Question

In: Computer Science

Show that the following attempt to solve the dangling else ambiguity is still ambiguous. statement →...

Show that the following attempt to solve the dangling else ambiguity is still ambiguous.


statement → if ( exp ) statement | matched-stmt
matched-stmt → if ( exp ) matched-stmt else statement | other
exp → 0 | 1

Solutions

Expert Solution

Solution

Consider the following string
if ( 0 ) if ( 0 ) other else if ( 0 ) other else other

We can show two possible leftmost derivations for this, demonstrating the grammar’s ambiguity

Derivation 1

statement -> if (exp)      statement

                    -> if (0)          statement

-> if (0)           matched-stmt

-> if (0)     if    (exp)    matched-stmt else   statement

-> if (0)    if (0)           matched-stmt else   statement

-> If (0)     if (0)             other                else   statement

  -> if (0)    if (0)             other                 else matched-stmt

  ->   if (0)     if (0)             other                 else if (exp)   matched-stmt else statement

  -> if (0)     if (0)             other                 else if (0)      matched-stmt   else statement

   -> if (0)      if (0)             other                  else if (0)      other                    else statement

-> if (0)        if (0)            other                  else if (0)      other                  else matched-stmt

-> if (0)       if (0)            other                  else if (0)      other                    else other

Derivation 2

statement           ->matched-stmt

->if        (exp)    matched-stmt   else        statement

->if        (0)          matched-stmt   else        statement

->if         (0)          if (exp) matched-stmt   else        statement           else        statement

->if         (0)          if (0)     matched-stmt   else        statement           else        statement

->if         (0)          if (0)      other     else       statement           else        statement

->if         (0)          if (0)     other    else       if (exp) statement           else        statement

->if         (0)          if (0)     other    else        if (0)     statement           else        statement

->if         (0)          if (0)      other     else       if (0)     matched-stmt   else        statement

->if         (0)         if (0)     other    else       if (0)     other    else       statement

->if         (0)          if (0)      other     else       if (0)      other     else       matched-stmt

->if         (0)          if (0)     other    else       if (0)      other     else        other

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i wrote the solution in word

after pasted here, format and alignment changed, really sorry for that

all the best

venereology answered 1 year ago
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