LL:

- top-down, chooses the next production to apply based on k symbol lookahead.
- for exercises we will usually consider LL(1) grammars
  - when given a nonterminal, it must choose which RHS to expand to using only a
    single token of lookahead.
- less powerful than LR:
  - consider this LR(0) grammar:
  - S -> A | B
    A -> a a
    B -> a b
  - not LL(1) (FIRST(A) intersect FIRST(B) = {a} =/= null)

  - substitute:
  - S -> a a | a b
  - left factor:
    S -> a C
    C -> a | b

- immediate left recursion:
  - open general algorithm:
  - http://en.wikipedia.org/wiki/Left_recursion#Removing_left_recursion
  - example from book:
  - C for ClockNoise

  - C -> C tick tock
    C -> tick tock

  - C -> tick tock C'
    C' -> epsilon
    C' -> tick tock C'

- more general example including indirect left recursion:
  - scroll down in browser

  - A -> B a
    B -> A b
    B -> b

  - what does this generate?
    - (b a)+

  - A -> B a
    B -> B a b
    B -> b

  - now remove direct left recursion:

  - A -> B a
    B -> b B'
    B' -> epsilon
    B' -> a b B'

  - is this LL(1)?
    - no, we can't choose between the two B' rules, because:
      - B' is nullable
      - a can follow B'
      - one of the productions starts with a

  - substitute:

  - A -> B
    B -> b B' a
    B' -> epsilon
    B' -> a b B'

  - A -> B
    B -> b C
    C -> B' a
    B' -> epsilon
    B' -> a b B'

  - A -> B
    B -> b C
    C -> a
    C -> a b B' a
    B' -> epsilon
    B' -> a b B'

  - A -> B
    B -> b C
    C -> a
    C -> a b C

  - A -> b C
    C -> a
    C -> a b C

  - rename:

  - A -> b B
    B -> a
    B -> a b B

  - left factor:

  - A -> b B
    B -> a B'
    B' -> epsilon
    B' -> b B

  - rename:

  - A -> b B
    B -> a C
    C -> epsilon
    C -> b B

- if time: show parser and generator

midterm review:
  - http://courses.cs.washington.edu/courses/cse401/15wi/exams/midterm-topics.html