# FIRST Set in Syntax Analysis

FIRST(X) for a grammar symbol X is the set of terminals that begin the strings derivable from X.

**Rules to compute FIRST set:**

- If x is a terminal, then FIRST(x) = { ‘x’ }
- If x-> Є, is a production rule, then add Є to FIRST(x).
- If X->Y1 Y2 Y3….Yn is a production,
- FIRST(X) = FIRST(Y1)
- If FIRST(Y1) contains Є then FIRST(X) = { FIRST(Y1) – Є } U { FIRST(Y2) }
- If FIRST (Yi) contains Є for all i = 1 to n, then add Є to FIRST(X).

**Example 1:**

Production Rules of Grammar E -> TE’ E’ -> +T E’|Є T -> F T’ T’ -> *F T’ | Є F -> (E) | idFIRST setsFIRST(E) = FIRST(T) = { ( , id } FIRST(E’) = { +, Є } FIRST(T) = FIRST(F) = { ( , id } FIRST(T’) = { *, Є } FIRST(F) = { ( , id }

**Example 2:**

Production Rules of Grammar S -> ACB | Cbb | Ba A -> da | BC B -> g | Є C -> h | ЄFIRST setsFIRST(S) = FIRST(A) U FIRST(B) U FIRST(C) = { d, g, h, Є} FIRST(A) = { d } U FIRST(B) = { d, g , Є } FIRST(B) = { g , Є } FIRST(C) = { h , Є }

**Notes: **

- The grammar used above is Context-Free Grammar (CFG). Syntax of most of the programming language can be specified using CFG.
- CFG is of the form A -> B , where A is a single Non-Terminal, and B can be a set of grammar symbols ( i.e. Terminals as well as Non-Terminals)

In the next article “FOLLOW sets in Compiler Design” we will see how to compute Follow sets.

This article is compiled by **Vaibhav Bajpai**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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