LR(1) for Bill McKeeman Dartmouth April 18, 2008 E ← T ┤ T ← F T ← T * F F ← i F ← ( T )

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LR(1) for Bill McKeeman Dartmouth April 18, 2008 E ← T ┤ T ← F T ← T * F F ← i F ← ( T )

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) a simple expression cfg end-of-file symbol

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ LR start state

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F closure for T ┤┤┤┤ marked rules lookahead kernel in red closure in green

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) closure for F ┤┤┤┤┤┤┤┤

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) T ← ▫ F T ← ▫ T * F another closure for T ┤┤┤┤**┤┤┤┤**

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) another closure for F ┤┤┤┤****┤┤┤┤****

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) merge lookaheads closure complete ┤*

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* new kernel E ← T ▫ ┤ T ← T ▫ * F┤* shift T

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* another new kernel E ← T ▫ ┤ T ← T ▫ * F┤* T ← F ▫┤* shift F

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) another new kernel E ← T ▫ ┤ T ← T ▫ * F┤* T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* shift i

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift ( another new kernel E ← T ▫ ┤ T ← T ▫ * F┤* T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 1 finish state 1

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) closure T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ▫ ┤ T ← T ▫ * F┤* 1

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift ┤ (final LR state) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ▫ ┤ T ← T ▫ * F┤* E ← T ┤ ▫ 1

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift * T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F┤* 1 2 finish states 2,3,4 3 4

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) closure T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤*

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift T T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) *

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift F T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift i T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) *

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) shift ( T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T )) * finish state 5 5

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) closure T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * 5

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* finish state 6 shift on F and I and ( finish state 7 repeat state 4 and

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤*T ← T * ▫ F) * F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * shift on ) and * finish states 8,9,10 4 5

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ) * closure 4 5

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ) * 4 5 F ← ( T ▫ ) T ← T ▫ * F ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T )) * shift on T and F and i and ( finish state 11, repeat states 9,10,11, finish states 12,

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ) * 4 5 F ← ( T ▫ ) T ← T ▫ * F ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T )) * T ← T * F ▫) * F ← i ▫) *F ← ( ▫ T )) * shift on F and i and ( finish state 14, repeat states 10,11 14

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ) * 4 5 F ← ( T ▫ ) T ← T ▫ * F ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T )) * T ← T * F ▫) * F ← i ▫) *F ← ( ▫ T )) * F ← ( T ) ▫ T ← T * ▫ F ) * 15 shift ) and *, finish state 15, repeat state 14 14

E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) T ← F ▫┤*F ← i ▫┤*E ← ▫ T ┤ T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ┤* ) * E ← T ┤ ▫E ← T ▫ ┤ T ← T ▫ * F┤* F ← ( T ▫ ) T ← T ▫ * F ┤* ) * T ← F ▫) *F ← i ▫) * 6 T ← T * F ▫┤*F ← i ▫┤*T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ┤* F ← ( ▫ T )┤* 5 7 F ← ( T ) ▫┤* F ← ( ▫ T ) T ← ▫ F T ← ▫ T * F F ← ▫ i F ← ▫ ( T ) ) * T ← T * ▫ F F ← ▫ i F ← ▫ ( T ) ) * 4 5 F ← ( T ▫ ) T ← T ▫ * F ) * T ← F ▫) *F ← i ▫) *F ← ( ▫ T )) * T ← T * F ▫) * F ← i ▫) *F ← ( ▫ T )) * F ← ( T ) ▫ T ← T * ▫ F ) * 15 finish states 16,

ETF┤i*() E ← T ┤ T ← F T ← T * F F ← i F ← ( T ) -1: -2: -3: -4: -5: The LR Matrix states symbols I * i ┤ 1 1i41i4 * i ┤ 1F1F 1F31F3 1T1T 1T21T2 1T2*71T2*7 i ┤ 1T2*7i41T2*7i4 ┤ 1T2*7F1T2*7F┤ 1 T 2 * 7 F 12 ┤ 1T1T┤ 1T21T2 ┤ 1 T 2 ┤ 6 E stackinput