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LL(1) Grammar Examples & Problems: Definition, Sets, Parse Tables

Learn LL(1) grammar concepts with examples and common problems such as left recursion and prefices, along with definition of LL(1) and its key properties. Explore how to identify an LL(1) grammar through sets and parse tables.

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LL(1) Grammar Examples & Problems: Definition, Sets, Parse Tables

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  1. LL(1) grammars Module 07.1COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

  2. Define LL(1) Grammar Examples. Select sets. Parse Tables. “Model” PL grammar: Not LL(1). Problems: Left recursion Common prefices. Topics

  3. Definition: A CFG G is LL(1) (Left-to-right, Left-most, 1-symbol lookahead) iff for all A∊ , and for all A→, A→,   , Select (A → ) ∩ Select (A → ) =  Select(A → ) = First() ∪ Follow(A) if  ⇒* ℇ First () = {t /  =>* tβ, for some β} Follow (A) = {t / S =>* γAtβ, for some γ, β} Yikes: We’ll treat First, Follow informally (Translators course) LL(1) grammars

  4. S → A {b,} A → bAd {b} → { d,} LL(1) grammars Example: Disjoint ! Grammar is LL(1) PT (not OPF): At most ONE entry in each table slot.

  5. S → A {b} A → bAd {b} → b {b} LL(1) grammars Example: { bn+1dn / n ≥ 0 } Not Disjoint ! Grammar is not LL(1) PT: More than one entry in at least one table slot.

  6. S →begin SL end {begin} T → P*T {(, id} → id := E; {id} → P {(, id} SL → SL S {begin,id} P → (E) {(} →S {begin,id} → id {id} E → E+T {(, id} → T {(, id} Select sets not disjoint LL(1) grammars Not LL(1)

  7. Left recursion always produces a non-LL(1) grammar, e.g. SL → SL S →S Common prefices always produce a non-LL(1) grammar, e.g T → P*T → P Non-LL(1) grammars

  8. S →begin SL end {begin} → id := E; {id} SL → SL S {begin,id} →S {begin,id} E → E+T {(, id} → T {(, id} T → P*T {(, id} → P {(, id} P → (E) {(} → id {id} Model grammar Problems: • SL is left recursive. • E is left recursive. • T → P * T have common → P prefices. Showing a grammar is not LL(1): easy. PL grammars: “mostly” LL(1). This is our “model” PL sample grammar. We’ll use it throughout.

  9. summary • Defined LL(1) Grammar • Examples. • Select sets. • Parse Tables. • “Model” PL grammar: • Not LL(1) • Problems w/grammar.

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