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Fixing non- ll (1) grammars

Learn how to address problems with model grammar by fixing common prefixes and left recursion to ensure LL(1) compliance.

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Fixing non- ll (1) grammars

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  1. Fixing non-ll(1) grammars Module 07.2COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

  2. Problems with model grammar Fixing common prefices Fixing left-recursion New grammar: LL(1) Topics

  3. 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 grammar. We’ll use it throughout.

  4. Change: T → P * T { (, id } → P { (, id } to: T → P X { (, id } X →* T { * } → { +, ; , ) } Follow(X) ⊇ Follow(T) due to T → P X ⊇ Follow(E)due to E → E+T , E → T = { +, ;, ) } due to E →E+T, S→id := E ; and P → (E) Fixing common prefices

  5. In general, change A → 1 → 2 . . . → n to A → X X →1 . . . →n Fixing common prefices • Hopefully all the’sbegin with different symbols. If not, repeat !

  6. We have (…((( T + T) + T) + T)…) Instead, we want (T) (+T) (+T) … (+T) Change: E → E + T { (, id } → T { (, id } To: E → T Y { (, id } Y → + T Y { + } → { ; , ) } Follow(Y)  Follow(E) = { ; , ) } Fixing left recursion of E Yikes: destroyed the left associatvity of ‘+’ ! Will fix this later. No longer contains ‘+’: we eliminated E → E + T

  7. In general, Change:A → A1 A →  1 . . . . . . → An → m to:A → 1 X X → 1X . . . . . . →m X→nX → Fixing left recursion • The ’s don’t begin with A.

  8. We have (…(((S)S)S)…) Instead, we want (S)(S) …(S) Change:SL → SL S { begin, id } → S { begin, id } To:SL → S Z { begin, id } Z →S Z { begin, id } → { end } Fixing left recursion of SL Destroyed the left associatvity of ‘ ’. Fixable, but won’t matter.

  9. Modified grammar S → begin SL end {begin} → id := E ; {id} SL → S Z {begin,id} Z →S Z {begin,id} → {end} E → T Y {(,id} Y → + T Y {+} → {;,)} T → P X {(,id} X → * T {*} → {;,+,)} P → (E) {(} → id {id} Grammar is LL(1) !

  10. summary • Problems with model grammar • Fixing common prefices • Fixing left-recursion • New grammar is LL(1)

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