Compute first sets

. If X is a terminal symbol then First(X) = {X}

. If X ε is a production then ε is in First(X)

. If X is a non terminal

and X Y ₁ Y ₂ 2 . Y_k is a production

then

if for some i, a is in First(Y_i )

and ε is in all of First(Y_j ) (such that j<i)

then a is in First(X)

. If ε is in First (Y₁ ) . First(Y_k ) then ε is in First(X)

To compute FIRST ( X ) for all grammar symbols X, apply the following rules until no more terminals or e can be added to any FIRST set.

1. If X is terminal, then First (X) is {X}.

2. If X ε is a production then add e to FIRST(X).

3. If X is a non terminal and X Y ₁ Y_k .........Y _k is a production, then place a in First (X) if for some i, a is in FIRST(Y_i ) and e is in all of FIRST(Y ₁ ), FIRST(Y ₂ ),.., FIRST(Y_i-1 );that is, Y₁ ..Y _i-1 * ε . If ε is in FIRST(Y_j ) for all i = 1,2,..,k, then add ε to FIRST(X). For example, everything in FIRST(Y₁ ) is surely in FIRST(X). If Y ₁ does not derive ε , then we add nothing more to FIRST(X), but if Y₁ * ε , then we add FIRST(Y₂ ) and so on.