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LL(1) grammars

LL(1) grammars. Module 07.1 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez. Define LL(1) Grammar Examples. Select sets. Parse Tables. “Model” PL grammar: Not LL(1). Problems: Left recursion Common prefices. Topics. Definition: A CFG G is LL(1)

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LL(1) grammars

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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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