derivation in reverse (bottom-up).2
(iv)Operator precedence parserNo (standard characterization)It is bottom-up/precedence-based and is not characterized as producing leftmost derivations; bottom-up groupings include it.

Therefore, the correct choice is: (i) LL parser.
LL(1) terminology: the second L in LL(1) indicates leftmost derivation.

Footnotes

  1. LL and LR Parsing Demystified - States: “LL parsers produce a leftmost derivation, while LR parsers produce a reversed rightmost derivation.” ↩

  2. Build LL(1) Parse Table (JFLAP) - Explains LL(1) and notes the second “L” means leftmost derivation. ↩ ↩2

  3. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩ ↩2

  4. Bottom-up parsing - Wikipedia - Lists operator-precedence parser and LR parser among bottom-up parsers. ↩ ↩2

  5. LR Parsers (CS notes) - Notes LR corresponds to a rightmost derivation in reverse (bottom-up). ↩

How derivation order connects to parser direction

Predict and expand

Top-down (LL family)

Expand non-terminals as you read input left-to-right; expand the leftmost non-terminal first ⇒ leftmost derivation.2"

Footnotes

  1. LL and LR Parsing Demystified - States: “LL parsers produce a leftmost derivation, while LR parsers produce a reversed rightmost derivation.” ↩

  2. Build LL(1) Parse Table (JFLAP) - Explains LL(1) and notes the second “L” means leftmost derivation. ↩

Shift and reduce

Bottom-up (LR family)

Build the parse from leaves upward; applying productions in reverse yields rightmost derivation in reverse.2"

Footnotes

  1. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

  2. LR Parsers (CS notes) - Notes LR corresponds to a rightmost derivation in reverse (bottom-up). ↩

Precedence-guided reductions

Bottom-up precedence parsing

A specialized shift/reduce strategy under the bottom-up umbrella (not leftmost-derivation characterized)."

Footnotes

  1. Bottom-up parsing - Wikipedia - Lists operator-precedence parser and LR parser among bottom-up parsers. ↩

How to reason: connect derivation order to parser strategy

  1. 1
    Step 1

    Leftmost derivation replaces the leftmost non-terminal at each step; rightmost derivation replaces the rightmost non-terminal.

  2. 2
    Step 2

    LL parsers are described as predictive/top-down and producing a leftmost derivation.2

    Footnotes

    1. LL and LR Parsing Demystified - States: “LL parsers produce a leftmost derivation, while LR parsers produce a reversed rightmost derivation.” ↩

    2. Build LL(1) Parse Table (JFLAP) - Explains LL(1) and notes the second “L” means leftmost derivation. ↩

  3. 3
    Step 3

    LR parsers are described as producing a rightmost derivation in reverse due to bottom-up reducing.2

    Footnotes

    1. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

    2. LR Parsers (CS notes) - Notes LR corresponds to a rightmost derivation in reverse (bottom-up). ↩

  4. 4
    Step 4

    Both fall under bottom-up parsing; standard references pair bottom-up parsers with rightmost-in-reverse (for LR) and do not claim leftmost derivations for operator precedence.2

    Footnotes

    1. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

    2. Bottom-up parsing - Wikipedia - Lists operator-precedence parser and LR parser among bottom-up parsers. ↩

Pro Tip

When a question says “uses leftmost derivation?”, focus on LL because LL explicitly encodes “leftmost derivation” in its naming/definition, while LR encodes “rightmost derivation in reverse.”3

Footnotes

  1. LL and LR Parsing Demystified - States: “LL parsers produce a leftmost derivation, while LR parsers produce a reversed rightmost derivation.” ↩

  2. Build LL(1) Parse Table (JFLAP) - Explains LL(1) and notes the second “L” means leftmost derivation. ↩

  3. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

Common confusion

“Bottom-up parsing” does not automatically mean “leftmost derivation.” In fact, standard descriptions of LR parsing state it corresponds to rightmost derivation in reverse, not leftmost derivation.2

Footnotes

  1. LR parser - Wikipedia - Defines LR as left-to-right scanning and producing a rightmost derivation in reverse; describes the bottom-up reduce process. ↩

  2. LR Parsers (CS notes) - Notes LR corresponds to a rightmost derivation in reverse (bottom-up). ↩

FAQs

Knowledge Check

Question 1 of 4
Q1Single choice

Which parser uses leftmost derivation?

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