When I learned about first and follow sets at university I found them difficult to follow, so I have tried to rewrite the rules I was taught for creating them so that they would be easier to understand. I hope it helps :)

- If X is a terminal
**then**First(X) is just X! - If there is a Production X → ε
**then**add ε to first(X) - If there is a Production X → Y1Y2..Yk
**then**add first(Y1Y2..Yk) to first(X) - First(Y1Y2..Yk) is
**either**- First(Y1) (if First(Y1) doesn't contain ε)
**OR**(if First(Y1) does contain ε) then First (Y1Y2..Yk) is everything in First(Y1) <except for ε > as well as everything in First(Y2..Yk)- If First(Y1) First(Y2)..First(Yk) all
contain ε
**then**add ε to First(Y1Y2..Yk) as well.

- First put $ (the end of input marker) in Follow(S) (S is the start symbol)
- If there is a production A →
aBb,
(where a can
be a whole string)
**then**everything in FIRST(b) except for ε is placed in FOLLOW(B). - If there is a production A → aB,
**then**everything in FOLLOW(A) is in FOLLOW(B) - If there is a production A → aBb,
where FIRST(b)
contains ε,
**then**everything in FOLLOW(A) is in FOLLOW(B)

The Grammar

E → TE'

E' → +TE'

E' → ε

T → FT'

T' → *FT'

T' → ε

F → (E)

F → id

First Sets | Follow Sets |

We Want to make First sets so first we list the sets we need FIRST(E) = {} FIRST(E') = {} FIRST(T) = {} FIRST(T') = {} FIRST(F) = {} First We apply rule 2 to T' → ε and E' → ε FIRST(E) = {} FIRST(E') = {ε} FIRST(T) = {} FIRST(T') = {ε} FIRST(F) = {} First We apply rule 3 to T' → *FT' this rule tells us that we can add everything in First(*FT') into First(T') Since First(*) useing rule 1 is * we can add * to First(T') FIRST(E) = {} FIRST(E') = {+,ε} FIRST(T) = {} FIRST(T') = {*,ε} FIRST(F) = {} First We apply rule 3 to T' → *FT' this rule tells us that we can add everything in First(*FT') into First(T') Since First(*) useing rule 1 is * we can add * to First(T') FIRST(E) = {} FIRST(E') = {+,ε} FIRST(T) = {} FIRST(T') = {*,ε} FIRST(F) = {} Two more productions begin with terminals F → (E) and F → id If we apply rule 3 to these we get... FIRST(E) = {} FIRST(E') = {+,ε} FIRST(T) = {} FIRST(T') = {*,ε} FIRST(F) = {'(',id} Next we apply rule 3 to T → FT' once again this tells us that we can add First(FT') to First(T) Since First(F) doesn't contain ε that means that First(FT') is just First(F) FIRST(E) = {} FIRST(E') = {+,ε} FIRST(T) = {'(',id} FIRST(T') = {*,ε} FIRST(F) = {'(',id} Lastly we apply rule 3 to E → TE' once again this tells us that we can add First(TE') to First(E) Since First(T) doesn't contain ε that means that First(TE') is just First(T) FIRST(E) = {'(',id} FIRST(E') = {+,ε} FIRST(T) = {'(',id} FIRST(T') = {*,ε} FIRST(F) = {'(',id} Doing anything else doesn't change the sets so we are done! |
We want to make Follow sets so first we list the sets we need FOLLOW(E) = {} FOLLOW(E') = {} FOLLOW(T) ={} FOLLOW(T') = {} FOLLOW(F) = {} The First thing we do is Add $ to the start Symbol 'E' FOLLOW(E) = {$} FOLLOW(E') = {} FOLLOW(T) ={} FOLLOW(T') = {} FOLLOW(F) = {} Next we apply rule 2 to E' →+TE' This says that everything in First(E') except forε should be in Follow(T) FOLLOW(E) = {$} FOLLOW(E') = {} FOLLOW(T) ={+} FOLLOW(T') = {} FOLLOW(F) = {} Next we apply rule 3 to E →TE' This says that we should add everything in Follow(E) into Follow(E') FOLLOW(E) = {$} FOLLOW(E') = {$} FOLLOW(T) ={+} FOLLOW(T') = {} FOLLOW(F) = {} Next we apply rule 3 to T → FT' This says that we should add everything in Follow(T) into Follow(T') FOLLOW(E) = {$} FOLLOW(E') = {$} FOLLOW(T) ={+} FOLLOW(T') = {+} FOLLOW(F) = {} Now we apply rule 2 to T' →*FT' This says that everything in First(T') except for ε should be in Follow(F) FOLLOW(E) = {$} FOLLOW(E') = {$} FOLLOW(T) ={+} FOLLOW(T') = {+} FOLLOW(F) = {*} Now we apply rule 2 to F → (E) This says that everything in First(')') should be in Follow(E) FOLLOW(E) = {$,)} FOLLOW(E') = {$} FOLLOW(T) ={+} FOLLOW(T') = {+} FOLLOW(F) = {*} Next we apply rule 3 to E → TE' This says that we should add everything in Follow(E) into Follow(E') FOLLOW(E) = {$,)} FOLLOW(E') = {$,)} FOLLOW(T) = {+} FOLLOW(T') = {+} FOLLOW(F) = {*} Next we apply rule 4 to E' → +TE' This says that we should add everything in Follow(E') into Follow(T) (because First(E') contains ε) FOLLOW(E) = {$,)} FOLLOW(E') = {$,)} FOLLOW(T) = {+,$,)} FOLLOW(T') = {+} FOLLOW(F) = {*} Next we apply rule 3 to T → FT' This says that we should add everything in Follow(T) into Follow(T') FOLLOW(E) = {$,)} FOLLOW(E') = {$,)} FOLLOW(T) = {+,$,)} FOLLOW(T') = {+,$,)} FOLLOW(F) = {*} Finaly we apply rule 4 to T' → *FT' This says that we should add everything in Follow(T') into Follow(F) FOLLOW(E) = {$,)} FOLLOW(E') = {$,)} FOLLOW(T) = {+,$,)} FOLLOW(T') = {+,$,)} FOLLOW(F) = {*,+,$,)} |

Author:James Brunskill (jmb.nz)